{"id":56588,"date":"2025-02-21T18:25:21","date_gmt":"2025-02-21T10:25:21","guid":{"rendered":"https:\/\/swarma.org\/?p=56588"},"modified":"2025-02-21T18:25:21","modified_gmt":"2025-02-21T10:25:21","slug":"%e8%ae%a1%e7%ae%97%e5%8a%9b%e5%ad%a6%ef%bc%88%e5%9b%a0%e6%9e%9c%e6%80%81%e7%90%86%e8%ae%ba%ef%bc%89-%e9%9b%86%e6%99%ba%e7%99%be%e7%a7%91","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=56588","title":{"rendered":"\u8ba1\u7b97\u529b\u5b66\uff08\u56e0\u679c\u6001\u7406\u8bba\uff09| \u96c6\u667a\u767e\u79d1"},"content":{"rendered":"
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\u8ba1\u7b97\u529b\u5b66\uff08Computational Mechanics\uff09\u662f\u4e00\u5957\u7528\u4e8e\u91cf\u5316\u6d8c\u73b0\u7684\u6846\u67b6\u3002\u5b83\u4ee5\u4e00\u79cd\u8ba1\u7b97\u7684\u89c6\u89d2\uff0c\u7814\u7a76\u89c2\u5bdf\u8005\u5efa\u7acb\u7684\u6a21\u578b\u5728\u8bc6\u522b\u6d8c\u73b0\u65f6\uff0c\u6a21\u578b\u53d1\u751f\u7684\u53d8\u5316\u3002\u8ba1\u7b97\u529b\u5b66\u4ee5\u4fe1\u606f\u8bba\u548c\u751f\u7269\u8fdb\u5316\u7684\u601d\u60f3\u4e3a\u57fa\u7840\uff0c\u662f\u76ee\u524d\u6700\u65e9\u7684\u5bf9\u6d8c\u73b0\u7684\u5b9a\u91cf\u5316\u7814\u7a76\u3002\u5728\u5e94\u7528\u5f53\u4e2d\uff0c\u8be5\u7406\u8bba\u63d0\u51fa\u4e86\u5bf9\u590d\u6742\u6027\u5ea6\u91cf\u7684\u65b0\u6307\u6807\uff0c\u5373\u7edf\u8ba1\u590d\u6742\u5ea6\uff0c\u540c\u65f6\u8fd8\u63d0\u51fa\u4e86\u4e00\u5957\u8bc6\u522b\u6d8c\u73b0\u7684\u7b97\u6cd5\u3002<\/span><\/strong><\/p>\n


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\u4e3a\u4e86\u7cfb\u7edf\u68b3\u7406\u56e0\u679c\u6d8c\u73b0\u6700\u65b0\u8fdb\u5c55\uff0c\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7cfb\u7edf\u79d1\u5b66\u5b66\u9662\u6559\u6388\u3001\u96c6\u667a\u4ff1\u4e50\u90e8\u521b\u59cb\u4eba\u5f20\u6c5f\u8001\u5e08\u9886\u8854\u53d1\u8d77\u300c\u56e0\u679c\u6d8c\u73b0\u7b2c\u516d\u5b63\u300d\u8bfb\u4e66\u4f1a<\/a>\uff0c\u8bfb\u4e66\u4f1a\u5c06\u4ece2025\u5e743\u670816\u65e5\u5f00\u59cb\uff0c\u6bcf\u5468\u65e5\u65e99:00-11:00\uff0c\u6301\u7eed\u65f6\u95f4\u9884\u8ba110\u5468\u5de6\u53f3\u3002\u6bcf\u5468\u8fdb\u884c\u7ebf\u4e0a\u4f1a\u8bae\uff0c\u4e0e\u4e3b\u8bb2\u4eba\u7b49\u793e\u533a\u6210\u5458\u5f53\u9762\u4ea4\u6d41\uff0c\u4e4b\u540e\u53ef\u4ee5\u83b7\u5f97\u89c6\u9891\u56de\u653e\u6301\u7eed\u5b66\u4e60\u3002\u8bda\u631a\u9080\u8bf7\u9886\u57df\u5185\u7814\u7a76\u8005\u3001\u5bfb\u6c42\u8de8\u9886\u57df\u878d\u5408\u7684\u7814\u7a76\u8005\u52a0\u5165\uff0c\u5171\u540c\u63a2\u8ba8\u3002<\/span><\/strong><\/p>\n


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1. \u5386\u53f2\u6e0a\u6e90<\/span><\/strong><\/section>\n

2. \u95ee\u9898\u80cc\u666f<\/span><\/strong><\/p>\n

2.1\t\u81ea\u7136\u548c\u793e\u4f1a\u73b0\u8c61\u4e2d\u7684\u6d8c\u73b0<\/span><\/section>\n
2.2\t\u8ba1\u7b97\u529b\u5b66\u4e2d\u7684\u6d8c\u73b0<\/span><\/section>\n
2.3\t\u8fdb\u5316\u7684\u7cfb\u7edf\u6a21\u578b<\/span><\/section>\n

3. \u56e0\u679c\u6001\u548c\u590d\u6742\u5ea6<\/span><\/strong><\/p>\n

3.1\t\u72b6\u6001\u7684\u5b9a\u4e49<\/span><\/section>\n
3.2\t\u56e0\u679c\u6001\u7684\u5b9a\u4e49<\/span><\/section>\n
3.2.1\t\u5212\u5206<\/span><\/section>\n
3.2.2\t\u56e0\u679c\u6001<\/span><\/section>\n
3.2.2.1\t\u9884\u6d4b\u7b49\u4ef7\u5173\u7cfb<\/span><\/section>\n
3.2.2.2\t\u56e0\u679c\u6001<\/span><\/section>\n
3.2.2.3\t\u4e3e\u4f8b\u8bf4\u660e<\/span><\/section>\n
3.2.2.4\t\u5c0f\u7ed3<\/span><\/section>\n
3.3\t\u56e0\u679c\u6001\u7684\u4e3b\u8981\u6027\u8d28<\/span><\/section>\n
3.3.1\t\u6700\u5927\u9884\u6d4b\u6027<\/span><\/section>\n
3.3.2\t\u6700\u5c0f\u968f\u673a\u6027<\/span><\/section>\n
3.4\t\u6591\u56fe\u91cd\u6784\u673a\u5668<\/span><\/section>\n
3.5\t\u7edf\u8ba1\u590d\u6742\u5ea6<\/span><\/section>\n

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3.5.2\t\u7edf\u8ba1\u590d\u6742\u5ea6<\/span><\/p>\n

3.5.3\t\u4e24\u79cd\u590d\u6742\u6027\u7684\u5bf9\u6bd4<\/span><\/p>\n

3.6\t\u9999\u519c\u71b5\u7387\u4e0e\u590d\u6742\u5ea6<\/span><\/section>\n
3.7\t\u6a21\u578b\u91cd\u6784<\/span><\/section>\n
3.8\t\u6a21\u578b\u91cd\u6784\u7b97\u6cd5<\/span><\/section>\n

4. \u6df7\u6c8c\u52a8\u529b\u5b66\u5b9e\u4f8b<\/span><\/strong><\/p>\n

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4.2\t\u7edf\u8ba1\u590d\u6742\u5ea6-\u71b5\u7387\u56fe<\/span><\/section>\n
4.3\t\u6a21\u578b\u5347\u7ea7<\/span><\/section>\n

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5.1\t\u8ba1\u7b97\u529b\u5b66\u4e0e\u56e0\u679c\u6d8c\u73b0<\/span><\/section>\n
5.1.1\t\u6982\u5ff5\u5bf9\u6bd4<\/span><\/section>\n
5.1.2\t\u6591\u56fe\u91cd\u6784\u673a\u5668\u4e0eNIS\u7cfb\u5217\u7684\u5bf9\u6bd4<\/span><\/section>\n
5.2\t\u8ba1\u7b97\u529b\u5b66\u4e0e\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u6210\u5757\u6027\u7406\u8bba<\/span><\/section>\n
5.3\t\u6591\u56fe\u91cd\u6784\u673a\u5668\u4e0e\u4e16\u754c\u6a21\u578b<\/span><\/section>\n
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\u8ba1\u7b97\u529b\u5b66\u7684\u9996\u6b21\u63d0\u51fa\u662f\u57281989\u5e74\uff0cCrutchfield\u5728\u4ed6\u7684\u4e00\u7bc7\u8bba\u6587\u4e2d[4]\uff0c\u57fa\u4e8e\u65f6\u95f4\u5e8f\u5217\u91cd\u6784\u7684\u72b6\u6001\u7a7a\u95f4[1] \u548c\u81ea\u52a8\u673a\u7406\u8bba[5][6][7]\u5b9a\u4e49\u4e86\u4e00\u79cd\u9884\u6d4b\u7b49\u4ef7\u5173\u7cfb\u3002\u5229\u7528\u8fd9\u79cd\u5173\u7cfb\u5206\u6790\u65f6\u95f4\u5e8f\u5217\u6570\u636e\uff0c\u8bc6\u522b\u548c\u91cf\u5316\u5176\u4e2d\u6709\u89c4\u5f8b\u7684\u90e8\u5206\uff0c\u8ba1\u7b97\u529b\u5b66\u5c31\u53ef\u4ee5\u6784\u5efa\u4e00\u4e2a\u80fd\u591f\u9884\u6d4b\u7cfb\u7edf\u672a\u6765\u884c\u4e3a\u7684\u6a21\u578b\u3002<\/span><\/section>\n

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\u8ba1\u7b97\u529b\u5b66\u7684\u6838\u5fc3\u6982\u5ff5\u662f\u56e0\u679c\u6001<\/span>\uff08Causal State\uff09<\/span>\uff0c\u5b83\u662f\u4e00\u79cd\u4e0e\u5fae\u89c2\u72b6\u6001\u9884\u6d4b\u7b49\u4ef7\u7684\u7279\u6b8a\u7684\u5b8f\u89c2\u6001\u3002\u57fa\u4e8e\u8fd9\u79cd\u9884\u6d4b\u7b49\u4ef7\u6027\u7684\u5b8f\u89c2\u6001\u5212\u5206\u601d\u60f3\u53ef\u4ee5\u8ffd\u6eaf\u523070\u5e74\u4ee3\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u6210\u5757\u6027<\/span>\uff08Lumpability\uff09<\/span>\u7406\u8bba\u3002Kemeny\u548cSnell\u57281969\u5e74\u9488\u5bf9\u9a6c\u5c14\u79d1\u592b\u94fe\u63d0\u51fa\u6210\u5757\u6027\u8fd9\u4e00\u6982\u5ff5\uff0c\u76ee\u7684\u5728\u4e8e\u5224\u65ad\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u52a8\u529b\u7cfb\u7edf\u662f\u5426\u662f\u53ef\u88ab\u7b80\u5316\u5f52\u5e76\u7684\u3002\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u94fe\uff0c\u6211\u4eec\u53ef\u4ee5\u5224\u65ad\u67d0\u79cd\u5212\u5206\u662f\u5426\u662f\u6210\u5757\u7684\u3002\u6210\u5757\u7684\u5212\u5206\u8981\u6c42\u5bf9\u72b6\u6001\u7684\u5f52\u5e76\u8981\u5c3d\u53ef\u80fd\u5730\u4fdd\u7559\u9a6c\u5c14\u53ef\u592b\u94fe\u4e2d\u7684\u539f\u59cb\u91cd\u8981\u4fe1\u606f\uff0c\u5e76\u4fdd\u8bc1\u5212\u5206\u64cd\u4f5c\u4e0e\u52a8\u529b\u5b66\u64cd\u4f5c\u7684\u53ef\u4ea4\u6362\u6027\u3002\u4e0d\u8fc7\u5728\u9a6c\u5c14\u79d1\u592b\u94fe\u4e2d\uff0c\u6210\u5757\u6027\u53ea\u662f\u5bf9\u4e8e\u5212\u5206\u7684\u4e00\u79cd\u8981\u6c42\uff0c\u800c\u6ca1\u6709\u8ffd\u6c42\u6700\u4f18\u7684\u5212\u5206\u3002\u5bf9\u6210\u5757\u6027\u7684\u8fdb\u4e00\u6b65\u4e86\u89e3\uff0c\u8bf7\u53c2\u8003\u8bcd\u6761\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u6210\u5757\u6027\u3002\u4e0e\u4e4b\u76f8\u6bd4\uff0c\u8ba1\u7b97\u529b\u5b66\u9996\u5148\u5173\u6ce8\u7684\u4e0d\u53ea\u662f\u9a6c\u5c14\u79d1\u592b\u52a8\u529b\u5b66\uff0c\u800c\u662f\u8981\u56ca\u62ec\u66f4\u5e7f\u6cdb\u7684\u52a8\u529b\u5b66\u5f62\u5f0f\u3002\u6b64\u5916\uff0c\u8ba1\u7b97\u529b\u5b66\u8bd5\u56fe\u63d0\u51fa\u4e00\u79cd\u6700\u4f18\u7684\u5212\u5206\uff0c\u80fd\u6781\u5927\u5730\u4fdd\u7559\u5bf9\u9884\u6d4b\u6709\u7528\u7684\u4fe1\u606f\u3002\u6b64\u5916\uff0c\u5f53\u4e00\u822c\u7684\u52a8\u529b\u5b66\u8fc7\u7a0b\u9000\u5316\u5230\u9a6c\u5c14\u79d1\u592b\u52a8\u529b\u5b66\u7684\u65f6\u5019\uff0c\u6210\u5757\u6027\u7684\u6210\u7acb\u6761\u4ef6\u5b9e\u9645\u4e0a\u4e0e\u56e0\u679c\u6001\u7684\u5b9a\u4e49\u5177\u6709\u4e00\u5b9a\u7684\u76f8\u4f3c\u6027\u3002<\/span><\/section>\n

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2. \u95ee\u9898\u80cc\u666f<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

<\/p>\n

2.1 \u81ea\u7136\u548c\u793e\u4f1a\u73b0\u8c61\u4e2d\u7684\u6d8c\u73b0<\/span><\/strong><\/span><\/h3>\n

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\u6709\u4e00\u4e9b\u81ea\u7136\u548c\u793e\u4f1a\u73b0\u8c61\u975e\u5e38\u5f15\u4eba\u5165\u80dc\uff0c\u4f46\u4e5f\u5f88\u4ee4\u4eba\u56f0\u60d1\uff0c\u6bd4\u5982\u884c\u4e3a\u7b80\u5355\u7684\u8682\u8681\u53ef\u4ee5\u5f62\u6210\u590d\u6742\u7684\u793e\u4f1a\uff0c\u5728\u6ca1\u6709\u63a7\u5236\u4e2d\u5fc3\u7684\u60c5\u51b5\u4e0b\u81ea\u53d1\u4ea7\u751f\u7279\u5f02\u5316\u7684\u793e\u4f1a\u5206\u5de5[8]\u3002\u5728\u6ca1\u6709\u9886\u5bfc\u8005\u5f15\u5bfc\u7684\u60c5\u51b5\u4e0b\u6210\u7fa4\u7684\u9e1f\u4ee5\u6b65\u8c03\u4e00\u81f4\u7684\u961f\u5f62\u98de\u884c\uff0c\u6210\u7fa4\u7684\u9c7c\u4ee5\u8fde\u8d2f\u7684\u9635\u5217\u6e38\u52a8\uff0c\u7a81\u7136\u4e00\u8d77\u8f6c\u5411[9]\u3002\u7ecf\u6d4e\u4e2d\u5546\u54c1\u7684\u6700\u4f73\u5b9a\u4ef7\u4f3c\u4e4e\u6e90\u4e8e\u4e3b\u4f53\u9075\u5b88\u5c40\u90e8\u7684\u5546\u4e1a\u89c4\u5219[10]\u3002\u8fd9\u4e9b\u73b0\u8c61\u4e2d\u7684\u5168\u5c40\u534f\u8c03\u662f\u5982\u4f55\u51fa\u73b0\u7684\uff1f\u662f\u5426\u6709\u5171\u540c\u7684\u673a\u5236\u5f15\u5bfc\u7740\u8fd9\u4e9b\u4e0d\u540c\u73b0\u8c61\u7684\u51fa\u73b0\uff1f\u5728\u590d\u6742\u7cfb\u7edf\u7406\u8bba\u4e2d\u628a\u8fd9\u7c7b\u8bb8\u591a\u72ec\u7acb\u5b50\u7cfb\u7edf\u76f8\u4e92\u4f5c\u7528\u540e\u4ea7\u751f\u9ad8\u5ea6\u7ed3\u6784\u5316\u7684\u96c6\u4f53\u884c\u4e3a\u7684\u73b0\u8c61\u79f0\u4f5c\u6d8c\u73b0\u3002<\/span><\/section>\n

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\u76ee\u524d\u5bf9\u6d8c\u73b0\u7684\u7814\u7a76\u7406\u8bba\u6709\u57fa\u4e8e\u6709\u6548\u4fe1\u606f\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u3001\u57fa\u4e8e\u4fe1\u606f\u5206\u89e3\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u3001\u57fa\u4e8e\u53ef\u9006\u6027\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\uff0c\u57fa\u4e8e\u8f6c\u79fb\u71b5\u7684\u52a8\u529b\u5b66\u89e3\u8026\u7406\u8bba[11]\u3001\u57fa\u4e8e\u683c\u5170\u6770\u56e0\u679c\u7684G-emergence\u7406\u8bba[12]\u7b49\u7b49\u3002\u8ba1\u7b97\u529b\u5b66\u662f\u57fa\u4e8e\u7edf\u8ba1\u590d\u6742\u5ea6\u5bf9\u6d8c\u73b0\u7684\u5b9a\u91cf\u5316\u7814\u7a76\u7406\u8bba\uff0c\u5b83\u63d0\u51fa\u7684\u65f6\u95f4\u6700\u65e9\uff0c\u867d\u7136\u5bf9\u6d8c\u73b0\u7684\u7684\u7814\u7a76\u65b9\u6cd5\u4e0e\u4e0a\u8ff0\u7406\u8bba\u5747\u4e0d\u540c\uff0c\u4f46\u6709\u5f88\u591a\u7814\u7a76\u601d\u8def\u662f\u76f8\u4f3c\u7684\uff0c\u5b83\u5b9a\u4e49\u7684\u7edf\u8ba1\u590d\u6742\u5ea6\u3001\u56e0\u679c\u6001\u3001\u6591\u56fe\u91cd\u6784\u673a\u5668\u7b49\u6982\u5ff5\u5bf9\u6d8c\u73b0\u7684\u7814\u7a76\u6709\u5f88\u5927\u542f\u53d1\u548c\u501f\u9274\u610f\u4e49\u3002<\/span><\/section>\n

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2.2 \u8ba1\u7b97\u529b\u5b66\u4e2d\u7684\u6d8c\u73b0<\/span><\/strong><\/span><\/h3>\n

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\u4ec0\u4e48\u662f\u6d8c\u73b0\uff1f\u4ece\u76f4\u89c9\u4e0a\u6765\u8bf4\uff0c\u6d8c\u73b0\u73b0\u8c61\u5c31\u662f\u7cfb\u7edf\u51fa\u73b0\u4e86\u65b0\u7684\u7279\u5f81\u3002\u4f46\u662f\u4ec0\u4e48\u662f\u201c\u65b0\u7279\u5f81\u201d\u5462\uff1f\u7279\u5f81\u7684\u65b0\u53c8\u201c\u65b0\u201d\u5728\u54ea\u91cc\uff1f\u6240\u4ee5\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u66f4\u7cbe\u786e\u7684\u8bed\u8a00\u5bf9\u6d8c\u73b0\u7684\u6982\u5ff5\u8fdb\u884c\u63cf\u8ff0\u3002\u6d8c\u73b0\u901a\u5e38\u88ab\u7406\u89e3\u4e3a\u4e00\u4e2a\u8fc7\u7a0b\uff0c\u8be5\u8fc7\u7a0b\u6240\u4ea7\u751f\u7684\u7ed3\u6784\u5e76\u4e0d\u80fd\u76f4\u63a5\u7531\u63a7\u5236\u7cfb\u7edf\u7684\u5b9a\u4e49\u6240\u7ea6\u675f\u4ee5\u53ca\u88ab\u77ac\u65f6\u529b\u6240\u63cf\u8ff0\u3002\u6bd4\u5982\u4e00\u5806\u968f\u673a\u8fd0\u52a8\u7684\u7c92\u5b50\uff0c\u867d\u7136\u5b83\u4eec\u53d7\u5230\u7684\u77ac\u65f6\u529b\u53ef\u4ee5\u7528\u8fd0\u52a8\u65b9\u7a0b\u63cf\u8ff0\uff0c\u4f46\u662f\u4ece\u5b8f\u89c2\u5c3a\u5ea6\u4e0a\u5374\u4f1a\u8868\u73b0\u51fa\u8bf8\u5982\u538b\u5f3a\u3001\u4f53\u79ef\u4ee5\u53ca\u6e29\u5ea6\u7b49\u65b0\u7279\u5f81\u3002\u6211\u4eec\u9700\u8981\u5f15\u5165\u6591\u56fe\u7684\u6982\u5ff5\u6765\u660e\u786e\u8bf4\u660e\u4ec0\u4e48\u662f\u65b0\u7279\u5f81\uff0c\u5426\u5219\u6d8c\u73b0\u8fd9\u4e00\u6982\u5ff5\u51e0\u4e4e\u6ca1\u6709\u5185\u5bb9\uff0c\u56e0\u4e3a\u51e0\u4e4e\u4efb\u4f55\u65f6\u95f4\u4f9d\u8d56\u7684\u7cfb\u7edf\u90fd\u4f1a\u8868\u73b0\u51fa\u6d8c\u73b0\u7279\u5f81\u3002<\/span><\/section>\n

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\u5728\u8ba1\u7b97\u529b\u5b66\u4e2d[13]\uff0c\u6591\u56fe\u901a\u5e38\u6307\u7684\u662f\u4ece\u65f6\u95f4\u5e8f\u5217\u4e2d\u603b\u7ed3\u51fa\u7684\u89c4\u5f8b\u6027\u7ed3\u6784\u3002\u5b9e\u9645\u4e0a\uff0c\u68c0\u6d4b\u5230\u7684\u6591\u56fe\u901a\u5e38\u662f\u901a\u8fc7\u89c2\u5bdf\u8005\u9009\u62e9\u7684\u7edf\u8ba1\u6570\u636e\u6765\u9690\u542b\u5047\u5b9a\u7684\uff0c\u53ef\u80fd\u67d0\u4e9b\u6591\u56fe\u7684\u529f\u80fd\u8868\u73b0\u4e0e\u5176\u6570\u5b66\u6a21\u578b\u4e00\u81f4\uff0c\u4f46\u8fd9\u4e9b\u6a21\u578b\u672c\u8eab\u4f9d\u8d56\u4e8e\u4e00\u7cfb\u5217\u7406\u8bba\u5047\u8bbe\u3002\u7b80\u800c\u8a00\u4e4b\uff0c\u6591\u56fe\u901a\u5e38\u662f\u88ab\u731c\u6d4b\u51fa\u6765\u7684\uff0c\u89c2\u5bdf\u8005\u901a\u8fc7\u56fa\u5b9a\u7684\u89c4\u5f8b\u5e93\u6765\u9884\u6d4b\u8fd9\u4e9b\u7ed3\u6784\uff0c\u7136\u540e\u518d\u8fdb\u884c\u9a8c\u8bc1\u3002\u53ef\u4ee5\u7528\u901a\u4fe1\u4fe1\u9053\u505a\u4e00\u4e2a\u7c7b\u6bd4\uff0c\u89c2\u5bdf\u8005\u5c31\u50cf\u662f\u4e00\u4e2a\u5df2\u7ecf\u624b\u63e1\u5bc6\u7801\u672c\u7684\u63a5\u6536\u8005\uff0c\u4efb\u4f55\u672a\u80fd\u901a\u8fc7\u5bc6\u7801\u672c\u89e3\u7801\u7684\u4fe1\u53f7\u672c\u8d28\u4e0a\u90fd\u662f\u566a\u58f0\uff0c\u5373\u89c2\u5bdf\u8005\u672a\u80fd\u8bc6\u522b\u7684\u6591\u56fe\u3002<\/span><\/section>\n

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\u5728\u7cfb\u7edf\u5185\u90e8\u7684\u534f\u8c03\u884c\u4e3a\u4e2d\uff0c\u6709\u4e00\u79cd\u6591\u56fe\u53d8\u5f97\u5c24\u4e3a\u91cd\u8981\uff0c\u8fd9\u79cd\u6591\u56fe\u4f1a\u76f8\u5bf9\u4e8e\u8be5\u7cfb\u7edf\u7684\u5176\u4ed6\u7ed3\u6784\u663e\u73b0\u5176\u201c\u65b0\u9896\u6027\u201d\u3002\u7531\u4e8e\u6ca1\u6709\u5916\u90e8\u7684\u53c2\u7167\u6765\u5b9a\u4e49\u8fd9\u79cd\u65b0\u9896\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u8fd9\u4e2a\u8fc7\u7a0b\u79f0\u4e3a\u5185\u5728\u6d8c\u73b0<\/span>\uff08Intrinsic Emergence\uff09<\/span>\u3002\u6bd4\u5982\u5728\u9ad8\u6548\u7684\u8d44\u672c\u5e02\u573a\u4e2d\uff0c\u4e3b\u4f53\u6839\u636e\u4ece\u96c6\u4f53\u884c\u4e3a\u4e2d\u6d8c\u73b0\u51fa\u7684\u6700\u4f18\u5b9a\u4ef7\uff0c\u8c03\u6574\u5176\u4e2a\u4eba\u751f\u4ea7-\u6295\u8d44\u548c\u80a1\u7968\u6240\u6709\u6743\u7b56\u7565[10]\u3002\u5bf9\u4e8e\u4e3b\u4f53\u7684\u8d44\u6e90\u914d\u7f6e\u51b3\u7b56\u800c\u8a00\uff0c\u901a\u8fc7\u5e02\u573a\u7684\u96c6\u4f53\u884c\u4e3a\u6d8c\u73b0\u51fa\u7684\u4ef7\u683c\u662f\u51c6\u786e\u7684\u4fe1\u53f7\uff0c\u5b83\u5b8c\u5168\u53cd\u6620\u4e86\u6240\u6709\u53ef\u7528\u4fe1\u606f\u3002\u5185\u5728\u6d8c\u73b0\u7684\u72ec\u7279\u4e4b\u5904\u5728\u4e8e\u7cfb\u7edf\u5f62\u6210\u7684\u6591\u56fe\u8d4b\u4e88\u4e86\u7cfb\u7edf\u989d\u5916\u7684\u529f\u80fd\u6027\uff0c\u5e76\u652f\u6301\u5168\u5c40\u4fe1\u606f\u5904\u7406\uff0c\u5982\u8bbe\u5b9a\u6700\u4f18\u4ef7\u683c\u7b49\u3002\u66f4\u5177\u4f53\u5730\u8bf4\uff0c\u5185\u5728\u6d8c\u73b0\u53ef\u4ee5\u76f4\u63a5\u5d4c\u5165\u7cfb\u7edf\u975e\u7ebf\u6027\u8ba1\u7b97\u8fc7\u7a0b\u4e4b\u4e2d\uff0c\u80fd\u591f\u88ab\u7cfb\u7edf\u76f4\u63a5\u5229\u7528\uff0c\u8fd9\u6837\u5c31\u8d4b\u4e88\u4e86\u7cfb\u7edf\u989d\u5916\u7684\u529f\u80fd\u6027\u3002<\/span><\/section>\n

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\u603b\u800c\u8a00\u4e4b\uff0c\u8ba1\u7b97\u529b\u5b66\u533a\u5206\u4e86\u4e09\u4e2a\u6982\u5ff5\uff1a<\/span><\/p>\n

    \n
  1. \n

    \u5bf9\u6d8c\u73b0\u7684\u76f4\u89c9\u5b9a\u4e49\uff1a\u7cfb\u7edf\u4e2d\u51fa\u73b0\u4efb\u4f55\u53ef\u4ee5\u88ab\u79f0\u4e3a\u65b0\u9896\u7684\u7279\u5f81\u3002<\/span><\/p>\n<\/li>\n

  2. \n

    \u6591\u56fe\u6d8c\u73b0<\/span>\uff08Pattern Formation\uff09<\/span>\uff1a\u89c2\u5bdf\u8005\u5728\u7cfb\u7edf\u4e2d\u8bc6\u522b\u51fa\u7684\u6709\u89c4\u5f8b\u7684\u7ed3\u6784\u3002<\/span><\/p>\n<\/li>\n

  3. \n
    \u5185\u5728\u6d8c\u73b0<\/span>\uff08Intrinsic Emergence\uff09<\/span>\uff1a\u7cfb\u7edf\u672c\u8eab\u6355\u6349\u5e76\u5229\u7528\u5b83\u81ea\u8eab\u51fa\u73b0\u7684\u6591\u56fe\u3002<\/span><\/section>\n<\/li>\n<\/ol>\n


    <\/span><\/h3>\n

    2.3 \u8fdb\u5316\u7684\u7cfb\u7edf\u6a21\u578b<\/span><\/strong><\/span><\/h3>\n

    <\/span><\/section>\n
    \u6211\u4eec\u53ef\u4ee5\u4ece\u591a\u667a\u80fd\u4f53\u7cfb\u7edf\u7684\u89c6\u89d2\u6765\u9610\u8ff0\u5185\u5728\u6d8c\u73b0\u7684\u95ee\u9898[13]\uff0c\u4ece\u800c\u4e3a\u4e00\u4e2a\u9ad8\u5ea6\u6709\u5e8f\u7684\u7cfb\u7edf\u662f\u600e\u4e48\u4ece\u6df7\u6c8c\u4e2d\u6d8c\u73b0\u7684\u63d0\u4f9b\u4e00\u79cd\u53ef\u80fd\u7684\u89e3\u91ca\u3002\u4f46\u662f\u8be5\u89c6\u89d2\u5728\u89e3\u91ca\u751f\u547d\u5f62\u5f0f\u7684\u591a\u6837\u6027\u65b9\u9762\u4f9d\u7136\u80fd\u529b\u6709\u9650\u3002\u56e0\u6b64\u8981\u5c06\u7cfb\u7edf\u9650\u5236\u5728\u4e00\u4e2a\u7ed3\u6784\u548c\u751f\u7269\u7279\u5f81\u660e\u786e\u7684\u786e\u5b9a\u6027\u52a8\u529b\u7cfb\u7edf<\/span>\uff08Deterministic Dynamical Systems\uff0c\u7b80\u79f0DS\uff09<\/span>\u4e2d\uff0c\u5e76\u628a\u5b83\u7b80\u5316\u4e3a\u5305\u62ec\u4e00\u4e2a\u73af\u5883\u548c\u4e00\u7ec4\u9002\u5e94\u6027\u89c2\u5bdf\u8005\u6216\u201c\u667a\u80fd\u4f53\u201d\u7684\u6a21\u578b\uff0c\u8fd9\u6837\u624d\u80fd\u6e05\u6670\u5730\u5b9a\u4e49\u667a\u80fd\u4f53\u7684\u6027\u8d28\u3002\u667a\u80fd\u4f53<\/span>\uff08Agent\uff09<\/span>\u8bd5\u56fe\u6784\u5efa\u548c\u7ef4\u6301\u4e00\u4e2a\u5bf9\u5176\u73af\u5883\u5177\u6709\u6700\u5927\u9884\u6d4b\u80fd\u529b\u7684\u5185\u90e8\u6a21\u578b\u3002\u6bcf\u4e2a\u667a\u80fd\u4f53\u7684\u73af\u5883\u662f\u5176\u4ed6\u667a\u80fd\u4f53\u7684\u96c6\u5408\uff0c\u53ef\u4ee5\u88ab\u89c6\u4e3a\u4e00\u4e2a\u968f\u673a\u7684\u52a8\u529b\u7cfb\u7edf<\/span>\uff08Stochastic Dynamical Systems\uff0c\u7b80\u79f0SDS\uff09<\/span>\u3002\u5728\u4efb\u4f55\u7ed9\u5b9a\u7684\u65f6\u523b\uff0c\u667a\u80fd\u4f53\u611f\u77e5\u5230\u7684\u662f\u5f53\u524d\u73af\u5883\u72b6\u6001\u7684\u6295\u5f71\u3002\u968f\u7740\u65f6\u95f4\u7684\u63a8\u79fb\uff0c\u611f\u5b98\u88c5\u7f6e\u4ea7\u751f\u4e00\u7cfb\u5217\u6d4b\u91cf\uff0c\u8fd9\u4e9b\u6d4b\u91cf\u5f15\u5bfc\u667a\u80fd\u4f53\u5229\u7528\u5176\u53ef\u7528\u8d44\u6e90<\/span>\uff08\u4e0b\u56fe\u4e2d\u7684\u201c\u57fa\u5c42\u201d\uff09<\/span>\u6765\u6784\u5efa\u73af\u5883\u6a21\u578b\u3002\u57fa\u4e8e\u73af\u5883\u6a21\u578b\u6355\u6349\u5230\u7684\u89c4\u5f8b\uff0c\u667a\u80fd\u4f53\u53ef\u4ee5\u901a\u8fc7\u6548\u5e94\u5668\u91c7\u53d6\u884c\u52a8\uff0c\u6700\u7ec8\u6539\u53d8\u73af\u5883\u72b6\u6001\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n
    \u4e0a\u56fe\u4e3a\u4ee5\u667a\u80fd\u4f53\u4e3a\u4e2d\u5fc3\u7684\u73af\u5883\u89c6\u56fe\uff1a\u5b87\u5b99\u53ef\u4ee5\u88ab\u89c6\u4e3a\u4e00\u4e2a\u786e\u5b9a\u6027\u52a8\u529b\u7cfb\u7edf\uff0c\u5373\u4f7f\u89c4\u5219\u548c\u521d\u59cb\u6761\u4ef6\u662f\u786e\u5b9a\u7684\uff0c\u968f\u7740\u89c4\u6a21\u7684\u589e\u957f\uff0c\u7cfb\u7edf\u4e5f\u4f1a\u53d8\u5f97\u6781\u4e3a\u590d\u6742\u3002\u6bcf\u4e2a\u667a\u80fd\u4f53\u6240\u770b\u5230\u7684\u73af\u5883\u662f\u4e00\u4e2a\u7531\u6240\u6709\u5176\u4ed6\u667a\u80fd\u4f53\u7ec4\u6210\u7684\u968f\u673a\u52a8\u529b\u7cfb\u7edf\u3002\u5176\u968f\u673a\u6027\u6e90\u4e8e\u5176\u5185\u5728\u7684\u968f\u673a\u6027\u548c\u6709\u9650\u7684\u8ba1\u7b97\u8d44\u6e90\u3002\u6bcf\u4e2a\u667a\u80fd\u4f53\u672c\u8eab\u4e5f\u662f\u4e00\u4e2a\u968f\u673a\u52a8\u529b\u7cfb\u7edf\uff0c\u56e0\u4e3a\u5b83\u53ef\u80fd\u4f1a\u4ece\u5176\u57fa\u5c42\u548c\u73af\u5883\u523a\u6fc0\u4e2d\u91c7\u6837\u6216\u53d7\u5230\u65e0\u6cd5\u63a7\u5236\u7684\u968f\u673a\u6027\u6240\u56f0\u6270\u3002\u57fa\u5c42\u4ee3\u8868\u4e86\u652f\u6301\u548c\u9650\u5236\u4fe1\u606f\u5904\u7406\u3001\u6a21\u578b\u6784\u5efa\u548c\u51b3\u7b56\u7684\u53ef\u7528\u8d44\u6e90\u3002\u7bad\u5934\u8868\u793a\u4fe1\u606f\u6d41\u5165\u548c\u6d41\u51fa\u667a\u80fd\u4f53\u7684\u65b9\u5411\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u667a\u80fd\u4f53\u9762\u4e34\u7684\u57fa\u672c\u95ee\u9898\u662f\u57fa\u4e8e\u5bf9\u73af\u5883\u72b6\u6001\u7684\u5efa\u6a21\uff0c\u6765\u5bf9\u672a\u6765\u73af\u5883\u8fdb\u884c\u9884\u6d4b\u3002\u8fd9\u9700\u8981\u4e00\u4e2a\u91cf\u5316\u7684\u7406\u8bba\u6765\u63cf\u8ff0\u667a\u80fd\u4f53\u5982\u4f55\u5904\u7406\u4fe1\u606f\u548c\u6784\u5efa\u6a21\u578b\u3002<\/span><\/section>\n

    <\/span><\/section>\n

    <\/h2>\n

    \n
    \n
    \n
    \n
    \n
    <\/section>\n
    <\/section>\n
    \n
    <\/section>\n<\/section>\n<\/section>\n
    \n

    3. \u56e0\u679c\u6001\u548c\u590d\u6742\u5ea6<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n
    <\/section>\n
    <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

    <\/p>\n

    \u667a\u80fd\u4f53\u9700\u8981\u4e00\u79cd\u6709\u6548\u7684\u63cf\u8ff0\u65b9\u5f0f\u5904\u7406\u6240\u63a5\u53d7\u5230\u7684\u73af\u5883\u4fe1\u606f\uff0c\u4f7f\u5176\u53ef\u4ee5\u628a\u73af\u5883\u4fe1\u606f\u538b\u7f29\u6210\u4e00\u4e2a\u6709\u9650\u7684\u72b6\u6001\u7a7a\u95f4\uff0c\u5e76\u5b58\u50a8\u4e8e\u5185\u90e8\u73af\u5883\u6a21\u578b\u4e2d\u3002\u4e3a\u4e86\u627e\u5230\u8fd9\u79cd\u6709\u6548\u7684\u63cf\u8ff0\u65b9\u5f0f\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u5b9a\u4e49\u6240\u8c13\u7684\u667a\u80fd\u4f53\u72b6\u6001\u7684\u6982\u5ff5\uff1a\u72b6\u6001\u53ef\u4ee5\u88ab\u7406\u89e3\u4e3a\u667a\u80fd\u4f53\u6240\u63a5\u6536\u5230\u7684\u5168\u90e8\u5386\u53f2\u4fe1\u606f\uff0c\u5373\u5386\u53f2\u4fe1\u606f\u5373\u72b6\u6001\u3002\u4e4b\u540e\uff0c\u6211\u4eec\u5c06\u5f15\u5165”\u56e0\u679c\u6001”\u7684\u6982\u5ff5\uff0c\u5b83\u76f8\u5f53\u4e8e\u662f\u5bf9\u72b6\u6001\u7684\u4e00\u79cd\u7c97\u7c92\u5316\u63cf\u8ff0\u3002\u4e0b\u9762\u7ed9\u51fa\u6b63\u5f0f\u5b9a\u4e49\uff1a<\/span><\/section>\n


    <\/span><\/h3>\n

    3.1 \u72b6\u6001\u7684\u5b9a\u4e49<\/span><\/strong><\/span><\/h3>\n

    <\/span><\/section>\n
    \u667a\u80fd\u4f53\u5bf9\u73af\u5883\u7684\u6d4b\u91cf\u7cbe\u5ea6\u4e00\u822c\u90fd\u662f\u6709\u9650\u7684\uff0c\u6d4b\u91cf\u7ed3\u679c\u53ea\u80fd\u63cf\u8ff0\u73af\u5883\u72b6\u6001\u7684\u67d0\u79cd\u6295\u5f71\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u73af\u5883\u4ece\u8fc7\u53bb\u5230\u672a\u6765\u7684\u53d8\u5316\u7528\u4e00\u4e2a\u79bb\u6563\u7684\u7a33\u5b9a\u968f\u673a\u8fc7\u7a0b\u63cf\u8ff0\uff0c\u72b6\u6001\u7684\u53d6\u503c\u7a7a\u95f4\u5219\u4e3a\u53cc\u65e0\u9650\u5e8f\u5217\u53ef\u6570\u96c6\u5408<\/span><\/sub>=<\/span>\u22ef<\/span>s<\/span>\u2212<\/span><\/sub><\/span>2<\/span><\/sub><\/span>s<\/span>\u2212<\/span><\/sub><\/span>1<\/span><\/sub><\/span>s<\/span>0<\/span><\/sub><\/span>s<\/span>1<\/span><\/sub><\/span>s<\/span>2<\/span><\/sub><\/span>\u22ef<\/span>\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u4e00\u4e2a\u667a\u80fd\u4f53\u7684\u72b6\u6001\u6307\u7684\u662f\u4e00\u4e2a\u65e0\u9650\u957f\u7684\u65f6\u95f4\u5e8f\u5217\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u57fa\u4e8e\u5f53\u524d\u7684\u65f6\u523b<\/span>t<\/span>\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06<\/span><\/sub>\u5206\u4e3a\u5355\u4fa7\u524d\u5411\u5e8f\u5217<\/span><\/sub>=<\/span>\u22ef<\/span>s<\/span>t<\/span><\/sub><\/span>\u2212<\/span><\/sub><\/span>3<\/span><\/sub><\/span>s<\/span>t<\/span><\/sub><\/span>\u2212<\/span><\/sub><\/span>2<\/span><\/sub><\/span>s<\/span>t<\/span><\/sub><\/span>\u2212<\/span><\/sub><\/span>1<\/span><\/sub><\/span>\u548c\u5355\u4fa7\u540e\u5411\u5e8f\u5217<\/sub><\/span>=<\/span>s<\/span>t<\/span><\/sub><\/span>s<\/span>t<\/span><\/sub><\/span>+<\/span><\/sub><\/span>1<\/span><\/sub><\/span>s<\/span>t<\/span><\/sub><\/span>+<\/span><\/sub><\/span>2<\/span><\/sub><\/span>s<\/span>t<\/span><\/sub><\/span>+<\/span><\/sub><\/span>3<\/span><\/sub><\/span>\u22ef<\/span>\u4e24\u4e2a\u90e8\u5206\uff0c\u6240\u6709\u53ef\u80fd\u7684\u672a\u6765\u5e8f\u5217<\/span><\/sub><\/span>\u5f62\u6210\u7684\u96c6\u5408\u8bb0\u4f5c<\/sub><\/span>\uff0c\u6240\u6709\u53ef\u80fd\u7684\u5386\u53f2\u5e8f\u5217<\/span><\/sub><\/span>\u5f62\u6210\u7684\u96c6\u5408\u8bb0\u4f5c<\/span><\/sub>\u3002\u67d0\u4e00\u4e2a\u65f6\u523b\u7684\u72b6\u6001\u6307\u7684\u662f\u622a\u6b62\u5230\u5f53\u524d\u65f6\u523b\u7684\u5386\u53f2\u5e8f\u5217\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7136\u540e\u6211\u4eec\u5c06\u5b9a\u4e49\u4e00\u4e2a\u53eb\u505a\u201c\u56e0\u679c\u6001\u201d\u7684\u6982\u5ff5\u3002<\/span><\/section>\n


    <\/span><\/h3>\n

    3.2 \u56e0\u679c\u6001\u7684\u5b9a\u4e49<\/span><\/strong><\/span><\/h3>\n


    <\/span><\/h4>\n

    3.2.1 \u5212\u5206<\/span><\/strong><\/h4>\n

    <\/span><\/section>\n
    \u901a\u8fc7\u5bf9\u72b6\u6001\u7a7a\u95f4\u8fdb\u884c\u5212\u5206<\/span>\uff08partition\uff09<\/span>\uff0c\u667a\u80fd\u4f53\u53ef\u4ee5\u7528\u4e00\u79cd\u66f4\u52a0\u7c97\u7cd9\u7684\u65b9\u5f0f\u6765\u63cf\u8ff0\u540c\u6837\u7684\u72b6\u6001\uff0c\u8fd9\u4e00\u8fc7\u7a0b\u4e5f\u88ab\u4eba\u4eec\u53eb\u505a\u7c97\u7c92\u5316\u3002\u5212\u5206\u53ef\u4ee5\u88ab\u7406\u89e3\u4e3a\u4e00\u79cd\u6620\u5c04\uff0c<\/span><\/sub><\/span>\uff0c\u5176\u4e2d<\/span><\/sub><\/span>\u662f\u72b6\u6001\u7a7a\u95f4\u7684\u5b50\u96c6\u7684\u96c6\u5408\uff0c\u8981\u6ee1\u8db3\u5176\u5143\u7d20\u5f7c\u6b64\u4e92\u65a5\uff0c\u800c\u4e14\u6240\u6709\u5143\u7d20\u7684\u5e76\u96c6\u7b49\u4e8e<\/span><\/sub>\u7684\u6761\u4ef6\u3002\u901a\u8fc7\u5212\u5206\u6620\u5c04\uff0c\u667a\u80fd\u4f53\u80fd\u591f\u5f97\u5230\u7684\u6240\u6709\u5b50\u96c6\u90fd\u53ef\u4ee5\u88ab\u89c6\u4e3a\u5bf9\u5e94\u7740\u4e00\u4e2a\u5b8f\u89c2\u6001\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/span><\/section>\n
    \u4e0a\u56fe\u4e3a\u67d0\u79cd\u5212\u5206\u7684\u793a\u610f\u56fe[14]\uff0c\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c<\/span><\/sub>\u4e0d\u5fc5\u5f62\u6210\u7d27\u81f4\u96c6\uff0c\u4e5f\u53ef\u4ee5\u662f\u5eb7\u6258\u96c6\u6216\u5176\u4ed6\u66f4\u7279\u6b8a\u7684\u7ed3\u6784\uff0c\u4e0a\u56fe\u4e3a\u4e86\u793a\u610f\u6e05\u695a\u624d\u8fd9\u6837\u753b\u7684\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4e8e\u662f\uff0c\u667a\u80fd\u4f53\u5c31\u9700\u8981\u5b66\u4e60\u5230\u4e00\u79cd\u6709\u6548\u7684\u5212\u5206\uff0c\u5373\u5982\u4f55\u4ece\u89c2\u6d4b\u5230\u7684\u72b6\u6001<\/span>\uff08\u53ef\u4ee5\u79f0\u4e4b\u4e3a\u5fae\u89c2\u6001\uff09<\/span>\u5230\u667a\u80fd\u4f53\u538b\u7f29\u540e\u5f97\u5230\u7684\u9690\u7a7a\u95f4\u4e0a\u7684\u72b6\u6001<\/span>\uff08\u53ef\u4ee5\u79f0\u4e3a\u5b8f\u89c2\u6001\uff09<\/span>\u80fd\u591f\u5f88\u597d\u5bf9\u5e94\uff0c\u4f7f\u5f97\u5b8f\u89c2\u6001\u66f4\u52a0\u6709\u6548\u5730\u53cd\u6620\u5fae\u89c2\u6001\u4e2d\u7684\u91cd\u8981\u4fe1\u606f\u3002\u90a3\u4e48\uff0c\u4ec0\u4e48\u53eb\u505a\u6709\u6548\u5462\uff1f<\/span><\/section>\n

    <\/span><\/section>\n

    3.2.2 \u56e0\u679c\u6001<\/span><\/strong><\/h4>\n

    <\/span><\/section>\n
    \u5bf9\u4e8e\u96c6\u5408<\/span><\/sub>\u7684\u5212\u5206\u53ef\u4ee5\u6709\u5f88\u591a\u79cd\uff0c\u82e5\u67d0\u4e00\u79cd\u5212\u5206\u80fd\u591f\u5728\u9884\u6d4b\u80fd\u529b\u6700\u5f3a\u7684\u540c\u65f6\u53c8\u975e\u5e38\u7b80\u6d01\uff0c\u90a3\u4e48\u5b83\u80af\u5b9a\u662f\u6700\u4f18\u7684\u5212\u5206\uff0c\u6211\u4eec\u628a\u8fd9\u79cd\u7528\u6700\u4f18\u7684\u5212\u5206\u65b9\u6cd5\u5f97\u5230\u7684\u5b8f\u89c2\u6001\u79f0\u4e3a\u56e0\u679c\u6001\u3002\u56e0\u679c\u6001\u5c31\u662f\u667a\u80fd\u4f53\u5bf9\u6d4b\u91cf\u7ed3\u679c\u8fdb\u884c\u5904\u7406\u540e\uff0c\u6839\u636e\u5176\u5185\u90e8\u6a21\u578b<\/span>\uff08\u5c24\u5176\u662f\u72b6\u6001\u7ed3\u6784\uff09<\/span>\u8bc6\u522b\u51fa\u7684\u6591\u56fe\uff0c\u5e76\u4e14\u8fd9\u79cd\u6591\u56fe\u4e0d\u968f\u65f6\u95f4\u53d1\u751f\u53d8\u5316\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4e0b\u9762\uff0c\u6211\u4eec\u7ed9\u51fa\u56e0\u679c\u6001\u7684\u5f62\u5f0f\u5316\u5b9a\u4e49\u3002<\/span><\/section>\n

    <\/span><\/h5>\n
    3.2.2.1 \u9884\u6d4b\u7b49\u4ef7\u5173\u7cfb<\/span><\/h5>\n

    <\/span><\/section>\n
    \u5bf9\u4e8e\u4efb\u610f\u65f6\u523b<\/span>t<\/span> \u548c<\/span>t<\/span>\u2032<\/span>\uff0c\u5728\u7ed9\u5b9a\u8fc7\u53bb\u72b6\u6001<\/span><\/sub>\u7684\u6761\u4ef6\u4e0b\uff0c\u672a\u6765\u72b6\u6001<\/span><\/sub>\u7684\u5206\u5e03\u4e0e\u7ed9\u5b9a\u8fc7\u53bb\u72b6\u6001<\/span><\/sub>\u7684\u6761\u4ef6\u4e0b\uff0c\u672a\u6765\u72b6\u6001<\/span><\/sub>\u7684\u5206\u5e03\u5b8c\u5168\u76f8\u540c\u3002\u90a3\u4e48\u6211\u4eec\u5c31\u79f0<\/span><\/sub>\u4e0e<\/span><\/sub><\/span>\u7b49\u4ef7\uff0c\u8bb0\u4e3a\uff1a<\/span><\/sub><\/span>\u223c<\/span><\/span><\/sub>\uff0c\u6216\u7b80\u8bb0\u4e3a<\/span>t<\/span>\u223c<\/span>t<\/span>\u2032<\/span>\uff0c\u5176\u4e2d\u201c<\/span>\u223c<\/span> \u201d \u8868\u793a\u7531\u7b49\u6548\u672a\u6765\u72b6\u6001\u6240\u5f15\u8d77\u7684\u7b49\u4ef7\u5173\u7cfb\uff0c\u4e5f\u53eb\u9884\u6d4b\u7b49\u4ef7\u6027<\/span>\uff08predictive equivalence\uff09<\/span>\uff0c\u53ef\u4ee5\u7528\u516c\u5f0f\u8868\u793a\u4e3a\uff1a<\/span><\/section>\n
    <\/section>\n

    <\/p>\n

    <\/section>\n
    \u4e5f\u5c31\u662f\u8bf4\uff0c\u82e5<\/span>t<\/span> \u548c<\/span>t<\/span>\u2032<\/span>\u5bf9\u672a\u6765\u72b6\u6001\u9884\u6d4b\u7684\u5206\u5e03\u76f8\u540c\uff0c\u5219\u5b83\u4eec\u5bf9\u5e94\u7684\u72b6\u6001\u5c31\u90fd\u5177\u6709\u4e00\u79cd\u7b49\u4ef7\u6027\uff0c\u8fd9\u5c31\u662f\u56e0\u679c\u6001\u5b9a\u4e49\u7684\u6765\u6e90\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    3.2.2.2 \u56e0\u679c\u6001<\/span><\/h5>\n

    <\/span><\/section>\n
    \u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u5c06\u56e0\u679c\u6001\u5b9a\u4e49\u4e3a\u4e00\u4e2a\u4ece\u72b6\u6001\u96c6\u5230\u72b6\u6001\u5b50\u96c6\u7684\u6620\u5c04\uff0c\u5373<\/span><\/sub>\uff0c\u5176\u4e2d<\/span><\/sub>\u662f<\/span><\/sub><\/span>\u7684\u5e42\u96c6\uff0c\u4e14<\/span>\u03f5<\/span>\u9700\u8981\u6ee1\u8db3\u5982\u4e0b\u6761\u4ef6\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/p>\n

    <\/section>\n

    <\/span><\/section>\n
    \u5176\u4e2d\uff0c<\/span><\/sub><\/span>\u4e3a\u5386\u53f2\u5e8f\u5217\u7684\u968f\u673a\u53d8\u91cf\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u6240\u6709\u7684\u56e0\u679c\u6001\u7684\u96c6\u5408\uff0c\u53ef\u4ee5\u7531\u9884\u6d4b\u7b49\u4ef7\u5173\u7cfb”<\/span>\u223c<\/span>“\u8bf1\u5bfc\u7684\u5bf9\u72b6\u6001\u7a7a\u95f4\u7684\u4e00\u79cd\u5212\u5206\u6765\u5b9a\u4e49\uff0c\u5373\u72b6\u6001\u96c6\u4e0e\u7b49\u4ef7\u5173\u7cfb\u7684\u5546\u96c6\uff1a<\/span>S<\/span>=<\/span><\/sub>\/<\/span>\u223c<\/span>\uff0c\u5176\u4e2d<\/span>S<\/span>\u4e3a\u56e0\u679c\u6001\u5212\u5206\u3002<\/span><\/section>\n

    <\/span><\/h5>\n
    3.2.2.3 \u4e3e\u4f8b\u8bf4\u660e<\/span><\/h5>\n

    <\/span><\/section>\n
    \u4e3a\u4e86\u8bf4\u660e\u56e0\u679c\u6001\u7684\u6982\u5ff5\uff0c\u6211\u4eec\u7ed8\u5236\u4e0b\u9762\u7684\u793a\u610f\u56fe\u4ee5\u4e3e\u4f8b\u8bf4\u660e\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/span><\/section>\n
    \u5982\u4e0a\u56fe\u6240\u793a[13]\uff0c\u5de6\u4fa7\u7684\u6570\u5b57\u4ee3\u8868<\/span>t<\/span>\u65f6\u523b\u7684\u72b6\u6001\u5e8f\u5217\uff0c\u53f3\u4fa7\u7684\u7bad\u5934\u5f62\u72b6\u4ee3\u8868\u5bf9\u672a\u6765\u72b6\u6001\u9884\u6d4b\u7684\u5206\u5e03\uff0c\u53ef\u4ee5\u89c2\u5bdf\u5230<\/span>t<\/span>9<\/span><\/sub>\u548c<\/span>t<\/span>13<\/span><\/sub>\u65f6\u523b\u7684\u7bad\u5934\u5f62\u72b6\u5b8c\u5168\u76f8\u540c\uff0c\u8bf4\u660e\u5b83\u4eec\u5bf9\u672a\u6765\u72b6\u6001\u9884\u6d4b\u7684\u5206\u5e03\u76f8\u540c\uff0c\u5219\u5904\u4e8e\u76f8\u540c\u7684\u56e0\u679c\u6001\uff1b\u540c\u6837\u7684\u9053\u7406\uff0c\u5728<\/span>t<\/span>11<\/span><\/sub>\u65f6\u523b\uff0c\u5b83\u7684\u7bad\u5934\u5f62\u72b6\u4e0e<\/span>t<\/span>9<\/span><\/sub>\u548c<\/span>t<\/span>13<\/span><\/sub>\u65f6\u523b\u4e0d\u540c\uff0c\u5219\u5904\u4e8e\u4e0d\u540c\u7684\u56e0\u679c\u6001\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    3.2.2.4 \u5c0f\u7ed3<\/span><\/h5>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/span><\/section>\n
    \u5185\u5728\u8ba1\u7b97<\/span>\uff08intrinsic computation\uff09<\/span>\u7684\u6838\u5fc3\u601d\u60f3\u662f\u9884\u6d4b\u7b49\u4ef7\u6027[15]\uff0c\u5373\u7cfb\u7edf\u7684\u5386\u53f2\u80fd\u591f\u7528\u6765\u9884\u6d4b\u5176\u672a\u6765\u884c\u4e3a\u7684\u4e00\u79cd\u7b49\u4ef7\u6027\u3002\u901a\u8fc7\u6784\u5efa\u9884\u6d4b\u6a21\u578b\uff0c\u5185\u5728\u8ba1\u7b97\u80fd\u591f\u8bc6\u522b\u7cfb\u7edf\u4e2d\u7684\u7ed3\u6784\uff0c\u5e76\u91cf\u5316\u8fd9\u4e9b\u7ed3\u6784\u7684\u590d\u6742\u6027\u548c\u7a33\u5b9a\u6027\u3002\u5b83\u53ef\u4ee5\u8ba9\u6211\u4eec\u80fd\u591f\u5c06\u81ea\u7ec4\u7ec7\u89c6\u4e3a\u7cfb\u7edf\u4e2d\u89c4\u5f8b\u6027\u548c\u89c4\u5219\u6027\u7684\u6d8c\u73b0\uff0c\u800c\u8fd9\u4e9b\u89c4\u5f8b\u6027\u548c\u89c4\u5219\u6027\u662f\u7cfb\u7edf\u5728\u7279\u5b9a\u7684\u521d\u59cb\u6761\u4ef6\u548c\u5916\u90e8\u9a71\u52a8\u4e0b\u81ea\u53d1\u5f62\u6210\u7684\u3002\u5185\u5728\u8ba1\u7b97\u7684\u4e00\u4e2a\u91cd\u8981\u5e94\u7528\u662f\u5728\u4e8e\u7406\u89e3\u4ece\u5b8c\u5168\u89c4\u5219\u5230\u5b8c\u5168\u65e0\u5e8f\u4e4b\u95f4\u7ec4\u7ec7\u7ed3\u6784\u7684\u5dee\u5f02\u548c\u8fc7\u6e21\u3002\u6bd4\u5982\uff0c\u6728\u661f\u7684\u5927\u7ea2\u6591\u662f\u4e00\u4e2a\u7ecf\u5178\u7684\u81ea\u7ec4\u7ec7\u73b0\u8c61\uff0c\u5176\u89c4\u6a21\u548c\u7a33\u5b9a\u6027\u65e0\u6cd5\u901a\u8fc7\u6d41\u4f53\u529b\u5b66\u65b9\u7a0b\u7684\u6c42\u89e3\u800c\u83b7\u5f97\u76f4\u63a5\u89e3\u91ca\u3002\u7136\u800c\uff0c\u5185\u5728\u8ba1\u7b97\u80fd\u591f\u901a\u8fc7\u5206\u6790\u8be5\u73b0\u8c61\u7684\u5386\u53f2\u6570\u636e\uff0c\u6784\u5efa\u51fa\u4e00\u4e2a\u80fd\u591f\u51c6\u786e\u9884\u6d4b\u5176\u672a\u6765\u884c\u4e3a\u7684\u6a21\u578b\uff0c\u4ece\u800c\u63ed\u793a\u51fa\u5176\u80cc\u540e\u7684\u81ea\u7ec4\u7ec7\u673a\u5236\u3002<\/span><\/section>\n

    <\/span><\/section>\n

    3.3 \u56e0\u679c\u6001\u7684\u4e3b\u8981\u6027\u8d28<\/span><\/strong><\/span><\/h3>\n

    <\/span><\/section>\n
    \u4e3a\u4ec0\u4e48\u6211\u4eec\u8981\u5173\u6ce8\u56e0\u679c\u6001\u8fd9\u6837\u4e00\u79cd\u7279\u5b9a\u7684\u5b8f\u89c2\u6001\u5462\uff1f\u4e0b\u9762\u662f\u56e0\u679c\u6001\u7684\u4e24\u4e2a\u4e3b\u8981\u6027\u8d28\uff0c\u80fd\u591f\u4f53\u73b0\u51fa\u56e0\u679c\u6001\u662f\u4e00\u79cd\u6700\u7406\u60f3\u7684\u5b8f\u89c2\u6001\uff1a<\/span><\/section>\n


    <\/span><\/h4>\n

    3.3.1 \u6700\u5927\u9884\u6d4b\u6027<\/span><\/strong><\/h4>\n

    <\/span><\/section>\n
    \u6027\u8d281\uff08\u56e0\u679c\u6001\u5177\u6709\u6700\u5927\u9884\u6d4b\u6027\uff09<\/span><\/strong>\uff1a\u5bf9\u4e8e\u5b8f\u89c2\u6001<\/span><\/sub><\/span>\u548c\u6b63\u6574\u6570<\/span>L<\/span>\uff0c\u90fd\u6709<\/span><\/sub>\uff0c<\/span><\/sub>\u4e3a\u957f\u5ea6\u4e3a<\/span>L<\/span>\u7684\u672a\u6765\u5e8f\u5217\u96c6\u5408\uff0c<\/span>S<\/span>\u4e3a\u56e0\u679c\u6001\u5212\u5206\uff0c\u6240\u6709\u53ef\u80fd\u7684\u5386\u53f2\u5e8f\u5217\u8bb0<\/span>\u4f5c<\/span><\/sub>\u3002<\/span><\/sub><\/span>\u548c<\/span><\/sub><\/span>\u662f<\/span><\/sub>\u7684\u6761\u4ef6\u71b5\u3002\u53ef\u4ee5\u7406\u89e3\u4e3a\u56e0\u679c\u6001\u96c6\u5408<\/span>S<\/span>\u662f\u5728\u6240\u6709\u7684\u5212\u5206\u5b8f\u89c2\u6001\u96c6\u5408<\/span>R<\/span>\u4e2d\uff0c\u9884\u6d4b\u80fd\u529b\u6700\u5f3a\u7684\u4e00\u79cd\u5b8f\u89c2\u6001\uff0c\u8bc1\u660e\u8fc7\u7a0b\u5982\u4e0b\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    \u6839\u636e\u56e0\u679c\u6001\u7684\u5b9a\u4e49\u53ef\u77e5\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n
    \u4e0a\u5f0f\u7b49\u4ef7\u4e8e<\/span><\/section>\n

    <\/span><\/section>\n

    <\/p>\n

    <\/section>\n

    <\/span><\/section>\n
    \u56e0\u4e3a<\/span><\/sub>\uff0c\u4e14<\/span><\/sub><\/section>\n

    <\/span><\/section>\n
    \u6240\u4ee5<\/span><\/sub><\/span><\/section>\n


    <\/span><\/h4>\n

    3.3.2 \u6700\u5c0f\u968f\u673a\u6027<\/span><\/strong><\/h4>\n

    <\/span><\/strong><\/section>\n
    \u6027\u8d282\uff08\u56e0\u679c\u6001\u5177\u6709\u6700\u5c0f\u968f\u673a\u6027\uff09<\/span><\/strong>\uff1a\u8bbe<\/span><\/sub>\u548c<\/sub><\/span>\u4e3a\u6ee1\u8db3\u6027\u8d281\u4e2d\u4e0d\u7b49\u5f0f\u7b49\u53f7\u6210\u7acb\u7684\u5b8f\u89c2\u6001\uff0c\u5219\u5bf9\u4e8e\u6240\u6709\u7684<\/sub>\u548c<\/sub>\uff0c\u90fd\u6709<\/span><\/sub>\uff0c\u5176\u4e2d<\/span><\/sub><\/span>\u548c<\/span>S<\/span>\u2032<\/span>\u5206\u522b\u662f\u8be5\u8fc7\u7a0b\u7684\u4e0b\u4e00\u65f6\u523b\u72b6\u6001\u548c\u4e0b\u4e00\u65f6\u523b\u56e0\u679c\u6001\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u8be5\u6027\u8d28\u53ef\u4ee5\u88ab\u7406\u89e3\u4e3a\u5728\u76f8\u540c\u9884\u6d4b\u80fd\u529b\u7684\u524d\u63d0\u4e0b\uff0c\u56e0\u679c\u6001\u96c6\u5408<\/span>S<\/span>\u5728\u6240\u6709\u7684\u5b8f\u89c2\u6001<\/span><\/sub><\/span><\/span>\u7684\u96c6\u5408\u4e2d\uff0c\u968f\u673a\u6027\u6700\u5c0f\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7528\u4e92\u4fe1\u606f\u7684\u89d2\u5ea6\u53bb\u7406\u89e3\u7684\u8bdd\uff0c\u4e0a\u5f0f\u7b49\u4ef7\u4e8e<\/span><\/sub>\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u56e0\u679c\u6001\u4e3a\u6240\u6709\u7684\u4e0e\u5b83\u81ea\u5df1\u7684\u4e0b\u4e00\u65f6\u523b\u7684\u4e92\u4fe1\u606f\u4e2d\u7684\u6700\u5927\u7684\u4e00\u4e2a\u5b8f\u89c2\u6001\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u82e5\u60f3\u66f4\u6df1\u5165\u7684\u7406\u89e3\u56e0\u679c\u6001\u7684\u6027\u8d28\u53ef\u4ee5\u9605\u8bfbCosma Rohilla Shalizi \u548cJames Crutchfield\u5408\u5199\u7684\u4e00\u7bc7\u8bba\u6587[14]\uff0c\u91cc\u9762\u6709\u56e0\u679c\u6001\u66f4\u591a\u7684\u6027\u8d28\u548c\u5bf9\u5e94\u7684\u5f62\u5f0f\u5316\u8bc1\u660e\u8fc7\u7a0b\u3002<\/span><\/section>\n

    <\/span><\/section>\n

    3.4 \u6591\u56fe\u91cd\u6784\u673a\u5668<\/span><\/strong><\/span><\/h3>\n

    <\/span><\/section>\n
    \u524d\u9762\u7ed9\u51fa\u4e86\u56e0\u679c\u6001\u7684\u5b9a\u4e49\uff0c\u63a5\u4e0b\u6765\u8ba8\u8bba\u4e00\u4e2a\u667a\u80fd\u4f53\u662f\u5982\u4f55\u4ece\u89c2\u6d4b\u5230\u7684\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u4e2d\uff0c\u81ea\u52a8\u5730\u53d1\u73b0\u56e0\u679c\u6001\u7684\u95ee\u9898\u3002\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u8ba1\u7b97\u529b\u5b66\u5efa\u7acb\u4e86\u540d\u4e3a\u6591\u56fe\u91cd\u6784\u673a\u5668<\/span>\uff08\u03f5-machine\uff09<\/span>\u7684\u6a21\u578b\uff0c\u5176\u4e2d\u56e0\u679c\u6001\u6240\u5bf9\u5e94\u7684\u5212\u5206\u6620\u5c04\u88ab\u8bb0\u4e3a<\/span>\u03f5<\/span>\u3002\u5b83\u53ef\u4ee5\u91cd\u6784\u6d4b\u91cf\u7ed3\u679c\u4e2d\u7684\u5e8f\u5217\uff0c\u53bb\u9664\u968f\u673a\u566a\u58f0\u540e\u8bc6\u522b\u5176\u4e2d\u7684\u56e0\u679c\u6001\u3002\u5b83\u7684\u5f62\u5f0f\u5316\u5b9a\u4e49\u53ef\u4ee5\u7528\u516c\u5f0f\u8868\u793a\u4e3a<\/span>M<\/span>=<\/span>(<\/span>S<\/span>,<\/span>T<\/span>)<\/span>\uff0c<\/span>S<\/span>\u4e3a\u56e0\u679c\u6001\u7684\u96c6\u5408\uff0c<\/span>T<\/span>\u4e3a\u56e0\u679c\u6001\u5230\u56e0\u679c\u6001\u8df3\u8f6c\u7684\u96c6\u5408\uff0c\u5b83\u7c7b\u4f3c\u4e8e\u4e00\u4e2a\u7c97\u7c92\u5316\u540e\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\u3002<\/span>T<\/span>\u53ef\u4ee5\u8868\u793a\u4e3a<\/span><\/sub>\uff0c\u5176\u4e2d<\/span> <\/sub><\/span>\u4e3a\u53ef\u6570\u96c6\u3002<\/span><\/sub><\/span>\u7684\u5b9a\u4e49\u4e3a\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/p>\n

    <\/section>\n

    <\/span><\/section>\n
    \u5176\u4e2d\uff1a <\/span>S<\/span>\u8868\u793a\u5f53\u524d\u56e0\u679c\u6001\u3002 <\/span>S<\/span>\u2032<\/span>\u8868\u793a\u4e0b\u4e00\u65f6\u523b\u56e0\u679c\u6001\u3002<\/span> <\/sub>\u4ee3\u8868\u672a\u6765\u5e8f\u5217\u7684\u7b2c\u4e00\u4e2a\u7b26\u53f7\uff0c\u6240\u4ee5\u56e0\u679c\u6001<\/span>S<\/span>\u2032<\/span>\u7684\u7b2c\u4e00\u4e2a\u7b26\u53f7\u90fd\u662f<\/span>s<\/span>\u3002 <\/span>s<\/span>\u662f\u4ece\u53ef\u6570\u96c6<\/span> <\/sub><\/span>\u4e2d\u53d6\u503c\u7684\u4e00\u4e2a\u7b26\u53f7\u3002 <\/span>S<\/span>i<\/span>\u548c<\/span>S<\/span>j<\/span><\/sub>\u5206\u522b\u8868\u793a\u7b2c<\/span>i<\/span>\u4e2a\u548c\u7b2c<\/span>j<\/span>\u4e2a\u56e0\u679c\u6001\uff0c\u5b83\u4eec\u662f\u5bf9\u5386\u53f2\u5e8f\u5217\u7684\u4e00\u79cd\u5212\u5206\u3002 <\/span><\/sub><\/span>\u8868\u793a\u5728\u5f53\u524d\u56e0\u679c\u6001\u4e3a<\/span>S<\/span>i<\/span><\/sub>\u7684\u6761\u4ef6\u4e0b\uff0c\u4e0b\u4e00\u4e2a\u56e0\u679c\u6001\u53d8\u4e3a<\/span>S<\/span>j<\/span><\/sub>\u4e14\u672a\u6765\u5e8f\u5217\u7b2c\u4e00\u4e2a\u7b26\u53f7\u4e3a<\/span>s<\/span>\u7684\u8f6c\u79fb\u6982\u7387\u3002\u8fd9\u4e2a\u516c\u5f0f\u53ef\u4ee5\u63cf\u8ff0\u6591\u56fe\u91cd\u6784\u673a\u5668\u4e2d\u56e0\u679c\u6001\u4e4b\u95f4\u7684\u8f6c\u79fb\u5173\u7cfb\u4ee5\u53ca\u4e0e\u8fc7\u7a0b\u8f93\u51fa\u7b26\u53f7\u7684\u5bf9\u5e94\u5173\u7cfb\uff0c\u4ece\u800c\u523b\u753b\u4e86\u8fc7\u7a0b\u7684\u52a8\u6001\u884c\u4e3a\u548c\u5185\u5728\u7ed3\u6784\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u6bcf\u4e2a<\/span>S<\/span>\u90fd\u5bf9\u5e94\u4e00\u4e2a<\/span>\u03f5<\/span>\u6620\u5c04\uff0c\u5b83\u548c<\/span>T<\/span>\u51fd\u6570\u4e00\u8d77\u7ec4\u6210\u4e00\u4e2a\u6709\u5e8f\u5bf9<\/span>{<\/span>\u03f5<\/span>,<\/span>T<\/span>}<\/span>\uff0c\u8fd9\u5c31\u662f\u201c\u6591\u56fe\u91cd\u6784\u673a\u5668\u201d<\/span>\uff08\u03f5-machine\uff09<\/span>\u3002\u540e\u6587\u201c\u6a21\u578b\u7684\u91cd\u6784\u201d\u4e00\u8282\u4e2d\u4f1a\u8be6\u7ec6\u4ecb\u7ecd\u5982\u4f55\u83b7\u5f97\u8fd9\u4e2a\u6591\u56fe\u91cd\u6784\u673a\u5668\uff0c\u4ee5\u53ca\u667a\u80fd\u4f53\u7684\u5185\u5728\u6a21\u578b\u4f1a\u5982\u4f55\u6839\u636e\u89c2\u6d4b\u5230\u7684\u65b0\u6570\u636e\uff0c\u52a8\u6001\u66f4\u65b0<\/span>\u03f5<\/span>\u6620\u5c04\u548c<\/span>T<\/span>\u51fd\u6570\u3002<\/span><\/section>\n

    <\/span><\/section>\n

    3.5 \u7edf\u8ba1\u590d\u6742\u5ea6<\/span><\/strong><\/span><\/h3>\n


    <\/span><\/h4>\n

    3.5.1 \u67ef\u6c0f\u590d\u6742\u5ea6\u7684\u95ee\u9898<\/span><\/strong><\/h4>\n

    <\/span><\/section>\n
    \u667a\u80fd\u4f53\u5728\u6784\u5efa\u548c\u4f18\u5316\u6591\u56fe\u91cd\u6784\u673a\u5668\u7684\u8fc7\u7a0b\u4e2d\uff0c\u7531\u4e8e\u8ba1\u7b97\u8d44\u6e90\u7684\u9650\u5236\uff0c\u4e0d\u80fd\u65e0\u9650\u5236\u5730\u589e\u52a0\u6a21\u578b\u7684\u5927\u5c0f\u3002\u56e0\u6b64\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u80fd\u591f\u91cf\u5316\u6a21\u578b\u590d\u6742\u5ea6\u7684\u6307\u6807\uff0c\u4ee5\u4fbf\u76d1\u63a7\u548c\u8c03\u6574\u6a21\u578b\u7684\u5927\u5c0f\uff0c\u786e\u4fdd\u6a21\u578b\u80fd\u5339\u914d\u5df2\u6709\u7684\u8ba1\u7b97\u8d44\u6e90\u3002\u67ef\u5f0f\u590d\u6742\u5ea6<\/span>K<\/span>(<\/span>x<\/span>)<\/span>\uff0c\u4e5f\u5c31\u662f\u5728\u901a\u7528\u786e\u5b9a\u6027\u56fe\u7075\u673a<\/span>\uff08Universal Turing Machine\uff0c\u7b80\u79f0UTM\uff09<\/span>\u4e0a\u8fd0\u884c\u65f6\u751f\u6210\u5b57\u7b26\u4e32<\/span>x<\/span>\u7684\u6700\u5c0f\u7a0b\u5e8f\u957f\u5ea6\uff0c\u662f\u4eba\u4eec\u5e38\u7528\u7684\u4e00\u4e2a\u590d\u6742\u6027\u5ea6\u91cf\u6307\u6807\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7136\u800c\uff0c\u67ef\u5f0f\u590d\u6742\u5ea6\u5b58\u5728\u4e24\u4e2a\u660e\u663e\u7684\u95ee\u9898\uff0c\u7b2c\u4e00\u4e2a\u95ee\u9898\u662f\u5b83\u7684\u4e0d\u53ef\u8ba1\u7b97\u6027\uff0c\u67ef\u6c0f\u590d\u6742\u5ea6\u4ec5\u4ec5\u662f\u4e00\u4e2a\u7406\u60f3\u5316\u7684\u6982\u5ff5\uff1b\u7b2c\u4e8c\u4e2a\u95ee\u9898\u662f\u5b83\u53ef\u80fd\u65e0\u6cd5\u5ea6\u91cf\u7a0b\u5e8f\u7684\u7ed3\u6784\u548c\u52a8\u6001\u7279\u6027\u3002\u56e0\u4e3a\u67ef\u5f0f\u590d\u6742\u5ea6<\/span>K<\/span>(<\/span>x<\/span>)<\/span>\u9700\u8981\u8003\u8651\u5b57\u7b26\u4e32\u4e2d\u7684\u6240\u6709\u6bd4\u7279\uff0c\u8fd9\u5c31\u5305\u62ec\u968f\u673a\u751f\u6210\u7684\u6bd4\u7279\u3002\u56e0\u6b64\uff0c\u67ef\u6c0f\u590d\u6742\u5ea6\u4f1a\u5728\u968f\u673a\u751f\u6210\u7684\u6bd4\u7279\u4e0a\u8ba1\u7b97\u51fa\u8f83\u5927\u7684\u590d\u6742\u6027\uff0c\u800c\u8fd9\u4e0e\u6211\u4eec\u7684\u76f4\u89c9\u4e0d\u7b26\uff1a\u590d\u6742\u6027\u4e0d\u80fd\u7b49\u4ef7\u4e8e\u968f\u673a\u6027\u3002<\/span><\/section>\n

    <\/span><\/section>\n

    3.5.2 \u7edf\u8ba1\u590d\u6742\u5ea6<\/span><\/strong><\/h4>\n

    <\/span><\/section>\n
    \u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e24\u4e2a\u660e\u663e\u95ee\u9898\uff0c\u8ba1\u7b97\u529b\u5b66\u63d0\u51fa\u4e86\u7edf\u8ba1\u590d\u6742\u5ea6<\/span>C<\/span>\u03bc<\/span><\/sub>(<\/span>x<\/span>)<\/span>\u7684\u6982\u5ff5\uff0c\u7528\u6765\u91cf\u5316\u6a21\u578b\u7684\u590d\u6742\u6027\uff0c\u5b83\u53ef\u4ee5\u53cd\u6620<\/span>x<\/span>\u7684\u7ed3\u6784\u548c\u52a8\u6001\u7279\u6027\uff0c\u4ee5\u53ca\u80fd\u591f\u8ba1\u7b97\u51fa\u6709\u6548\u5efa\u6a21\u6240\u9700\u7684\u8ba1\u7b97\u8d44\u6e90\u3002\u5b83\u7684\u516c\u5f0f\u4e3a\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/p>\n

    <\/section>\n

    <\/span><\/section>\n
    \u8fd9\u91cc\uff0c <\/span>C<\/span>\u03bc<\/span><\/sub>(<\/span>x<\/span>)<\/span>\u662f\u7edf\u8ba1\u590d\u6742\u5ea6[4]\uff0c\u8868\u793a\u65f6\u95f4\u5e8f\u5217<\/span>x<\/span>\u7684\u590d\u6742\u6027\u5ea6\u91cf\u3002\u5b83\u53cd\u6620\u4e86\u5728\u7ed9\u5b9a\u7cbe\u5ea6<\/span>\u03bc<\/span>\u4e0b\uff0c\u80fd\u591f\u751f\u6210\u8be5\u5e8f\u5217\u7684\u6700\u5c0f\u4f2f\u52aa\u5229\u56fe\u7075\u673a\u7684\u7a0b\u5e8f\u957f\u5ea6\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u8fd9\u91cc\uff0c\u4f2f\u52aa\u5229\u56fe\u7075\u673a<\/span>\uff08Bernoulli-Turing machine\uff0c\u7b80\u79f0BTM\uff09<\/span>\u662f\u4e00\u79cd\u6982\u7387\u6027\u56fe\u7075\u673a\uff0c\u662f\u786e\u5b9a\u6027\u56fe\u7075\u673a\u7684\u4e00\u79cd\u6269\u5c55\u3002\u5b83\u901a\u8fc7\u5f15\u5165\u968f\u673a\u6570\u53d1\u751f\u5668\uff0c\u53ef\u4ee5\u751f\u6210\u79bb\u6563\u7684\u968f\u673a\u5e8f\u5217\u3002\u4f2f\u52aa\u5229\u56fe\u7075\u673a\u5305\u542b\u8f93\u5165\u7eb8\u5e26\u3001\u8f93\u51fa\u7eb8\u5e26\u3001\u6709\u9650\u72b6\u6001\u63a7\u5236\u5355\u5143\u548c\u5de5\u4f5c\u7eb8\u5e26\u3002\u5728\u8fd0\u884c\u8fc7\u7a0b\u4e2d\uff0c\u4f2f\u52aa\u5229\u56fe\u7075\u673a\u6309\u7167\u5e38\u89c4\u56fe\u7075\u673a\u7684\u65b9\u5f0f\u8bfb\u53d6\u7eb8\u5e26\u4e0a\u7684\u7b26\u53f7\u548c\u81ea\u8eab\u7684\u5f53\u524d\u72b6\u6001\uff0c\u5e76\u4f9d\u636e\u5185\u7f6e\u7684\u89c4\u5219\u8868\u8fdb\u884c\u64cd\u4f5c\u3002\u4e0e\u666e\u901a\u56fe\u7075\u673a\u4e0d\u540c\u7684\u662f\uff0c\u5176\u89c4\u5219\u8868\u4e2d\u6709\u4e00\u4e9b\u53ef\u968f\u673a\u6267\u884c\u7684\u89c4\u5219\uff0c\u5b83\u4f1a\u6839\u636e\u968f\u673a\u6570\u53d1\u751f\u5668\u7684\u91c7\u6837\u7ed3\u679c\u6765\u51b3\u5b9a\u5177\u4f53\u7684\u6267\u884c\u8def\u5f84\u3002\u4f8b\u5982\uff0c\u5728\u67d0\u4e2a\u72b6\u6001\u4e0b\uff0c\u56fe\u7075\u673a\u53ef\u80fd\u6709\u4e24\u79cd\u53ef\u9009\u7684\u64cd\u4f5c\uff0c\u666e\u901a\u56fe\u7075\u673a\u6839\u636e\u786e\u5b9a\u7684\u89c4\u5219\u9009\u62e9\u5176\u4e2d\u4e00\u79cd\uff0c\u800c\u4f2f\u52aa\u5229\u56fe\u7075\u673a\u5219\u901a\u8fc7\u968f\u673a\u6e90<\/span>\uff08\u5373\u968f\u673a\u6570\u53d1\u751f\u5668\uff09<\/span>\u4ee5\u4e00\u5b9a\u7684\u6982\u7387\u6765\u6267\u884c\u5176\u4e2d\u7684\u67d0\u4e00\u79cd\u64cd\u4f5c\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    M<\/span>min<\/span><\/sub>(<\/span>x<\/span>\u2223<\/span>BTM<\/span>)<\/span>\u4ee3\u8868\u5728\u80fd\u591f\u6355\u6349\u6570\u636e<\/span>x<\/span>\u6761\u4ef6\u4e0b\u7684\u6240\u6709\u4f2f\u52aa\u5229\u56fe\u7075\u673a\u4e2d\u7684\u6700\u5c0f\u7684\u6a21\u578b[16]\u3002\u8fd9\u4e2a\u6a21\u578b\u662f\u80fd\u591f\u5728\u5141\u8bb8\u8bef\u5dee\u4e3a<\/span>\u03bc<\/span>\u7684\u6761\u4ef6\u4e0b\u6709\u6548\u9884\u6d4b<\/span>x<\/span>\u7684\u6700\u7b80\u5355\u5f62\u5f0f\u3002<\/span>\u2016<\/span>\u22c5<\/span>\u2016<\/span>\u8fd9\u4e2a\u7b26\u53f7\u8868\u793a\u5bf9\u6a21\u578b\u590d\u6742\u5ea6\u7684\u91cf\u5316\uff0c\u4f8b\u5982\u56fe\u7075\u673a\u7684\u6307\u4ee4\u8868\u957f\u5ea6\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7531\u4e8e\u5185\u90e8\u6a21\u578b<\/span>\uff08\u03f5-machine\uff09<\/span>\u4f5c\u4e3a\u4e00\u79cd\u4f2f\u52aa\u5229\u56fe\u7075\u673a\uff0c\u672c\u8eab\u4e5f\u662f\u7528\u5b57\u7b26\u4e32<\/span>\uff08\u56e0\u679c\u6001\uff09<\/span>\u6765\u63cf\u8ff0\u7684\uff0c\u6240\u4ee5\u53ef\u4ee5\u7528\u957f\u5ea6\u3001\u9999\u519c\u71b5\u7b49\u6307\u6807\u6765\u5ea6\u91cf\u5185\u90e8\u6a21\u578b\u7684\u590d\u6742\u5ea6\u3002\u5f53\u6211\u4eec\u4f7f\u7528\u9999\u519c\u71b5\u6765\u523b\u753b\u5185\u90e8\u6a21\u578b\u7684\u590d\u6742\u5ea6\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u7ed9\u51fa\u5bf9\u4e8e\u89c2\u6d4b\u5e8f\u5217\u6765\u8bf4\u4e00\u4e2a\u7b49\u4ef7\u7684\u53ef\u8ba1\u7b97\u7684\u5b9a\u4e49[4]\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/p>\n

    <\/section>\n

    <\/span><\/section>\n
    \u5176\u4e2d<\/span>S<\/span>\u4e3a\u89c2\u6d4b\u6570\u636e<\/span>x<\/span>\u7684\u56e0\u679c\u6001\u96c6\u5408\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7edf\u8ba1\u590d\u6742\u5ea6\u7684\u4e00\u4e2a\u7279\u5f81\u662f\uff0c\u5bf9\u4e8e\u5b8c\u5168\u968f\u673a\u5bf9\u8c61\uff0c\u6709<\/span>C<\/span>\u03bc<\/span><\/sub>(<\/span>x<\/span>)<\/span>=<\/span>0<\/span>\uff0c\u5982\u629b\u786c\u5e01\u4ea7\u751f\u7684\u5e8f\u5217\uff1b\u4ee5\u53ca\u5bf9\u4e8e\u7b80\u5355\u7684\u5468\u671f\u6027\u8fc7\u7a0b\uff0c\u5982<\/span>x<\/span>=<\/span>00000000<\/span>\u2026<\/span>0<\/span>\uff0c\u90fd\u4f1a\u6709<\/span>C<\/span>\u03bc<\/span><\/sub>(<\/span>x<\/span>)<\/span>=<\/span>0<\/span>\u3002\u56e0\u6b64\uff0c\u7edf\u8ba1\u590d\u6742\u5ea6\u7684\u503c\u5bf9\u4e8e<\/span>\uff08\u7b80\u5355\u7684\uff09<\/span>\u5468\u671f\u6027\u8fc7\u7a0b\u548c\u5b8c\u5168\u968f\u673a\u8fc7\u7a0b\u90fd\u5f88\u5c0f\u3002\u6240\u4ee5\uff0c\u4e0e\u67ef\u6c0f\u590d\u6742\u5ea6\u76f8\u6bd4\uff0c\u7edf\u8ba1\u590d\u6742\u5ea6\u8fd9\u79cd\u5ea6\u91cf<\/span>C<\/span>\u03bc<\/span><\/sub>(<\/span>x<\/span>)<\/span>\uff0c\u76f8\u6bd4\u4e8e\u67ef\u6c0f\u590d\u6742\u5ea6\u6765\u8bf4\uff0c\u5254\u9664\u4e86\u901a\u7528\u56fe\u7075\u673a\u5728\u6a21\u62df\u968f\u673a\u6bd4\u7279\u65f6\u6240\u82b1\u8d39\u7684\u8ba1\u7b97\u52aa\u529b\u3002<\/span><\/section>\n

    <\/span><\/section>\n

    3.5.3 \u4e24\u79cd\u590d\u6742\u6027\u7684\u5bf9\u6bd4<\/span><\/strong><\/h4>\n

    <\/span><\/section>\n
    \u4e0b\u56fe\u5c55\u793a\u4e86\u67ef\u5f0f\u590d\u6742\u5ea6\u548c\u7edf\u8ba1\u590d\u6742\u5ea6\u968f\u7740\u5e8f\u5217\u4ece\u7b80\u5355\u5468\u671f\u6027\u53d8\u4e3a\u5b8c\u5168\u968f\u673a\u7684\u8fc7\u7a0b\u4e2d\u4e8c\u8005\u7684\u5dee\u5f02\u3002\u5982\u56fe(a)\u6240\u793a\uff0c\u67ef\u5f0f\u590d\u6742\u5ea6\u4f1a\u968f\u7740\u5e8f\u5217\u968f\u673a\u6027\u7684\u589e\u52a0\u800c\u5355\u8c03\u9012\u589e\u3002\u76f8\u53cd\uff0c\u7edf\u8ba1\u590d\u6742\u5ea6\u5728\u5468\u671f\u548c\u968f\u673a\u4e24\u4e2a\u6781\u7aef\u70b9\u4e0a\u5747\u4e3a\u96f6\uff0c\u5e76\u5728\u4e2d\u95f4\u8fbe\u5230\u6700\u5927\u503c<\/span>\uff08\u89c1\u56fe(b)\uff09<\/span>\u3002\u8fd9\u53cd\u6620\u51fa\u5982\u4e0b\u7684\u89c2\u70b9\uff1a\u968f\u673a\u6027\u5728\u7edf\u8ba1\u4e0a\u662f\u7b80\u5355\u7684\uff0c\u4e00\u4e2a\u5b8c\u5168\u968f\u673a\u7684\u8fc7\u7a0b\u5177\u6709\u96f6\u7edf\u8ba1\u590d\u6742\u5ea6\uff1b\u5468\u671f\u6027\u5728\u7edf\u8ba1\u4e0a\u4e5f\u662f\u7b80\u5355\u7684\uff0c\u4e00\u4e2a\u5b8c\u5168\u662f\u5468\u671f\u6027\u7684\u8fc7\u7a0b\u5177\u6709\u8f83\u4f4e\u7684\u7edf\u8ba1\u590d\u6742\u5ea6\u3002\u590d\u6742\u8fc7\u7a0b\u662f\u5728\u8fd9\u4e24\u4e2a\u6781\u7aef\u4e4b\u95f4\u4ea7\u751f\uff0c\u5e76\u4e14\u662f\u53ef\u9884\u6d4b\u673a\u5236\u548c\u968f\u673a\u673a\u5236\u7684\u6df7\u5408\uff0c\u6709\u4e2d\u7b49\u7a0b\u5ea6\u968f\u673a\u6027\u7684\u6570\u636e\u5177\u6709\u6700\u5927\u7684\u7edf\u8ba1\u590d\u6742\u5ea6\u3002<\/span><\/section>\n
    <\/section>\n

    <\/p>\n


    <\/span><\/h3>\n

    3.6 \u9999\u519c\u71b5\u7387\u4e0e\u590d\u6742\u5ea6<\/span><\/strong><\/span><\/h3>\n

    <\/span><\/section>\n
    \u4e0a\u6587\u4e2d\u63d0\u5230\u7684\u4e00\u4e2a\u5e8f\u5217\u7684\u968f\u673a\u6027\u53ef\u4ee5\u7528\u9999\u519c\u71b5\u7387<\/span>\uff08Shannon Entropy Rate\uff09<\/span>\u6765\u5ea6\u91cf\uff0c\u9999\u519c\u71b5\u7387\u662f\u4fe1\u606f\u8bba\u4e2d\u7684\u4e00\u4e2a\u6982\u5ff5\uff0c\u5b83\u662f\u9999\u519c\u71b5\u7684\u6269\u5c55\uff0c\u4e3b\u8981\u7528\u4e8e\u63cf\u8ff0\u65f6\u95f4\u5e8f\u5217\u5728\u5355\u4f4d\u65f6\u95f4\u4e0a\u7684\u5e73\u5747\u4fe1\u606f\u91cf\u3002\u5728\u8fd9\u91cc\uff0c\u9999\u519c\u71b5\u7387\u53ef\u4ee5\u5b9a\u4e49\u4e3a\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/p>\n

    <\/section>\n

    <\/span><\/section>\n
    \u5176\u4e2d\uff0c<\/span>s<\/span>L<\/span><\/sup>\u662f\u73af\u5883\u4fe1\u606f\u751f\u6210\u7684\u79bb\u6563\u7b26\u53f7\u5e8f\u5217\uff0c<\/span>L<\/span>\u4e3a\u5e8f\u5217\u7684\u957f\u5ea6\uff0c<\/span>P<\/span>(<\/span>s<\/span>L<\/span><\/sup>)<\/span>\u662f\u5e8f\u5217<\/span>s<\/span>L<\/span><\/sup>\u7684\u8fb9\u9645\u5206\u5e03\uff0c<\/span>H<\/span>\u662f\u9999\u519c\u71b5\u3002\u5728\u5efa\u6a21\u6846\u67b6\u4e2d\uff0c<\/span>h<\/span>\u53ef\u4ee5\u89e3\u91ca\u4e3a\u667a\u80fd\u4f53\u5728\u9884\u6d4b\u5e8f\u5217<\/span>s<\/span>L<\/span><\/sup>\u7684\u540e\u7eed\u7b26\u53f7\u65f6\u7684\u8bef\u5dee\u7387\u3002\u7531\u8be5\u516c\u5f0f\u53ef\u89c1\uff0c\u71b5\u7387\u4e5f\u5c31\u662f\u81ea\u4fe1\u606f\u7684\u5e73\u5747\u503c\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u9999\u519c\u71b5\u7387\u662f\u5f52\u4e00\u5316\u7684\u5ea6\u91cf\u4fe1\u606f\u4e0d\u786e\u5b9a\u6027\u7a0b\u5ea6\u7684\u6307\u6807\uff0c\u4fe1\u606f\u7684\u4e0d\u786e\u5b9a\u6027\u8d8a\u9ad8\uff0c\u9999\u519c\u71b5\u7387\u8d8a\u5927\u3002\u5bf9\u4e8e\u7b80\u5355\u7684\u5468\u671f\u6027\u8fc7\u7a0b\uff0c\u5982<\/span>x<\/span>=<\/span>00000000<\/span>\u2026<\/span>0<\/span>\uff0c\u9999\u519c\u71b5\u7387\u4e3a0\uff0c\u5bf9\u4e8e\u5b8c\u5168\u968f\u673a\u7684\u5bf9\u8c61\uff0c\u5982\u629b\u786c\u5e01\u4ea7\u751f\u7684\u5e8f\u5217\uff0c\u9999\u519c\u71b5\u7387\u4e3a1\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u9999\u519c\u71b5\u7387\u4e0e\u67ef\u5f0f\u590d\u6742\u5ea6<\/span>K<\/span>(<\/span>x<\/span>)<\/span>\u7684\u5173\u7cfb\u4e3a\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/p>\n

    <\/section>\n

    <\/span><\/section>\n
    \u4e0a\u6587\u4e2d\u6211\u4eec\u4ecb\u7ecd\u4e86\u67ef\u5f0f\u590d\u6742\u5ea6\u3001\u7edf\u8ba1\u590d\u6742\u5ea6\u548c\u9999\u519c\u71b5\u7387\u8fd9\u4e09\u4e2a\u4e0e\u590d\u6742\u6027\u76f8\u5173\u7684\u6307\u6807\uff0c\u5176\u5b9e\u8fd9\u4e09\u8005\u4e4b\u95f4\u5b58\u5728\u4e00\u4e2a\u8fd1\u4f3c\u5173\u7cfb\uff0c\u53ef\u4ee5\u7528\u516c\u5f0f\u8868\u793a\u4e3a\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/p>\n

    <\/section>\n

    <\/span><\/section>\n
    \u5982\u679c\u5728\u5df2\u786e\u5b9a\u63cf\u8ff0\u8bed\u8a00<\/span>\uff08\u7a0b\u5e8f\uff09<\/span>\u7684\u60c5\u51b5\u4e0b\uff0c\u67ef\u5f0f\u590d\u6742\u5ea6<\/span>K<\/span>(<\/span>s<\/span>L<\/span><\/sup>)<\/span>\u53ef\u4ee5\u7406\u89e3\u4e3a\u63cf\u8ff0<\/span>s<\/span>L<\/span><\/sup>\u6240\u7528\u7684\u603b\u4fe1\u606f\u91cf\u3002<\/span>h<\/span>L<\/span>\u4e3a\u5141\u8bb8\u635f\u5931\u7684\u4fe1\u606f\u91cf\u3002\u7edf\u8ba1\u590d\u6742\u5ea6<\/span>C<\/span>\u03bc<\/span><\/sub>(<\/span>s<\/span>L<\/span><\/sup>)<\/span>\u53ef\u4ee5\u7406\u89e3\u4e3a\u5141\u8bb8\u5b58\u5728\u8bef\u5dee\u7387<\/span>h<\/span>\u7684\u60c5\u51b5\u4e0b\uff0c\u63cf\u8ff0<\/span>s<\/span>L<\/span><\/sup>\u6240\u7528\u7684\u6700\u5c11\u4fe1\u606f\u91cf\u3002<\/span><\/section>\n


    <\/span><\/h3>\n

    3.7 \u6a21\u578b\u91cd\u6784<\/span><\/strong><\/span><\/h3>\n

    <\/span><\/section>\n
    \u7531\u4e8e\u667a\u80fd\u4f53\u7684\u8ba1\u7b97\u8d44\u6e90\u662f\u6709\u9650\u7684\uff0c\u5f53\u6d4b\u91cf\u7ed3\u679c\u4e2d\u7684\u6570\u636e\u91cf\u8d85\u8fc7\u6a21\u578b\u80fd\u591f\u5904\u7406\u7684\u6781\u9650\u65f6\uff0c\u6211\u4eec\u5c31\u9700\u8981\u6784\u9020\u6a21\u578b\uff0c\u4ee5\u66f4\u7b80\u6d01\u5730\u63cf\u8ff0\u6570\u636e\u3002\u8fd9\u6837\u505a\u7684\u76ee\u7684\u662f\u5728\u4fdd\u6301\u8ba1\u7b97\u8d44\u6e90\u4e0d\u53d8\u7684\u60c5\u51b5\u4e0b\uff0c\u786e\u4fdd\u667a\u80fd\u4f53\u4ecd\u7136\u80fd\u591f\u5bf9\u5916\u754c\u8fdb\u884c\u6709\u6548\u7684\u9884\u6d4b\u3002\u8fd9\u4e00\u8fc7\u7a0b\u53ef\u4ee5\u53cd\u590d\u8fed\u4ee3\u5730\u8fdb\u884c\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u56e0\u679c\u6001\u5e8f\u5217\u4e5f\u53ef\u4ee5\u88ab\u770b\u505a\u662f\u539f\u59cb\u72b6\u6001\u5e8f\u5217\uff0c\u56e0\u6b64\u667a\u80fd\u4f53\u53ef\u4ee5\u5728\u56e0\u679c\u6001\u57fa\u7840\u4e0a\u518d\u6b21\u91cd\u6784\u751f\u6210\u8be5\u56e0\u679c\u6001\u7684\u6a21\u578b\u3002\u4e8e\u662f\uff0c\u8fd9\u4fbf\u5f62\u6210\u4e86\u4e00\u7cfb\u5217\u4e0d\u65ad\u5347\u7ea7\u7684\u5c42\u7ea7\u5316\u7684\u91cd\u6784\u8fc7\u7a0b\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u91cd\u6784\u7684\u65b9\u6cd5\u4e3b\u8981\u662f\u901a\u8fc7\u5bfb\u627e\u539f\u6709\u6a21\u578b\u4e2d\u76f8\u4f3c\u7684\u72b6\u6001\u7ec4\uff0c\u4ece\u800c\u5f62\u6210\u56e0\u679c\u6001\uff1b\u7136\u540e\uff0c\u5728\u5df2\u7ecf\u8bc6\u522b\u51fa\u7684\u56e0\u679c\u6001\u4e2d\uff0c\u6211\u4eec\u8fdb\u4e00\u6b65\u62bd\u8c61\u51fa\u66f4\u9ad8\u5c42\u7ea7\u7684\u56e0\u679c\u6001\u7ec4\u3002\u8fd9\u6837\uff0c\u968f\u7740\u6570\u636e\u91cf\u7684\u589e\u5927\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4e0d\u65ad\u5730\u5728\u4e0a\u4e00\u5c42\u7ea7\u62bd\u8c61\u51fa\u66f4\u9ad8\u7684\u5c42\u7ea7\uff0c\u4ece\u800c\u5728\u8ba1\u7b97\u8d44\u6e90\u6709\u9650\u7684\u60c5\u51b5\u4e0b\uff0c\u4ecd\u7136\u80fd\u591f\u5e94\u5bf9\u66f4\u5927\u91cf\u7684\u6570\u636e\u3002\u8b6c\u5982\uff0c\u5f53\u667a\u80fd\u4f53\u89c2\u6d4b\u5230\u201c121212\u201d\u65f6\uff0c\u4f1a\u628a\u201c12\u201d\u770b\u6210\u662f\u4e00\u4e2a\u6a21\u5757\uff0c\u7528\u4e00\u4e2a\u5b57\u7b26\u201cA\u201d\u6765\u8868\u793a\uff0c\u4e8e\u662f\u539f\u672c\u7684\u5fae\u89c2\u6001\u5b57\u7b26\u4e32\u5c31\u53ef\u4ee5\u88ab\u91cd\u6784\u4e3a\u201cAAA\u201d\u8fd9\u6837\u7684\u5b8f\u89c2\u6001\u5b57\u7b26\u4e32\uff0c\u590d\u6742\u5ea6\u5c31\u964d\u4f4e\u4e86\u3002\u800c\u5f53\u6a21\u578b\u8fdb\u4e00\u6b65\u89c2\u6d4b\u5230\u66f4\u957f\u7684\u5b57\u7b26\u4e32\u662f\u201c12121231212123\u201d\u65f6\uff0c\u5b83\u4fbf\u9700\u8981\u8df3\u51fa\u539f\u672c\u7684\u5206\u7ec4\uff0c\u800c\u628a\u201c1212123\u201d\u770b\u6210\u662f\u4e00\u4e2a\u65b0\u7684\u6a21\u5757\uff0c\u53ef\u4ee5\u7528\u4e00\u4e2a\u5b57\u7b26\u201cB\u201d\u6765\u8868\u793a\uff0c\u4e8e\u662f\u5185\u90e8\u6a21\u578b\u53ef\u4ee5\u8fdb\u4e00\u6b65\u7528\u201cBB\u201d\u8fd9\u6837\u7684\u65b0\u5b57\u7b26\u4e32\u6765\u8868\u793a\u540c\u4e00\u4e2a\u89c2\u6d4b\u5bf9\u8c61\u3002\u8fd9\u4fbf\u662f\u4e00\u6b21\u6a21\u578b\u91cd\u6784\u4e0d\u65ad\u5347\u7ea7\u7684\u8fc7\u7a0b\u3002\u4e0b\u8868\u4e2d\u5217\u4e3e\u4e86\u4e00\u79cd\u6a21\u578b\u91cd\u6784\u7684\u53ef\u80fd\u9014\u5f84\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/span><\/section>\n
    \u4e0a\u8868\u4e3a\u56e0\u679c\u65f6\u95f4\u5e8f\u5217\u5efa\u6a21\u5c42\u7ea7\uff0c\u5c55\u793a\u4e86\u53ef\u80fd\u7684\u524d\u56db\u4e2a\u5c42\u7ea7\uff0c\u6bcf\u4e2a\u5c42\u7ea7\u6839\u636e\u5176\u6a21\u578b\u7c7b\u522b\u5b9a\u4e49\u3002\u4f46\u8fd9\u4e2a\u8fc7\u7a0b\u4ec5\u4ec5\u662f\u4e00\u4e2a\u793a\u4f8b\uff0c\u53ef\u4ee5\u4e0d\u6b62\u56db\u4e2a\u5c42\u7ea7\u3002\u6a21\u578b\u672c\u8eab\u7531\u72b6\u6001<\/span>\uff08\u5706\u5708\u6216\u65b9\u5757\uff09<\/span>\u548c\u8f6c\u79fb<\/span>\uff08\u6807\u8bb0\u7bad\u5934\uff09<\/span>\u7ec4\u6210\uff0c\u6bcf\u4e2a\u6a21\u578b\u90fd\u6709\u4e00\u4e2a\u72ec\u7279\u7684\u8d77\u59cb\u72b6\u6001\uff0c\u7531\u4e00\u4e2a\u53cc\u91cd\u5706\u5708\u8868\u793a\u3002\u6570\u636e\u6d41\u672c\u8eab\u662f\u6700\u4f4e\u5c42\u7ea7\uff0c\u901a\u8fc7\u5c06\u5e8f\u5217\u6d4b\u91cf\u5206\u7ec4\u4e3a\u91cd\u590d\u5b50\u5e8f\u5217\uff0c\u4ece\u6570\u636e\u6d41\u4e2d\u6784\u5efa\u51fa\u6df1\u5ea6\u4e3a<\/span>D<\/span>\u7684\u6811\u3002\u4e0b\u4e00\u4e2a\u5c42\u7ea7\u7684\u6a21\u578b\uff0c\u5373\u5177\u6709\u72b6\u6001\u548c\u8f6c\u79fb\u7684\u6709\u9650\u81ea\u52a8\u673a<\/span>\uff08Finite Automaton\uff0c\u7b80\u79f0FA\uff09<\/span>\uff0c\u53ef\u4ee5\u901a\u8fc7\u5c06\u6811\u8282\u70b9\u5206\u7ec4\u4ece\u6811\u4e2d\u91cd\u6784\u3002\u56fe\u4e2d\u6240\u793a\u7684\u6700\u540e\u4e00\u4e2a\u5c42\u7ea7\uff0c\u5b57\u7b26\u4e32\u751f\u6210\u673a\u5668<\/span>\uff08Pattern Matching\uff0c\u7b80\u79f0PM\uff09<\/span>\uff0c\u53ef\u4ee5\u901a\u8fc7\u5c06\u6709\u9650\u72b6\u6001\u81ea\u52a8\u673a\u7684\u72b6\u6001\u8fdb\u884c\u5206\u7ec4\u5e76\u63a8\u65ad\u51fa\u64cd\u63a7\u5bc4\u5b58\u5668\u4e2d\u5b57\u7b26\u4e32\u7684\u751f\u6210\u89c4\u5219\u6765\u6784\u5efa\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u8003\u8651\u4e00\u4e2a\u7531<\/span>m<\/span>\u4e2a\u6d4b\u91cf\u7ed3\u679c\u6784\u6210\u7684\u6570\u636e\u6d41<\/span>s<\/span>\uff0c\u5982\u679c\u5b83\u662f\u5468\u671f\u6027\u7684\uff0c\u90a3\u4e48\u7b2c0\u7ea7<\/span>\uff08Level 0\uff09<\/span>\uff0c\u5373\u6d4b\u91cf\u7ed3\u679c\u672c\u8eab\uff0c\u5b83\u7684\u8868\u793a\u65b9\u6cd5\u4f9d\u8d56\u4e8e<\/span>m<\/span>\u3002\u5728\u6781\u9650<\/span>m<\/span>\u2192<\/span>\u221e<\/span>\u60c5\u51b5\u4e0b\uff0c\u7b2c0\u7ea7\u4f1a\u4ea7\u751f\u4e00\u4e2a\u590d\u6742\u5ea6\u65e0\u7a77\u5927\u7684\u8868\u793a\u3002\u5f53\u7136\uff0c\u7b2c0\u7ea7\u662f\u6700\u51c6\u786e\u7684\u6570\u636e\u6a21\u578b\uff0c\u5c3d\u7ba1\u5b83\u51e0\u4e4e\u6ca1\u6709\u4efb\u4f55\u5e2e\u52a9\uff0c\u51e0\u4e4e\u4e0d\u503c\u5f97\u88ab\u79f0\u4e3a\u201c\u6a21\u578b\u201d\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u4e00\u4e2a\u6df1\u5ea6\u4e3a<\/span>D<\/span>\u7684\u6811\u5c06\u7ed9\u51fa\u4e00\u4e2a\u6709\u9650\u8868\u793a\uff0c\u5373\u4f7f\u6570\u636e\u6d41\u7684\u957f\u5ea6\u662f\u65e0\u9650\u7684\uff0c\u53ea\u8981\u6570\u636e\u6d41\u5177\u6709\u5c0f\u4e8e\u7b49\u4e8e<\/span>D<\/span>\u7684\u5468\u671f\u3002\u8fd9\u4e2a\u6811\u6709\u957f\u5ea6\u4e3a<\/span>D<\/span>\u7684\u8def\u5f84\uff0c\u7531\u6570\u636e\u6d41\u7684\u5468\u671f\u7ed9\u51fa\u3002\u8fd9\u4e9b\u8def\u5f84\u4e2d\u7684\u6bcf\u4e00\u4e2a\u90fd\u5bf9\u5e94\u4e8e<\/span>s<\/span>\u4e2d\u91cd\u590d\u6a21\u5f0f\u7684\u4e00\u4e2a\u4e0d\u540c\u9636\u6bb5\u3002\u5982\u679c<\/span>s<\/span>\u662f\u975e\u5468\u671f\u6027\u7684\uff0c\u90a3\u4e48\u6811\u6a21\u578b\u7c7b\u5c06\u4e0d\u518d\u662f\u6709\u9650\u7684\uff0c\u5e76\u4e14\u4e0e<\/span>m<\/span>\u65e0\u5173\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5982\u679c\u6570\u636e\u6d41\u5177\u6709\u6b63\u71b5\u7387\uff08<\/span>\uff1e<\/span>h<\/span>\uff1e<\/span>0<\/span>\uff09\uff0c\u90a3\u4e48\u6811\u7684\u5927\u5c0f\u5c06\u5448\u6307\u6570\u589e\u957f\uff0c<\/span>\u2248<\/span>\u2016<\/span> <\/sub><\/span>\u2016<\/span>D<\/span><\/sup><\/span>h<\/span><\/sup><\/span> \uff0c\u56e0\u4e3a<\/span>D<\/span>\u7684\u589e\u52a0\u89e3\u91ca\u4e86<\/span>s<\/span> \u4e2d\u957f\u5ea6<\/span>D<\/span>\u4e0d\u65ad\u589e\u52a0\u7684\u5b50\u5e8f\u5217\u3002\u7c97\u7565\u5730\u8bf4\uff0c\u5982\u679c\u6570\u636e\u6d41\u5177\u6709\u968f\u65f6\u95f4\u8870\u51cf\u5f97\u8db3\u591f\u5feb\u7684\u76f8\u5173\u6027\uff0c\u5219\u4e0b\u4e00\u7ea7<\/span>\uff08\u968f\u673a\uff09<\/span>\u6709\u9650\u81ea\u52a8\u673a\u5c06\u7ed9\u51fa\u6709\u9650\u8868\u793a\u3002\u72b6\u6001\u6570<\/span>\u2016<\/span>V<\/span>\u2016<\/span>\u8868\u793a\u6570\u636e\u6d41\u4e2d\u7684\u5185\u5b58\u91cf\uff0c\u56e0\u6b64\u8868\u793a<\/span>s<\/span>\u4e2d\u6d4b\u91cf\u503c\u4e4b\u95f4\u5b58\u5728\u76f8\u5173\u6027\u7684\u5178\u578b\u65f6\u95f4\u957f\u5ea6\u3002\u4f46\u4e5f\u6709\u53ef\u80fd\u7b2c 2 \u7ea7\u4e0d\u63d0\u4f9b\u6709\u9650\u8868\u793a\u3002\u90a3\u4e48\u5c31\u9700\u8981\u53e6\u4e00\u4e2a\u7ea7\u522b<\/span>\uff08\u7b2c 3 \u7ea7\uff09<\/span>\u3002<\/span><\/section>\n

    <\/span><\/section>\n

    3.8 \u6a21\u578b\u91cd\u6784\u7b97\u6cd5<\/span><\/strong><\/span><\/h3>\n
    <\/section>\n
    \u4e0a\u9762\u4ecb\u7ecd\u4e86\u6591\u56fe\u91cd\u6784\u673a\u5668\uff0c\u662f\u667a\u80fd\u4f53\u8bc6\u522b\u56e0\u679c\u6001\u7684\u4e00\u79cd\u65b9\u5f0f\u3002\u82e5\u7ed3\u5408\u6a21\u578b\u91cd\u6784\u7684\u6982\u5ff5\uff0c\u6211\u4eec\u53ef\u4ee5\u7ed9\u51fa\u6591\u56fe\u91cd\u6784\u673a\u5668\u7684\u5b8c\u6574\u5b9a\u4e49\uff1a\u6591\u56fe\u91cd\u6784\u673a\u5668<\/span>\uff08\u03f5-machine\uff09<\/span>\u662f\u80fd\u591f\u7528\u6700\u5c11\u7684\u8ba1\u7b97\u8d44\u6e90\u5bf9\u6d4b\u91cf\u7ed3\u679c\u8fdb\u884c\u6709\u9650\u63cf\u8ff0\u540c\u65f6\u590d\u6742\u5ea6\u6700\u5c0f\u7684\u6a21\u578b\u3002\u6a21\u578b\u91cd\u6784\u7684\u7b97\u6cd5\u6b65\u9aa4\u5982\u4e0b\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    1. \u5728\u6700\u4f4e\u6c34\u5e73\u4e0a\uff0c\u8bbe\u5b9a0\u7ea7\u6a21\u578b\u4e3a\u63cf\u8ff0\u6570\u636e\u672c\u8eab\uff0c\u5373<\/span>M<\/span>0<\/span><\/sub><\/span>=<\/span>s<\/span>\uff0c\u5c06\u521d\u59cb\u5c42\u7ea7<\/span>l<\/span>\u8bbe\u7f6e\u4e3a\u6bd40\u7ea7\u9ad8\u4e00\u7ea7\uff0c\u5373<\/span>l<\/span>=<\/span>1<\/span>\uff1b<\/span><\/section>\n

    <\/span><\/section>\n
    2. \u4ece\u66f4\u4f4e\u6a21\u578b\u91cd\u6784\u6a21\u578b<\/span>M<\/span>l<\/span><\/sub><\/span>=<\/span>M<\/span>l<\/span><\/sub><\/span>\u2212<\/span><\/sub><\/span>1<\/span><\/sub><\/span>\/<\/span>\u223c<\/span>\uff0c\u5176\u4e2d<\/span>\u223c<\/span>\u8868\u793a<\/span>l<\/span>\u7ea7\u4e0a\u7684\u56e0\u679c\u7b49\u4ef7\u7c7b\uff1b<\/span><\/section>\n

    <\/span><\/section>\n
    M<\/span>l<\/span><\/sub><\/span>=<\/span>M<\/span>l<\/span><\/sub><\/span>\u2212<\/span><\/sub><\/span>1<\/span><\/sub><\/span>\/<\/span>\u223c<\/span>\u7684\u542b\u4e49\u662f\uff0c\u5728<\/span>l<\/span>\u2212<\/span>1<\/span>\u7ea7\u4e0a\u88ab\u533a\u522b\u5bf9\u5f85\u7684\u72b6\u6001\u5728<\/span>l<\/span>\u7ea7\u4e0a\u53ef\u4ee5\u88ab\u89c6\u4e3a\u540c\u4e00\u4e2a\u56e0\u679c\u6001\u3002\u6b64\u65f6\u56e0\u679c\u6001\u96c6\u5408<\/span>S<\/span>\u548c\u56e0\u679c\u6001\u4e0a\u7684\u8f6c\u79fb\u6982\u7387\u6620\u5c04\u96c6\u5408<\/span>T<\/span>\u90fd\u88ab\u66f4\u65b0\u4e86\uff1b<\/span><\/section>\n

    <\/span><\/section>\n
    3. \u6536\u96c6\u66f4\u591a\u7684\u6570\u636e\uff0c\u589e\u5927\u5e8f\u5217\u957f\u5ea6<\/span>L<\/span>\uff0c\u5f97\u5230\u66f4\u52a0\u7cbe\u786e\u7684\u4e00\u7cfb\u5217\u6a21\u578b<\/span>M<\/span>l<\/span><\/sub><\/span>\u548c\u56e0\u679c\u6001\u96c6\u5408<\/span>S<\/span>\uff1b<\/span><\/section>\n

    <\/span><\/section>\n
    4. \u6839\u636e\u7edf\u8ba1\u590d\u6742\u5ea6\u53ef\u8ba1\u7b97\u7684\u5b9a\u4e49<\/span>C<\/span>\u03bc<\/span><\/sub>(<\/span>x<\/span>)<\/span>\u2261<\/span>H<\/span>[<\/span>S<\/span>]<\/span>\uff0c\u8ba1\u7b97\u6a21\u578b<\/span>M<\/span>l<\/span><\/sub>\u7684\u7edf\u8ba1\u590d\u6742\u5ea6\u3002\u5982\u679c\u968f\u7740<\/span>L<\/span>\u589e\u5927\uff0c\u6a21\u578b\u7684\u7edf\u8ba1\u590d\u6742\u5ea6\u53d1\u6563\uff0c\u5373<\/span><\/sub>\uff0c\u90a3\u4e48\u56de\u5230\u7b2c\u4e8c\u6b65\uff0c\u5f97\u5230\u66f4\u9ad8\u7ea7\u6a21\u578b<\/span>M<\/span>l<\/span><\/sub>+<\/span><\/sub>1<\/span><\/sub>\uff1b<\/span><\/section>\n

    <\/span><\/section>\n
    5. \u5982\u679c\u6a21\u578b\u590d\u6742\u5ea6\u6536\u655b\uff0c\u610f\u5473\u7740\u7b97\u6cd5\u5df2\u7ecf\u91cd\u5efa\u597d\u4e86\u4e00\u4e2a\u5408\u9002\u7684\u6591\u56fe\u91cd\u6784\u673a\u5668\uff0c\u7a0b\u5e8f\u9000\u51fa\u3002<\/span><\/section>\n

    <\/span><\/section>\n

    <\/h2>\n

    \n
    \n
    \n
    \n
    \n
    <\/section>\n
    <\/section>\n
    \n
    <\/section>\n<\/section>\n<\/section>\n
    \n

    4. \u6df7\u6c8c\u52a8\u529b\u5b66\u5b9e\u4f8b<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n
    <\/section>\n
    <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

    <\/p>\n

    4.1 \u903b\u8f91\u65af\u8c1b\u6620\u5c04<\/span><\/strong><\/span><\/h3>\n

    <\/span><\/section>\n
    \u63a5\u4e0b\u6765\u5c06\u6f14\u793a\u5982\u4f55\u5c06\u8ba1\u7b97\u529b\u5b66\u548c\u6a21\u578b\u91cd\u6784\u7b97\u6cd5\u5e94\u7528\u4e8e\u4e00\u4e2a\u5177\u4f53\u7684\u5b9e\u9645\u6848\u4f8b[13]\u3002\u8fd9\u4e2a\u6848\u4f8b\u662f\u6df7\u6c8c\u52a8\u529b\u5b66\u4e2d\u7684\u903b\u8f91\u65af\u8c1b\u6620\u5c04<\/span> (logistic map)<\/span>\uff0c\u4f5c\u8005\u7279\u522b\u5c55\u793a\u4e86\u7b97\u6cd5\u5728\u5468\u671f\u500d\u589e\u7684\u6df7\u6c8c\u8def\u5f84\u4e0a\u7684\u8868\u73b0\u3002\u7528\u4e8e\u91cd\u5efa\u6a21\u578b\u7684\u6570\u636e\u6d41\u6765\u81ea\u903b\u8f91\u65af\u8c1b\u6620\u5c04\u7684\u8f68\u8ff9\uff0c\u8be5\u8f68\u8ff9\u662f\u901a\u8fc7\u8fed\u4ee3\u6620\u5c04<\/span>x<\/span>n<\/span><\/sub>+<\/span><\/sub>1<\/span><\/sub>=<\/span>f<\/span>(<\/span>x<\/span>n<\/span><\/sub>)<\/span>\u751f\u6210\u7684\uff0c\u8fed\u4ee3\u51fd\u6570\u4e3a<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span>r<\/span>x<\/span>(<\/span>1<\/span>\u2212<\/span>x<\/span>)<\/span>\uff0c\u5176\u4e2d\u975e\u7ebf\u6027\u53c2\u6570<\/span>r<\/span>\u2208<\/span>[<\/span>0<\/span>,<\/span>4<\/span>]<\/span>\uff0c\u521d\u59cb\u6761\u4ef6<\/span>x<\/span>0<\/span><\/sub><\/span>\u2208<\/span>[<\/span>0<\/span>,<\/span>1<\/span>]<\/span>\uff0c\u8fed\u4ee3\u51fd\u6570\u7684\u6700\u5927\u503c\u51fa\u73b0\u5728<\/span>x<\/span>c<\/span><\/sub><\/span>=<\/span>1\/<\/span>2<\/span>\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/span><\/section>\n
    \u4e0a\u56fe\u4e3a\u8fed\u4ee3\u51fd\u6570<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span>r<\/span>x<\/span>(<\/span>1<\/span>\u2212<\/span>x<\/span>)<\/span>\u4e2d\u6781\u9650\u72b6\u6001<\/span>x<\/span>\u4e0e\u53c2\u6570<\/span>r<\/span>\u7684\u5173\u7cfb\u56fe[13]\uff0c\u5f53<\/span>\uff1c<\/span>r<\/span>\uff1c<\/span>3.5699<\/span>.<\/span>.<\/span>.<\/span>\u65f6\u51fd\u6570\u5b58\u5728\u500d\u5468\u671f\u73b0\u8c61\uff0c\u5f53<\/span>\uff1e<\/span>r<\/span>\uff1e<\/span>3.5699<\/span>.<\/span>.<\/span>.<\/span>\u65f6\u4f1a\u51fa\u73b0\u6df7\u6c8c\u73b0\u8c61\u3002\u7531\u4e8e\u89c2\u5bdf\u8005\u89c2\u6d4b\u7684\u7cbe\u7ec6\u7a0b\u5ea6\u6709\u9650\uff0c\u82e5\u8981\u8bc6\u522b\u6df7\u6c8c\u4e2d\u7684\u6709\u5e8f\u7ed3\u6784\uff0c\u5c31\u9700\u8981\u5bf9<\/span>x<\/span>\u8fdb\u884c\u7c97\u7c92\u5316\u64cd\u4f5c\uff0c\u65b9\u6cd5\u662f\u901a\u8fc7\u4e8c\u5143\u5206\u5272\u89c2\u5bdf\u8f68\u8ff9<\/span>x<\/span>=<\/span>x<\/span>0<\/span><\/sub><\/span>x<\/span>1<\/span><\/sub>x<\/span>2<\/span><\/sub><\/span>x<\/span>3<\/span><\/sub><\/span>\u2026<\/span> \uff0c\u5c06\u5176\u8f6c\u6362\u4e3a\u79bb\u6563\u5e8f\u5217<\/span><\/sub><\/span>=<\/span>{<\/span>x<\/span>n<\/span><\/sub>\u2208<\/span>[<\/span>0<\/span>,<\/span>x<\/span>c<\/span><\/sub>)<\/span>\u21d2<\/span>s<\/span>=<\/span>0<\/span>,<\/span>x<\/span>n<\/span><\/sub>\u2208<\/span>[<\/span>x<\/span>c<\/span><\/sub>,<\/span>1<\/span>]<\/span>\u21d2<\/span>s<\/span>=<\/span>1<\/span>}<\/span>\uff0c\u8fd9\u79cd\u5212\u5206\u662f\u201c\u751f\u6210\u201d\u7684\uff0c\u8fd9\u610f\u5473\u7740\u8db3\u591f\u957f\u7684\u4e8c\u8fdb\u5236\u5e8f\u5217\u6765\u81ea\u4efb\u610f\u5c0f\u7684\u521d\u59cb\u6761\u4ef6\u95f4\u9694\u3002\u56e0\u6b64\uff0c\u53ef\u4ee5\u4f7f\u7528\u7c97\u7c92\u5316\u7684\u89c2\u6d4b<\/span>P<\/span>\u6765\u7814\u7a76\u903b\u8f91\u65af\u8c1b\u6620\u5c04\u4e2d\u7684\u4fe1\u606f\u5904\u7406\u3002<\/span><\/section>\n

    <\/span><\/section>\n

    4.2 \u7edf\u8ba1\u590d\u6742\u5ea6-\u71b5\u7387\u56fe<\/span><\/strong><\/span><\/h3>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/span><\/section>\n
    \u4e0a\u56fe\uff08a\uff09\u4e3a\u903b\u8f91\u65af\u8c1b\u6620\u5c04\u4e2d\u7edf\u8ba1\u590d\u6742\u5ea6<\/span>C<\/span>\u03bc<\/span><\/sub>\u4e0e\u9999\u519c\u71b5\u7387<\/span>H<\/span>(<\/span>L<\/span>)<\/span>\/<\/span>L<\/span>\u7684\u5173\u7cfb[13]\uff0c\u4e09\u89d2\u5f62\u8868\u793a<\/span>(<\/span>C<\/span>\u03bc<\/span><\/sub>,<\/span>H<\/span>(<\/span>L<\/span>)<\/span>\/<\/span>L<\/span>)<\/span>\u7684\u5927\u6982\u4f4d\u7f6e\uff0c\u5bf9\u5e94\u975e\u7ebf\u6027\u53c2\u6570<\/span>r<\/span>\u7684 193 \u4e2a\u53d6\u503c\uff0c\u5176\u4e2d\u5b50\u5e8f\u5217\u957f\u5ea6<\/span>L<\/span>=<\/span>16<\/span>\uff0c\u8986\u76d6\u90e8\u5206\u5b9e\u9a8c\u6570\u636e\u7684\u7c97\u5b9e\u7ebf\u662f<\/span>C<\/span>\u03bc<\/span><\/sub>=<\/span>0<\/span>\u65f6\u5bf9<\/span>H<\/span>(<\/span>L<\/span>)<\/span>\/<\/span>L<\/span>\u5f97\u51fa\u7684\u89e3\u6790\u89e3\u66f2\u7ebf\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u672c\u56fe\u8868\u73b0\u4e86\u4e24\u4e2a\u91cd\u8981\u7279\u5f81\u3002\u7b2c\u4e00\u4e2a\u7279\u5f81\u662f\u71b5\u7387\u7684\u6781\u503c\u5bfc\u81f4\u96f6\u590d\u6742\u5ea6\uff0c\u4e5f\u5c31\u662f\u8bf4\u5728<\/span>H<\/span>(<\/span>L<\/span>)<\/span>\/<\/span>L<\/span>=<\/span>0<\/span>\u5904\u6700\u7b80\u5355\u7684\u5468\u671f\u8fc7\u7a0b\u548c\u5728<\/span>H<\/span>(<\/span>L<\/span>)<\/span>\/<\/span>L<\/span>=<\/span>1<\/span>\u5904\u6700\u968f\u673a\u7684\u8fc7\u7a0b\u5728\u7edf\u8ba1\u590d\u6742\u6027\u4e0a\u770b\u90fd\u662f\u7b80\u5355\u7684\uff0c\u5b83\u4eec\u90fd\u5177\u6709\u96f6\u590d\u6742\u5ea6\uff0c\u56e0\u4e3a\u5b83\u4eec\u662f\u7531\u5177\u6709\u5355\u4e00\u72b6\u6001\u7684\u6591\u56fe\u91cd\u6784\u673a\u5668\u63cf\u8ff0\u7684\uff1b\u7b2c\u4e8c\u4e2a\u7279\u5f81\u662f\u5728\u4e24\u4e2a\u6781\u7aef\u60c5\u51b5\u4e4b\u95f4\uff0c\u590d\u6742\u5ea6\u660e\u663e\u5347\u9ad8\uff0c\u5e76\u5728\u4e34\u754c\u71b5\u7387\u503c<\/span>H<\/span>c<\/span><\/sub>\u9644\u8fd1\u51fa\u73b0\u660e\u663e\u5cf0\u503c<\/span>\uff08\u6b64\u5904<\/span>r<\/span>=<\/span>3.5699<\/span>.<\/span>.<\/span>.<\/span>\uff09<\/span>\u3002<\/span>r<\/span>c<\/span><\/sub>=<\/span>3.5699<\/span>.<\/span>.<\/span>.<\/span>\u521a\u597d\u662f\u903b\u8f91\u65af\u8482\u6620\u5c04\u7684\u4e34\u754c\u76f8\u53d8\u70b9\uff0c\u5f53<\/span>r<\/span><<\/span>r<\/span>c<\/span><\/sub>\u65f6\uff0c\u6a21\u578b\u5904\u4e8e\u5468\u671f\u884c\u4e3a\uff1b\u5f53<\/span>r<\/span>><\/span>r<\/span>c<\/span><\/sub>\u65f6\uff0c\u6a21\u578b\u8fdb\u5165\u6df7\u6c8c\u884c\u4e3a\u533a\u57df\u3002\u56e0\u6b64\uff0c\u5f53\u71b5\u7387<\/span>H<\/span>(<\/span>L<\/span>)<\/span>\/<\/span>L<\/span><<\/span>H<\/span>c<\/span><\/sub>\u65f6\uff0c\u6b64\u65f6\u7684\u6570\u636e\u96c6\u662f\u7531\u5448\u5468\u671f\u6027<\/span>\uff08\u5305\u62ec\u5728\u6df7\u6c8c\u533a\u57df\u4e5f\u5448\u5468\u671f\u6027\u7684\u53c2\u6570\uff09<\/span>\u53d8\u5316\u7684\u53c2\u6570\u4e0b\u4ea7\u751f\uff0c\u5927\u4e8e<\/span>H<\/span>c<\/span><\/sub>\u65f6\u6570\u636e\u96c6\u7531\u6df7\u6c8c\u7684\u53c2\u6570\u4e0b\u4ea7\u751f\u3002\u672c\u56fe\u53ef\u4ee5\u5bf9\u7167\u7edf\u8ba1\u590d\u6742\u5ea6\u5c0f\u8282\u4e2d\u7684\u56fe\uff08b\uff09\u4e00\u8d77\u7406\u89e3\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4e0a\u56fe\uff08b\uff09\u4e3a\u903b\u8f91\u65af\u8c1b\u6620\u5c04\u4e2d\u5728<\/span>H<\/span>c<\/span><\/sub>\uff08<\/span>r<\/span>=<\/span>3.5699<\/span>.<\/span>.<\/span>.<\/span>\uff09<\/span>\u5904\uff0c<\/span>L<\/span>\u4e0e\u5b8f\u89c2\u6001\u6570\u91cf<\/span>|<\/span>V<\/span>|<\/span>\u7684\u5173\u7cfb\uff0c\u5e8f\u5217\u7684\u957f\u5ea6<\/span>L<\/span>=<\/span>64<\/span>\u65f6\uff0c<\/span>|<\/span>V<\/span>|<\/span>=<\/span>196<\/span>\uff0c\u4ece\u56fe\u4e2d\u53ef\u4ee5\u770b\u51fa\uff0c\u968f\u7740<\/span>L<\/span>\u7684\u589e\u957f\uff0c<\/span>|<\/span>V<\/span>|<\/span>\u7684\u503c\u662f\u53d1\u6563\u7684\uff0c\u82e5\u8981\u7528\u6709\u9650\u7684<\/span>L<\/span>\u6765\u63cf\u8ff0<\/span>|<\/span>V<\/span>|<\/span>\uff0c\u5c31\u9700\u8981\u5c06\u6a21\u578b\u8fdb\u884c\u91cd\u6784\uff0c\u5347\u7ea7\u4e3a\u63cf\u8ff0\u80fd\u529b\u66f4\u5f3a\u7684\u6a21\u578b\u3002<\/span><\/section>\n

    <\/span><\/section>\n

    4.3 \u6a21\u578b\u5347\u7ea7<\/span><\/strong><\/span><\/h3>\n

    <\/span><\/section>\n
    \u4e0b\u9762\u4e09\u5f20\u56fe[13]\u5c55\u793a\u4e86\u6a21\u578b\u91cd\u6784\u5347\u7ea7\u8fdb\u5316\u7684\u4e00\u79cd\u8def\u5f84\u3002(a),(b),(c)\u4e09\u5f20\u56fe\u5206\u522b\u5bf9\u5e94\u4e86\u7531\u4f4e\u5230\u9ad8\u4e0d\u540c\u9636\u6b21\u7684\u91cd\u6784\u673a\u5668\u7684\u72b6\u6001\u8f6c\u79fb\u56fe\u3002\u56fe\u4e2d\u7684\u5706\u5708\u4ee3\u8868\u72b6\u6001\uff0c\u8fde\u8fb9\u4ee3\u8868\u72b6\u6001\u4e4b\u95f4\u7684\u8f6c\u79fb\uff0c\u8fde\u8fb9\u4e0a\u7684\u6570\u5b57\u4ee3\u8868\u4e00\u6b21\u4f2f\u52aa\u5229\u8fc7\u7a0b\u91c7\u6837\u76840\u62161\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/span><\/section>\n
    \u4e0a\u56fe\uff08a\uff09\u4e3a\u903b\u8f91\u65af\u8c1b\u6620\u5c04\u5728<\/span>H<\/span>c<\/span><\/sub>\uff08<\/span>r<\/span>=<\/span>3.5699<\/span>.<\/span>.<\/span>.<\/span>\uff09\u5904\uff0c\u5e8f\u5217\u957f\u5ea6<\/span>L<\/span>=<\/span>16<\/span>\u65f6\u7528\u6591\u56fe\u91cd\u6784\u673a\u5668\u91cd\u6784\u540e\u768447\u4e2a\u72b6\u6001\u7684\u72b6\u6001\u8f6c\u79fb\u56fe\u3002\u56fe\u4e2d\u6bcf\u6761\u95ed\u5408\u7684\u94fe\u8def\u957f\u5ea6\u90fd\u662f16\u6b65\uff0c\u4f8b\u5982\u521d\u59cb\u5706\u5708-1-3-5-9-12-16-19-21-23-27-31-35-39-41-43-45\u8fd9\u6761\u8def\u5f84\uff0c\u5b83\u7684\u603b\u6b65\u6570\u4e3a16\uff0c\u6bcf\u4e24\u6b65\u4e4b\u95f4\u7684\u6570\u5b57\u662f\u901a\u8fc7\u4f2f\u52aa\u5229\u8fc7\u7a0b\u91c7\u6837\u7684\u4e8c\u5143\u5206\u5272\u7684\u7ed3\u679c\uff0c\u6bcf\u4e2a\u5206\u652f\u4ee3\u8868\u5b83\u7ecf\u5386\u4e86\u4e00\u6b21\u4f2f\u52aa\u5229\u968f\u673a\u8fc7\u7a0b\u3002\u4f46\u662f\u56fe\uff08a\uff09\u6355\u6349\u5230\u7684\u89c4\u5f8b\u5e76\u4e0d\u660e\u663e\uff0c\u6211\u4eec\u5c06\u5b83\u8fdb\u884c\u4e00\u4e2a\u7b80\u5355\u7684\u8f6c\u6362\uff0c\u7528\u6bcf\u4e24\u6b65\u4e4b\u95f4\u7684\u6570\u5b57\u7ec4\u6210\u7684\u5e8f\u5217\u66ff\u6362\u673a\u5668\u4e2d\u672a\u5206\u652f\u7684\u8def\u5f84\u540e\u5c31\u5f97\u5230\u56fe\uff08b\uff09\uff0c\u56fe\uff08b\uff09\u4e2d\u7684\u5206\u652f\u72b6\u6001\u76f8\u5f53\u6709\u89c4\u5f8b\u3002\u66f4\u8fdb\u4e00\u6b65\u5c06\u56fe\uff08b\uff09\u5347\u7ea7\u4e3a\u7528\u5b57\u7b26\u751f\u6210\u5668\u6765\u63cf\u8ff0\u589e\u957f\u7684\u89c4\u5f8b\u6027\u5c31\u5f97\u5230\u4e86\u56fe\uff08c\uff09\u3002\u8be5\u56fe\u7684\u6709\u9650\u81ea\u52a8\u673a\u6709\u4e24\u79cd\u72b6\u6001<\/span>\uff08\u539f\u6709\u7c7b\u578b\u7528\u5706\u5708\u8868\u793a\uff0c\u65b0\u7c7b\u578b\u7528\u65b9\u5757\u8868\u793a\uff09<\/span>\u548c\u4e24\u4e2a\u5bc4\u5b58\u5668 A \u548c B\uff0cA \u548c B\u7528\u4e8e\u4fdd\u5b58\u4e8c\u8fdb\u5236\u5b57\u7b26\u4e32\uff0c\u521d\u59cb\u72b6\u6001 A \u4e2d\u4fdd\u5b58\u7684\u662f0\uff0cB\u4e2d\u4fdd\u5b58\u7684\u662f1\uff0cB’\u8868\u793a\u5bf9\u4fdd\u5b58\u5728B\u4e2d\u7684\u5b57\u7b26\u4e32\u7684\u6700\u540e\u4e00\u4f4d\u53d6\u53cd\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u56fe\uff08b\uff09\u4e2d\u7684\u5b57\u7b26\u4e32\u64cd\u4f5c\u53ef\u4ee5\u901a\u8fc7\u5c06 A \u7684\u5185\u5bb9\u526f\u672c\u9644\u52a0\u5230 B \u4e0a\uff0c\u5e76\u7528 B \u7684\u5185\u5bb9\u7684\u4e24\u4e2a\u526f\u672c\u66ff\u6362 A \u7684\u5185\u5bb9\u6765\u63cf\u8ff0\u3002\u8fd9\u4e9b\u5b57\u7b26\u4e32\u5728\u65b9\u5757\u5904\u8fed\u4ee3\uff0c\u8fed\u4ee3\u5f0f\u8868\u793a\u4e3a<\/span>A<\/span>\u2192<\/span>B<\/span>B<\/span> \u548c<\/span>B<\/span>\u2192<\/span>B<\/span>A<\/span>\u3002\u4f8b\u5982\u56fe\uff08c\uff09\u4e2d\u4ece\u8d77\u59cb\u70b9-2-4-7-13\u8fd9\u6761\u94fe\u8def\uff0c\u8d77\u59cb\u5b57\u7b26\u662f1\uff0c\u53ef\u4ee5\u7528B\u63cf\u8ff0\uff0c\u57284-7\u5904\u53d1\u751f\u53d8\u5316\uff0c\u7528B’\u63cf\u8ff0\uff0c\u57287\u5904\u4ea7\u751f\u4e86\u65b0\u7684\u7c7b\u578b\uff0cB\u4e2d\u5b57\u7b26\u53d8\u4e3a10\uff0c\u5728\u8fd9\u91ccB’\u5c31\u662f11\uff0c\u4f9d\u6b64\u7c7b\u63a8\uff0c\u5c31\u5f97\u5230\u4e86\u56fe\uff08c\uff09\u3002\u663e\u7136\uff08c\uff09\u7684\u63cf\u8ff0\u65b9\u5f0f\u6bd4\uff08a\uff09\u7684\u65b9\u5f0f\u66f4\u52a0\u8282\u7701\u8ba1\u7b97\u8d44\u6e90\uff0c\u5b83\u7684\u63cf\u8ff0\u80fd\u529b\u4e5f\u66f4\u5f3a\u3002<\/span><\/section>\n


    <\/span><\/h2>\n
    <\/section>\n

    \n
    \n
    \n
    \n
    \n
    <\/section>\n
    <\/section>\n
    \n
    <\/section>\n<\/section>\n<\/section>\n
    \n

    5. \u4e0e\u76f8\u5173\u7814\u7a76\u7684\u6bd4\u8f83<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n
    <\/section>\n
    <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

    <\/p>\n

    5.1 \u8ba1\u7b97\u529b\u5b66\u4e0e\u56e0\u679c\u6d8c\u73b0<\/span><\/strong><\/span><\/h3>\n


    <\/span><\/strong><\/h4>\n

    5.1.1 \u6982\u5ff5\u5bf9\u6bd4<\/span><\/strong><\/h4>\n

    <\/span><\/section>\n
    \u8ba1\u7b97\u529b\u5b66\u7684\u8bb8\u591a\u6982\u5ff5\u4e0a\u90fd\u53ef\u4ee5\u5728\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u6846\u67b6\u4e0b\u627e\u5230\u5bf9\u5e94\uff0c\u901a\u8fc7\u8fdb\u884c\u4e24\u8005\u4e4b\u95f4\u7684\u5bf9\u5e94\u548c\u6bd4\u8f83\uff0c\u6211\u4eec\u53ef\u4ee5\u62d3\u5c55\u5bf9\u6d8c\u73b0\u7684\u7406\u89e3\u548c\u7814\u7a76\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u8ba1\u7b97\u529b\u5b66\u548c\u56e0\u679c\u6d8c\u73b0\u7684\u6982\u5ff5\u5bf9\u6bd4<\/span><\/strong><\/section>\n

    <\/p>\n

    <\/section>\n
    5.1.2 \u6591\u56fe\u91cd\u6784\u673a\u5668\u4e0eNIS\u7cfb\u5217\u7684\u5bf9\u6bd4<\/span><\/strong><\/section>\n

    <\/span><\/section>\n
    \u8ba1\u7b97\u529b\u5b66\u4e2d\u7684\u6591\u56fe\u91cd\u6784\u673a\u5668<\/span>\uff08\u03f5-machine\uff09<\/span>\u548c\u8bc6\u522b\u56e0\u679c\u6d8c\u73b0\u7684NIS\u548cNIS+\u90fd\u53ef\u4ee5\u7406\u89e3\u4e3a\u662f\u667a\u80fd\u4f53\u89c2\u5bdf\u5916\u90e8\u4e16\u754c\u7684\u5185\u90e8\u6a21\u578b\u3002\u6591\u56fe\u91cd\u6784\u673a\u5668\u901a\u8fc7\u91cd\u6784\u7b97\u6cd5\u5f97\u5230\u7406\u60f3\u7684\u5212\u5206\u548c\u56e0\u679c\u6001\u7684\u8fc7\u7a0b\uff0c\u4e0eNIS\u6216NIS+\u901a\u8fc7\u6700\u5927\u5316\u5b8f\u89c2\u52a8\u529b\u5b66\u7684\u6709\u6548\u4fe1\u606f<\/span>\uff08Effective information\uff0cEI\uff09<\/span>\u5f97\u5230\u6700\u4f73\u7c97\u7c92\u5316\u7b56\u7565\u4e0e\u6d8c\u73b0\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\u7684\u8fc7\u7a0b\u662f\u7c7b\u4f3c\u7684\u3002\u53ef\u4ee5\u8bf4\uff0cNIS\u6216NIS+\u5c31\u662f\u4e00\u4e2a\u901a\u8fc7\u795e\u7ecf\u7f51\u7edc\u3001\u673a\u5668\u5b66\u4e60\u6280\u672f\u5b9e\u73b0\u7684\u6591\u56fe\u91cd\u6784\u673a\u5668<\/span>\uff08\u03f5-machine\uff09<\/span>\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4e8c\u8005\u7684\u7b49\u4ef7\u53ef\u4ee5\u4f53\u73b0\u5728\u4e24\u65b9\u9762\uff1a\u4e00\u65b9\u9762\u6211\u4eec\u5e0c\u671b\u91cd\u6784\u7684\u6a21\u578b\u5e94\u8be5\u8db3\u591f\u7b80\u6d01<\/span>\uff08\u56e0\u679c\u6001\u5177\u6709\u6700\u5c0f\u968f\u673a\u6027\uff0cNIS+\u4e2d\u6700\u5927\u5316\u5b8f\u89c2\u7684EI\uff09<\/span>\uff1b\u53e6\u4e00\u65b9\u9762\u5219\u5e0c\u671b\u5b8f\u89c2\u6a21\u578b\u4ecd\u4fdd\u7559\u5fae\u89c2\u6001\u53d8\u5316\u7684\u91cd\u8981\u4fe1\u606f\uff0c\u6709\u80fd\u529b\u9884\u6d4b\u672a\u6765\u7684\u5fae\u89c2\u6001\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u8ba1\u7b97\u529b\u5b66\u4e2d\uff0c\u56e0\u679c\u6001\u7684\u5b9a\u4e49\u4fdd\u8bc1\u4e86\u5b83\u5bf9\u5fae\u89c2\u6001\u5177\u6709\u6700\u5927\u9884\u6d4b\u6027\uff0c\u800c\u9999\u519c\u71b5\u7387\u4fbf\u53ef\u4ee5\u8861\u91cf\u8be5\u9884\u6d4b\u8bef\u5dee\u7684\u5927\u5c0f\u3002\u5728NIS\u6216NIS+\u4e2d\uff0c\u6709\u6548\u4fe1\u606f\u7684\u6700\u5927\u5316\u4fdd\u8bc1\u4e86\u6a21\u578b\u7684\u7b80\u6d01\u6027\uff0c\u800c\u5fae\u89c2\u6001\u9884\u6d4b\u8bef\u5dee\u7684\u7ea6\u675f\u5219\u4f53\u73b0\u4e86\u6a21\u578b\u51c6\u786e\u6027\u7684\u8981\u6c42\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u53e6\u5916\uff0c\u6211\u4eec\u5728\u524d\u6587\u8ba8\u8bba\u4e86\u7edf\u8ba1\u590d\u6742\u5ea6\u5173\u4e8e\u71b5\u7387\u7684\u53d8\u5316\u66f2\u7ebf\uff0c\u8be5\u56fe\u8bf4\u660e\uff0c\u6d8c\u73b0\u53d1\u751f\u5728\u968f\u673a\u6027\u7a0b\u5ea6\u4e2d\u7b49\u7684\u60c5\u5f62\u4e0b\u3002\u800c\u5728NIS+\u7684\u6846\u67b6\u4e2d\uff0c\u6211\u4eec\u7528\u673a\u5668\u7684\u91cd\u6784\u9884\u6d4b\u8bef\u5dee\u6765\u7ea6\u675f\u6a21\u578b\uff0c\u8981\u6c42\u5176\u5728\u4fdd\u8bc1\u5bf9\u5fae\u89c2\u9884\u6d4b\u5c3d\u53ef\u80fd\u51c6\u786e<\/span>\uff08\u8bef\u5dee\u4f4e\u4e8e\u4e00\u5b9a\u9608\u503c\uff09<\/span>\u7684\u524d\u63d0\u4e0b\uff0c\u6700\u5927\u5316\u5b8f\u89c2\u7684EI\u3002\u6b64\u65f6\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u8ba1\u7b97\u5b8f\u5fae\u89c2\u7684EI\u4ee5\u53ca\u5b83\u4eec\u7684\u5dee\u503c\u6765\u5224\u65ad\u662f\u5426\u53d1\u751f\u56e0\u679c\u6d8c\u73b0\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u6700\u9ad8\u5f3a\u5ea6\u7684\u56e0\u679c\u6d8c\u73b0\u4e5f\u53d1\u751f\u5728\u89c2\u6d4b\u566a\u97f3\u5904\u4e8e\u4e2d\u7b49\u5f3a\u5ea6\u65f6\u3002<\/span><\/section>\n

    <\/span><\/section>\n

    <\/p>\n

    <\/span><\/section>\n


    <\/span><\/p>\n

    \u4e0a\u56fe\u4e2d\uff0c\u5de6\u56fe\u662f\u524d\u6587\u4e2d\u51fa\u73b0\u8fc7\u7684\u793a\u610f\u56fe\u3002\u5b83\u63cf\u8ff0\u4e86\u7edf\u8ba1\u590d\u6742\u5ea6\u4e0e\u6570\u636e\u968f\u673a\u6027\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u5176\u4e2d\u968f\u673a\u6027\u901a\u8fc7\u9999\u519c\u71b5\u7387\u6765\u5ea6\u91cf<\/span>\uff08\u89c1\u524d\u6587\u4e2d\u7684\u5b9e\u9a8c\u90e8\u5206\uff09<\/span>\u3002\u5f53\u968f\u673a\u6027\u5904\u4e8e\u4e2d\u7b49\u5f3a\u5ea6\u65f6\uff0c\u7edf\u8ba1\u590d\u6742\u5ea6\u51fa\u73b0\u5cf0\u503c\u3002\u53f3\u56fe\u6765\u81eaNIS+\u5e94\u7528\u5728SIR<\/span>\uff08\u75c5\u6bd2\u611f\u67d3\u52a8\u529b\u5b66\uff09<\/span>\u4e3a\u6a21\u578b\u7684\u751f\u6210\u6570\u636e\u4e0a\u7684\u5b9e\u9a8c\u3002\u5176\u4e2d\u6a2a\u8f74\u4e3a\u8be5\u6570\u636e\u4e2d\u89c2\u6d4b\u566a\u97f3\u7684\u5f3a\u5ea6\uff0c\u7eb5\u8f74\u4e3a\u56e0\u679c\u6d8c\u73b0\u5f3a\u5ea6\u0394<\/span>J<\/span><\/span>\u3002\u603b\u51715\u6b21\u91cd\u590d\u5b9e\u9a8c\uff0c\u5b9e\u7ebf\u8868\u793a5\u6b21\u5b9e\u9a8c\u7684\u5747\u503c\uff0c\u586b\u5145\u6761\u5e26\u7684\u5bbd\u5ea6\u4e3a5\u6b21\u5b9e\u9a8c\u7ed3\u679c\u7684\u6807\u51c6\u5dee\u5927\u5c0f\u3002\u8be6\u60c5\u53ef\u53c2\u8003\u8bcd\u6761NIS+<\/a>\u3002<\/span><\/p>\n


    <\/span><\/p>\n

    \u53f3\u56fe\u4e2d\uff0c\u0394<\/span>J<\/span><\/span>\u5728\u03c3=10\u2212<\/sup><\/span>2<\/sup><\/span><\/span>\u548c\u03c3=10\u22121<\/sup><\/span><\/span>\u4e4b\u95f4\u8fbe\u5230\u5cf0\u503c\uff0c\u8fd9\u4e0e\u4f5c\u8005\u6a21\u62df\u4e2d\u4f7f\u7528\u7684\u65f6\u95f4\u6b65\u957f\uff08d<\/span>t<\/span>=<\/span>0.01<\/span><\/span>\uff09\u7684\u5927\u5c0f\u76f8\u5bf9\u5e94\uff0c\u662f\u566a\u97f3\u4e0e\u4fe1\u53f7\u6bd4\u4f8b\u5927\u81f4\u76f8\u540c\u7684\u60c5\u5f62\u3002\u5bf9\u6bd4\u5de6\u53f3\u4e24\u5f20\u56fe\uff0cNIS+\u6240\u8bc6\u522b\u7684\u56e0\u679c\u6d8c\u73b0\u5f3a\u5ea6\u4e0e\u7edf\u8ba1\u590d\u6742\u5ea6\u6709\u7740\u76f8\u4f3c\u7684\u53d8\u5316\u8d8b\u52bf\u548c\u6027\u8d28\u3002<\/span><\/p>\n

    <\/section>\n

    5.2 \u8ba1\u7b97\u529b\u5b66\u4e0e\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u6210\u5757\u6027\u7406\u8bba<\/span><\/strong><\/span><\/h3>\n

    <\/span><\/section>\n
    \u9a6c\u5c14\u79d1\u592b\u94fe\u662f\u8ba1\u7b97\u529b\u5b66\u7684\u4e00\u7c7b\u7279\u6b8a\u60c5\u5f62\uff0c\u5373\u5f53\u672a\u6765\u72b6\u6001\u4ec5\u4f9d\u8d56\u4e8e\u4e0a\u4e00\u6b65\u5386\u53f2\u7684\u60c5\u5f62\u3002\u5728\u9a6c\u5c14\u79d1\u592b\u94fe\u4e2d\uff0c\u4eba\u4eec\u5f88\u65e9\u5c31\u5f00\u59cb\u8ba8\u8bba\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u6210\u5757\u6027<\/span>\uff08lumpability\uff09<\/span>\uff0c\u6240\u8c13\u7684\u6210\u5757\u6027\u662f\u4e00\u79cd\u63cf\u8ff0\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u72b6\u6001\u662f\u5426\u53ef\u805a\u7c7b\u5e76\u7ea6\u7b80\u7684\u6027\u8d28\u3002\u5224\u65ad\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u94fe\u4e0a\u7684\u5212\u5206\u662f\u5426\u662f\u6210\u5757\u7684<\/span>\uff08lumpable\uff09<\/span>\uff0c\u662f\u770b\u5b83\u7684\u9a6c\u5c14\u79d1\u592b\u72b6\u6001\u8f6c\u79fb\u77e9\u9635<\/span>P<\/span>\u4e2d\u7684\u5143\u7d20\u7ecf\u8fc7\u5212\u5206\u80fd\u4e0d\u80fd\u7ed3\u6210\u4e00\u4e2a\u4e2a\u5c0f\u65b9\u5757<\/span>\uff08\u4e5f\u5c31\u662f\u6309\u7167\u805a\u7c7b\u5bf9\u9a6c\u5c14\u79d1\u592b\u94fe\u8fdb\u884c\u7c97\u7c92\u5316\u8868\u793a\uff09<\/span>\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5bf9\u4e8e\u6210\u5757\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u6765\u8bf4\uff0c\u6211\u4eec\u53ef\u4ee5\u628a<\/span>N<\/span>\u4e2a\u5fae\u89c2\u72b6\u6001\u5212\u5206\u6210<\/span>M<\/span><<\/span>N<\/span>\u4e2a\u5b8f\u89c2\u72b6\u6001\uff0c\u5728\u8fd9\u4e2a\u5212\u5206\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u80fd\u5b9a\u4e49\u5fae\u89c2\u72b6\u6001<\/span>s<\/span>1<\/span><\/sub>\u5230\u5b8f\u89c2\u72b6\u6001<\/span>A<\/span>1<\/span><\/sub>\u7684\u8f6c\u79fb\u6982\u7387\u5c31\u7b49\u4e8e<\/span>s<\/span>1<\/span><\/sub>\u5230<\/span>A<\/span>1<\/span><\/sub>\u4e2d\u7684\u5404\u4e2a\u5fae\u89c2\u72b6\u6001\u7684\u8f6c\u79fb\u6982\u7387\u7684\u52a0\u548c\u3002\u6211\u4eec\u4f1a\u53d1\u73b0\uff0c\u5728\u6210\u5757\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u4e2d\uff0c\u5b8f\u89c2\u72b6\u6001\u4e2d\u7684\u6bcf\u4e00\u4e2a\u5fae\u89c2\u72b6\u6001\u8f6c\u79fb\u5230\u53e6\u4e00\u4e2a\u5b8f\u89c2\u72b6\u6001\u7684\u8f6c\u79fb\u6982\u7387\u90fd\u662f\u4e00\u6837\u7684\u3002\u8fd9\u6837\u4f1a\u4f7f\u5f97\u9a6c\u5c14\u79d1\u592b\u72b6\u6001\u8f6c\u79fb\u6982\u7387\u77e9\u9635<\/span>P<\/span>\u8fd9\u4e2a\u65b9\u9635\u4e2d\uff0c\u51fa\u73b0\u4e00\u4e2a\u4e2a\u65b9\u5757\uff0c\u6240\u4ee5\u79f0\u4e4b\u4e3a\u6210\u5757\u6027\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5224\u65ad\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u94fe\u5bf9\u7ed9\u5b9a\u5212\u5206 <\/span>A<\/span> \u662f\u5426\u6210\u5757\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6\u4e3a\uff1a\u5bf9\u4e8e<\/span>\u2200<\/span>i<\/span>,<\/span>j<\/span>\u4e3a\u4e24\u4e2a\u5206\u7ec4\u7684\u4e0b\u6807, \u90a3\u4e48\u5bf9\u4e8e\u4efb\u610f\u4e24\u4e2a\u5206\u7ec4<\/span>A<\/span>i<\/span><\/sub>\u4e2d\u7684\u5fae\u89c2\u6001\uff1a<\/span><\/sub>\uff0c\u90fd\u5fc5\u987b\u6ee1\u8db3\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/p>\n

    <\/section>\n
    \u5176\u4e2d\uff0c<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n
    <\/section>\n
    \u53e6\u4e00\u65b9\u9762\uff0c\u5728\u8ba8\u8bba\u56e0\u679c\u6001\u7684\u65f6\u5019\uff0c\u6211\u4eec\u4e5f\u6709\u7c7b\u4f3c\u7684\u6761\u4ef6\u3002\u5bf9\u4e8e\u67d0\u4e2a\u5212\u5206\u5f97\u5230\u7684\u5b8f\u89c2\u6001\u96c6\u5408<\/span><\/sub><\/span>\uff0c\u5176\u4e3a\u56e0\u679c\u6001\u7684\u5145\u8981\u6761\u4ef6\u662f\uff1a\u5bf9\u4e8e\u4efb\u610f\u7684\u5b8f\u89c2\u6001<\/span><\/sub><\/span>\uff0c\u5bf9\u4e8e\u4efb\u610f\u7684<\/span><\/sub>\uff0c\u6709\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/p>\n

    <\/section>\n
    \u5176\u4e2d<\/sub>\u3002<\/span><\/section>\n
    \u5982\u679c\u5c06\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u72b6\u6001\u5206\u7ec4\u5c31\u770b\u4f5c\u662f\u56e0\u679c\u6001\u7406\u8bba\u4e2d\u7684\u7c97\u7c92\u5316\u5212\u5206\uff0c\u90a3\u4e48\u6210\u5757\u6027\u7684\u8981\u6c42\u548c\u56e0\u679c\u6001\u7684\u8981\u6c42\u975e\u5e38\u76f8\u4f3c\uff0c\u5b83\u4eec\u90fd\u7ed9\u51fa\u4e86\u4e00\u79cd\u5bf9\u672a\u6765\u72b6\u6001\u505a\u9884\u6d4b\u7684\u7b49\u4ef7\u6027\u3002\u4f46\u662f\uff0c\u4e8c\u8005\u53c8\u6709\u533a\u522b\uff0c\u533a\u522b\u6709\u4ee5\u4e0b\u4e09\u70b9\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    1. \u9a6c\u5c14\u53ef\u592b\u6027\u5047\u8bbe<\/span><\/strong><\/section>\n

    <\/span><\/section>\n
    \u56e0\u679c\u6001\u5e76\u6ca1\u6709\u9a6c\u5c14\u79d1\u592b\u6027\u7684\u5047\u8bbe\uff0c\u4f46\u6211\u4eec\u603b\u53ef\u4ee5\u628a\u4e00\u4e2a\u5e8f\u5217\u770b\u6210\u662f\u4e00\u4e2a\u72b6\u6001\uff0c\u4e8e\u662f\u5c31\u80fd\u5f97\u5230\u5e8f\u5217\u6620\u5c04\u5230\u5e8f\u5217\u7684\u9a6c\u5c14\u79d1\u592b\u8f6c\u79fb\u77e9\u9635\u3002\u5728\u8be5\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u6bd4\u8f83\u56e0\u679c\u6001\u5bf9\u5e94\u7684\u5212\u5206\u6620\u5c04\u548c\u6ee1\u8db3\u6210\u5757\u6027\u7684\u5212\u5206\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    2. \u5fae\u89c2\u548c\u5b8f\u89c2\u6700\u5927\u9884\u6d4b\u6027<\/span><\/strong><\/section>\n

    <\/span><\/strong><\/section>\n
    \u4e0a\u6587\u63d0\u5230\uff0c\u56e0\u679c\u6001\u7684\u72b6\u6001\u5212\u5206\u65b9\u5f0f\u80fd\u4fdd\u6301\u5fae\u89c2\u5c42\u9762\u4e0a\u7684\u6700\u5927\u9884\u6d4b\u6027\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u6839\u636e\u5fae\u89c2\u72b6\u6001\u627e\u5230\u5bf9\u5e94\u7684\u56e0\u679c\u6001\u4e4b\u540e\uff0c\u5373\u4f7f\u6211\u4eec\u4e0d\u77e5\u9053\u539f\u672c\u7684\u5fae\u89c2\u72b6\u6001\u4e86\uff0c\u6211\u4eec\u8fd8\u662f\u80fd\u51c6\u786e\u7684\u5f97\u5230\u672a\u6765\u7684\u5fae\u89c2\u72b6\u6001\u7684\u5206\u5e03\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u800c\u6210\u5757\u6027\u4e0e\u5176\u4e0d\u540c\u7684\u662f\uff0c\u6211\u4eec\u6839\u636e\u5fae\u89c2\u72b6\u6001\u627e\u5230\u5bf9\u5e94\u7684\u5b8f\u89c2\u72b6\u6001\u4e4b\u540e\uff0c\u80fd\u591f\u51c6\u786e\u7684\u5f97\u5230\u672a\u6765\u7684\u5b8f\u89c2\u72b6\u6001\u7684\u5206\u5e03\u3002\u4f46\u662f\u5728\u7c97\u7c92\u5316\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u4f1a\u4e22\u5931\u5fae\u89c2\u72b6\u6001\u7684\u8fa8\u522b\u4fe1\u606f\uff0c\u800c\u8fd9\u4e2a\u4fe1\u606f\u7684\u635f\u5931\u662f\u4e0d\u53ef\u9006\u7684\u3002\u6240\u4ee5\uff0c\u6211\u4eec\u5c31\u65e0\u6cd5\u4ece\u5b8f\u89c2\u72b6\u6001\u518d\u8fd8\u539f\u5230\u5fae\u89c2\u72b6\u6001\u4e86\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u6240\u4ee5\uff0c\u56e0\u679c\u6001\u540c\u65f6\u4fdd\u6301\u4e86\u5fae\u89c2\u548c\u5b8f\u89c2\u7684\u6700\u5927\u9884\u6d4b\u6027\uff0c\u800c\u6210\u5757\u6027\u53ea\u80fd\u4fdd\u6301\u5b8f\u89c2\u7684\u6700\u5927\u9884\u6d4b\u6027\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    3. \u56e0\u679c\u6001\u6bd4\u6210\u5757\u6027\u66f4\u4e25\u683c\uff0c\u5212\u5206\u7684\u6210\u5757\u6027\u662f\u6ee1\u8db3\u56e0\u679c\u6001\u8981\u6c42\u7684\u5fc5\u8981\u6761\u4ef6<\/span><\/strong><\/section>\n

    <\/span><\/section>\n
    \u6309\u7167\u4e0a\u9762\u7684\u53d9\u8ff0\uff0c\u6211\u4eec\u4f1a\u53d1\u73b0\uff0c\u56e0\u679c\u6001\u662f\u6bd4\u6210\u5757\u6027\u66f4\u4e25\u683c\u7684\u9650\u5236\uff0c\u56e0\u4e3a\u5b83\u8981\u6c42\u5728\u72b6\u6001\u8f6c\u79fb\u77e9\u9635\u4e2d\uff0c\u5c5e\u4e8e\u540c\u4e00\u4e2a\u56e0\u679c\u6001\u4e2d\u7684\u72b6\u6001\u7684\u884c\u5fc5\u987b\u5b8c\u5168\u4e00\u81f4\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u56e0\u679c\u6001\u7684\u5212\u5206\u4e00\u5b9a\u662f\u4e00\u79cd\u6210\u5757\u7684\u72b6\u6001\u5212\u5206\uff0c\u4f46\u53cd\u4e4b\u5219\u4e0d\u4e00\u5b9a\u3002\u6240\u4ee5\u8bf4\uff0c\u5212\u5206\u7684\u6210\u5757\u6027\u662f\u6ee1\u8db3\u56e0\u679c\u6001\u8981\u6c42\u7684\u5fc5\u8981\u4e0d\u5145\u5206\u6761\u4ef6\u3002<\/span><\/section>\n
    \u4e8c\u8005\u4e4b\u95f4\u7684\u533a\u522b\u4e5f\u53ef\u4ee5\u7528\u4e0b\u56fe\u8fdb\u884c\u76f4\u89c2\u8868\u793a\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/span><\/section>\n
    \u8be5\u56fe\u5c55\u793a\u4e86\u6211\u4eec\u662f\u600e\u4e48\u5904\u7406\u548c\u7406\u89e3\u56e0\u679c\u6001\u548c\u6210\u5757\u6027\u7684\u3002\u9996\u5148\uff0c\u6211\u4eec\u628a\u6bcf\u6761\u5e8f\u5217\u770b\u4f5c\u662f\u4e00\u4e2a\u72b6\u6001\uff0c\u628a\u5e8f\u5217\u538b\u7f29\u5230\u4e86\u4e00\u4e2a<\/span>t<\/span>\u65f6\u523b\u7684\u72b6\u6001\u7a7a\u95f4\uff0c\u5e76\u7528\u4e00\u4e2a\u8f6c\u79fb\u77e9\u9635\u6765\u63cf\u8ff0\u72b6\u6001<\/span>\uff08\u5e8f\u5217\uff09<\/span>\u4e4b\u95f4\u7684\u8f6c\u79fb\u6982\u7387\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5728\u56e0\u679c\u6001\u4e2d\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5bf9\u6bd4\u8f6c\u79fb\u77e9\u9635\u7684\u884c\uff0c\u628a\u76f8\u540c\u7684\u884c\u5212\u5206\u6210\u4e00\u7ec4\uff1b\u800c\u5728\u6210\u5757\u6027\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u540c\u65f6\u8003\u8651\u77e9\u9635\u7684\u884c\u4e0e\u5217\uff0c\u901a\u8fc7\u6bd4\u8f83\u6bcf\u4e00\u884c\u5230\u67d0\u51e0\u5217\u7684\u8f6c\u79fb\u6982\u7387\u6765\u505a\u5206\u7ec4\u3002<\/span><\/section>\n

    <\/span><\/section>\n

    5.3 \u6591\u56fe\u91cd\u6784\u673a\u5668\u4e0e\u4e16\u754c\u6a21\u578b<\/span><\/strong><\/span><\/h3>\n

    <\/span><\/section>\n
    \u8ba1\u7b97\u529b\u5b66\u4e2d\u7684\u6591\u56fe\u91cd\u6784\u673a\u5668\u5173\u5fc3\u667a\u80fd\u4f53\u662f\u5982\u4f55\u4ece\u89c2\u6d4b\u5230\u7684\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u4e2d\u81ea\u52a8\u5730\u53d1\u73b0\u56e0\u679c\u6001\uff0c\u5e76\u6784\u5efa\u5185\u5728\u7684\u73af\u5883\u6a21\u578b\u7684\uff0c\u8fd9\u4e00\u70b9\u4e0e\u5f3a\u5316\u5b66\u4e60\u9886\u57df\u4e2d\u7684\u4e16\u754c\u6a21\u578b<\/span>\uff08\u4e5f\u88ab\u79f0\u4e3a\u4ee5\u53ca\u6a21\u578b\u7684\u5f3a\u5316\u5b66\u4e60\uff09<\/span>\u7684\u60f3\u6cd5\u4e0d\u8c0b\u800c\u5408\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5f3a\u5316\u5b66\u4e60\u6240\u89e3\u51b3\u7684\u95ee\u9898\u901a\u5e38\u53ef\u4ee5\u5efa\u6a21\u4e3a\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b<\/span>\uff08Markov Decision Process\uff0c\u7f29\u5199MDP\uff09<\/span>\uff0c\u5f62\u5f0f\u4e0a\u53ef\u8868\u793a\u4e3a<\/span>(<\/span>S<\/span>,<\/span>A<\/span>,<\/span>T<\/span>,<\/span>R<\/span>,<\/span>\u03b3<\/span>)<\/span>,\u5176\u4e2d\u96c6\u5408<\/span>S<\/span>\u4e3a\u72b6\u6001\u7a7a\u95f4\u5305\u542b\u6240\u6709\u53ef\u80fd\u7684\u72b6\u6001\uff0c\u6bcf\u4e2a\u72b6\u6001<\/span>s<\/span>\u2208<\/span>S<\/span>\u63cf\u8ff0\u4e86\u7cfb\u7edf\u5728\u67d0\u4e00\u65f6\u523b\u7684\u60c5\u5f62\u3002\u96c6\u5408<\/span>A<\/span>\u4e3a\u52a8\u4f5c\u7a7a\u95f4\uff0c\u5305\u542b\u6240\u6709\u7684\u52a8\u4f5c\u3002<\/span>T<\/span>\u4e3a\u72b6\u6001\u8f6c\u79fb\u6982\u7387\uff0c<\/span>T<\/span>(<\/span>s<\/span>\u2032<\/span>|<\/span>s<\/span>,<\/span>a<\/span>)<\/span>\u8868\u793a\u5728\u72b6\u6001<\/span>s<\/span>\u4e0b\u6267\u884c\u52a8\u4f5c<\/span>a<\/span>\u8f6c\u79fb\u5230<\/span>s<\/span>\u2032<\/span>\u7684\u6982\u7387\u3002\u5956\u52b1\u51fd\u6570<\/span>R<\/span>(<\/span>s<\/span>,<\/span>a<\/span>)<\/span>\u5b9a\u4e49\u4e86\u5728\u72b6\u6001<\/span>s<\/span>\u91c7\u53d6\u52a8\u4f5c<\/span>a<\/span>\u540e\u83b7\u5f97\u7684\u5373\u65f6\u5956\u52b1\uff0c\u6298\u73b0\u56e0\u5b50<\/span>\u03b3<\/span>\u662f\u4e00\u4e2a\u5728 [0, 1] \u4e4b\u95f4\u7684\u6570\uff0c\u7528\u4e8e\u6298\u6263\u672a\u6765\u5956\u52b1\u7684\u5f71\u54cd\u3002\u5f53\u667a\u80fd\u4f53\u7684\u89c2\u6d4b<\/span>o<\/span>\u7b49\u4e8e\u7cfb\u7edf\u72b6\u6001<\/span>s<\/span>\u65f6\uff0c\u5bf9\u5e94\u4e00\u822c\u7684\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b\uff0c\u5f53\u667a\u80fd\u4f53\u65e0\u6cd5\u76f4\u63a5\u89c2\u6d4b\u5230\u7cfb\u7edf\u5b8c\u6574\u7684\u72b6\u6001\u65f6\uff0c\u95ee\u9898\u53ef\u4ee5\u63cf\u8ff0\u4e3a\u90e8\u5206\u53ef\u89c2\u6d4b\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b<\/span>\uff08Partially Observable Markov Decision Process\uff0c\u7f29\u5199POMDP\uff09<\/span>\uff0cPOMDP\u53ef\u4ee5\u63cf\u8ff0\u4e3a\u4e00\u4e2a7\u5143\u7ec4<\/span>(<\/span>S<\/span>,<\/span>A<\/span>,<\/span>T<\/span>,<\/span>R<\/span>,<\/span>\u03a9<\/span>,<\/span>O<\/span>,<\/span>\u03b3<\/span>)<\/span>\uff0c<\/span>\u03a9<\/span>\u8868\u793a\u89c2\u6d4b\u7a7a\u95f4\uff0c\u667a\u80fd\u4f53\u7684\u89c2\u6d4b<\/span>o<\/span>\u2208<\/span>\u03a9<\/span>\uff0c\u6982\u7387\u4e3a<\/span>O<\/span>(<\/span>o<\/span>|<\/span>s<\/span>\u2032<\/span>,<\/span>a<\/span>)<\/span>\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5728\u5f3a\u5316\u5b66\u4e60\u4e16\u754c\u6a21\u578b\u4e2d\uff0c\u667a\u80fd\u4f53\u6839\u636e\u548c\u771f\u5b9e\u73af\u5883\u4e92\u52a8\u8fc7\u7a0b\u6240\u4ea7\u751f\u7684\u6570\u636e\u8bad\u7ec3\u4e00\u4e2a\u5185\u5d4c\u7684\u4e16\u754c\u6a21\u578b\uff0c\u4e16\u754c\u6a21\u578b\u4f5c\u4e3a\u5bf9\u771f\u5b9e\u73af\u5883\u7684\u66ff\u4ee3\uff0c\u4ece\u800c\u53ef\u4ee5\u901a\u8fc7\u548c\u4e16\u754c\u6a21\u578b\u4e92\u52a8\u5b66\u4e60\u884c\u52a8\u7b56\u7565\uff0c\u51cf\u5c11\u548c\u771f\u5b9e\u73af\u5883\u7684\u4e92\u52a8\u3002\u5bf9\u4e8e\u89c2\u6d4b\u4e0d\u5305\u542b\u5b8c\u6574\u7684\u72b6\u6001\u4fe1\u606f\u7684POMDP\u95ee\u9898\uff0c\u4ee5\u53ca\u89c2\u6d4b\u7ef4\u5ea6\u8fc7\u9ad8\u5bfc\u81f4\u96be\u4ee5\u51c6\u786e\u5efa\u6a21\u7684MDP\u95ee\u9898\uff0c\u4eba\u4eec\u901a\u5e38\u8ba9Agent\u53bb\u5b66\u4e60\u4e00\u4e2a\u72b6\u6001\u7684\u7c97\u7c92\u5316\u8868\u5f81\uff0c\u8fd9\u79cd\u65b9\u5f0f\u53ef\u4ee5\u5e2e\u52a9\u7b97\u6cd5\u63d0\u5347\u5b66\u4e60\u6548\u7387\u548c\u4efb\u52a1\u8868\u73b0\u3002\u8fd9\u79cd\u7c97\u7c92\u5316\u8868\u5f81\u5c31\u662f\u6240\u8c13\u7684\u201c\u4e16\u754c\u6a21\u578b\u201d\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u56e0\u6b64\uff0c\u5f3a\u5316\u5b66\u4e60\u7684\u4e16\u754c\u6a21\u578b\u5f80\u5f80\u9700\u8981\u5b66\u4e60\u4e00\u4e2a\u4f4e\u7ef4\u7684\u9690\u72b6\u6001\u52a8\u529b\u5b66\u3002\u9690\u72b6\u6001\u7684\u4e16\u754c\u6a21\u578b\u53ef\u4ee5\u8868\u793a\u4e3a<\/span>T<\/span>(<\/span>z<\/span>\u2032<\/span>|<\/span>z<\/span>,<\/span>a<\/span>)<\/span>\uff0c\u5176\u4e2d<\/span>z<\/span>\u8868\u793a\u7c97\u7c92\u5316\u4e4b\u540e\u7684\u9690\u72b6\u6001<\/span>\uff08\u6216\u8005\u5b8f\u89c2\u72b6\u6001\uff09<\/span>\uff0c\u8fd9\u4e00\u70b9\u548c\u8ba1\u7b97\u529b\u5b66\u4e2d\u7684\u56e0\u679c\u6001\uff0c\u4ee5\u53ca\u56e0\u679c\u6001\u7684\u8f6c\u79fb\u6982\u7387\u5177\u6709\u4e00\u5b9a\u7684\u76f8\u4f3c\u4e4b\u5904\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4e16\u754c\u6a21\u578b\u4e0e\u8ba1\u7b97\u529b\u5b66\u4e2d\u6591\u56fe\u91cd\u6784\u673a\u5668\u5b58\u5728\u51e0\u70b9\u5dee\u5f02\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    1. \u5f3a\u5316\u5b66\u4e60\u4e16\u754c\u6a21\u578b\u4e2d\u7684\u72b6\u6001\u8f6c\u79fb\u5305\u542b\u52a8\u4f5c\uff0c\u800c\u5728\u6591\u56fe\u91cd\u6784\u673a\u5668\u4e2d\u5efa\u6a21\u56e0\u679c\u6001\u7684\u8f6c\u79fb\uff0c\u4e0d\u6d89\u53ca\u667a\u80fd\u4f53\u52a8\u4f5c\u7684\u5efa\u6a21\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    2. \u5728\u4e16\u754c\u6a21\u578b\u7684\u5b66\u4e60\u4e2d\uff0c\u5b8f\u89c2\u72b6\u6001\u7c97\u7c92\u5316\u7684\u53e6\u4e00\u4e2a\u9700\u8981\u8003\u8651\u7684\u70b9\u662f\u72b6\u6001\u8f6c\u79fb\u548c\u7c97\u7c92\u5316\u7684\u53ef\u4ea4\u6362\u6027\uff0c\u4e5f\u5c31\u662f\u4ece<\/span>s<\/span>\u7c97\u7c92\u5316\u7684\u8868\u793a<\/span>z<\/span>\u7ecf\u8fc7\u5b8f\u89c2\u52a8\u529b\u5b66<\/span>\uff08\u4e16\u754c\u6a21\u578b\uff09<\/span>\u8f6c\u79fb\u5230\u4e0b\u4e00\u65f6\u523b\u7684\u5b8f\u89c2\u72b6\u6001\u5206\u5e03<\/span>P<\/span>1<\/span><\/sub><\/span>(<\/span>z<\/span>\u2032<\/span>)<\/span>\uff0c\u5e94\u8be5\u5c3d\u53ef\u80fd\u63a5\u8fd1\u4ece<\/span>s<\/span>\u7ecf\u8fc7\u5fae\u89c2\u52a8\u529b\u5b66<\/span>\uff08\u672a\u505a\u8868\u5f81\u5b66\u4e60\uff09<\/span>\u8f6c\u79fb\u5230<\/span>s<\/span>\u2032<\/span>\uff0c\u7136\u540e\u518d\u6784\u5efa\u8868\u5f81<\/span>z<\/span>\u2032<\/span>\uff0c\u4ece\u800c\u5f97\u5230\u7684\u5b8f\u89c2\u72b6\u6001\u5206\u5e03<\/span>P<\/span>2<\/span><\/sub><\/span>(<\/span>z<\/span>\u2032<\/span>)<\/span>\uff0c\u4e5f\u5c31\u662f<\/span>P<\/span>1<\/span><\/sub><\/span>(<\/span>z<\/span>)<\/span>\u2248<\/span>P<\/span>2<\/span><\/sub><\/span>(<\/span>z<\/span>\u2032<\/span>)<\/span>\u3002\u800c\u6591\u56fe\u91cd\u6784\u673a\u5668\u4e2d\u72b6\u6001\u7684\u7c97\u7c92\u5316\u4e0d\u6d89\u53ca\u8fd9\u4e00\u95ee\u9898\u7684\u8ba8\u8bba\u3002<\/span><\/section>\n\n\n<\/tr>\n<\/tbody>\n<\/table>\n

    <\/p>\n

    <\/p>\n

    \u4f5c\u8005\u7b80\u4ecb\uff1a<\/span><\/strong><\/span><\/p>\n

    <\/section>\n
    <\/span><\/strong><\/span><\/section>\n

    <\/p>\n


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    <\/p>\n

    \n
    \n
    \u672c\u8bcd\u6761\u7531\u96c6\u667a\u4ff1\u4e50\u90e8\u4f17\u5305\u751f\u4ea7\uff0c\u96be\u514d\u5b58\u5728\u7eb0\u6f0f\u548c\u95ee\u9898\uff0c\u6b22\u8fce\u5927\u5bb6\u7559\u8a00\u53cd\u9988\u6216\u8005\u524d\u5f80\u5bf9\u5e94\u7684\u767e\u79d1\u8bcd\u6761\u9875\u9762\u8fdb\u884c\u4fee\u6539\uff0c\u4e00\u7ecf\u4fee\u6539\uff0c\u53ef\u4ee5\u83b7\u5f97\u5bf9\u5e94\u7684\u79ef\u5206\u5956\u52b1\u5662\uff01<\/section>\n<\/section>\n<\/blockquote>\n
    <\/section>\n
    <\/section>\n
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    \u52a0\u5165\u6211\u4eec<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

    <\/section>\n
    \u4eb2\u7231\u7684\u793e\u533a\u6210\u5458\u548c\u77e5\u8bc6\u7231\u597d\u8005\uff1a<\/span><\/section>\n
    <\/section>\n
    \u6211\u4eec\u6b63\u5728\u5bfb\u627e\u5bf9\u77e5\u8bc6\u5206\u4eab\u5145\u6ee1\u70ed\u60c5\u7684\u5fd7\u613f\u8005\uff0c\u52a0\u5165\u6211\u4eec\u7684\u96c6\u667a\u767e\u79d1\u8bcd\u6761\u7f16\u5199\u56e2\u961f\uff01\u65e0\u8bba\u4f60\u662f\u67d0\u4e2a\u9886\u57df\u7684\u4e13\u5bb6\uff0c\u8fd8\u662f\u5bf9\u67d0\u4e00\u4e3b\u9898\u6709\u6d53\u539a\u5174\u8da3\uff0c\u6211\u4eec\u90fd\u6b22\u8fce\u4f60\u7684\u52a0\u5165\u3002\u901a\u8fc7\u7f16\u5199\u548c\u7f16\u8f91\u767e\u79d1\u8bcd\u6761\uff0c\u4f60\u5c06\u6709\u673a\u4f1a\u4e3a\u5168\u7403\u8bfb\u8005\u63d0\u4f9b\u51c6\u786e\u3001\u6743\u5a01\u7684\u4fe1\u606f\uff0c\u540c\u65f6\u63d0\u5347\u81ea\u5df1\u7684\u5199\u4f5c\u548c\u7814\u7a76\u80fd\u529b\u3002<\/span><\/section>\n
    <\/section>\n

    \u6211\u4eec\u9700\u8981\u7684\u5e2e\u52a9<\/span><\/strong><\/span><\/p>\n

    \u7f16\u5199\u65b0\u7684\u96c6\u667a\u767e\u79d1\u8bcd\u6761\uff0c\u6db5\u76d6\u590d\u6742\u7cfb\u7edf\u3001\u4eba\u5de5\u667a\u80fd\u7b49\u591a\u4e2a\u9886\u57df<\/span><\/p>\n

    \u66f4\u65b0\u548c\u5b8c\u5584\u73b0\u6709\u8bcd\u6761\uff0c\u786e\u4fdd\u4fe1\u606f\u7684\u51c6\u786e\u6027\u548c\u65f6\u6548\u6027<\/span><\/p>\n

    \u6821\u5bf9\u548c\u5ba1\u6838\u5176\u4ed6\u5fd7\u613f\u8005\u63d0\u4ea4\u7684\u5185\u5bb9\uff0c\u786e\u4fdd\u8bcd\u6761\u8d28\u91cf<\/span><\/section>\n

    <\/span><\/strong><\/span><\/section>\n

    \u6211\u4eec\u5e0c\u671b\u4f60\u5177\u5907<\/span><\/strong><\/span><\/p>\n

    \u826f\u597d\u7684\u5199\u4f5c\u80fd\u529b\uff0c\u80fd\u591f\u6e05\u6670\u3001\u7b80\u6d01\u5730\u8868\u8fbe\u590d\u6742\u7684\u6982\u5ff5<\/span><\/p>\n

    \u5bf9\u67d0\u4e00\u9886\u57df\u6709\u6df1\u5165\u4e86\u89e3\u6216\u6d53\u539a\u5174\u8da3<\/span><\/p>\n

    \u5177\u5907\u57fa\u672c\u7684\u7f51\u7edc\u641c\u7d22\u548c\u4fe1\u606f\u6574\u7406\u80fd\u529b<\/span><\/p>\n

    \u6709\u8d23\u4efb\u5fc3\u548c\u56e2\u961f\u5408\u4f5c\u7cbe\u795e\uff0c\u613f\u610f\u4e3a\u77e5\u8bc6\u5171\u4eab\u8d21\u732e\u529b\u91cf<\/span><\/p>\n

    \u5982\u679c\u4f60\u5bf9\u77e5\u8bc6\u5206\u4eab\u5145\u6ee1\u70ed\u60c5\uff0c\u613f\u610f\u4e3a\u5168\u7403\u8bfb\u8005\u63d0\u4f9b\u6709\u4ef7\u503c\u7684\u4fe1\u606f\uff0c\u8bf7\u7acb\u5373\u52a0\u5165\u6211\u4eec\uff01<\/span><\/section>\n
    <\/section>\n
    <\/section>\n
    \u626b\u7801\u586b\u8868\uff0c\u6dfb\u52a0\u8d1f\u8d23\u4eba\u5fae\u4fe1<\/span><\/section>\n

    <\/span><\/section>\n
    \u8ba9\u6211\u4eec\u4e00\u8d77\uff0c\u7528\u77e5\u8bc6\u8fde\u63a5\u4e16\u754c\uff01<\/span><\/section>\n
    <\/section>\n

    <\/p>\n

    \n
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    \u53c2\u8003\u6587\u732e<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

    \n
    \n
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    \n
      \n
    1. \n

       Packard, N. H.; Crutchfield, J. P.; Farmer, J. D.; Shaw, R. S. (1980). “Geometry from a time series”. Physical Review Letters. 45 (9): 712.<\/p>\n<\/li>\n

    2. \n

       Takens, D. A. (1981). Detecting strange attractors in fluid turbulence. 898. Berlin: Springer-Verlag. pp. 366.<\/p>\n<\/li>\n

    3. \n

       Brandstater, A.; Swift, J.; Swinney, Harry L.; Wolf, A.; Farmer, J. D.; Jen, E.; Crutchfield, J. P. (1983). “Low – dimensional chaos in a hydrodynamic system”. Physical Review Letters. 51 (16): 1442.<\/p>\n<\/li>\n

    4. \n

       Crutchfield, James P.; Young, Karl (1989). “Inferring Statistical Complexity”. Physical Review Letters. 63 (2): 105\u2013108.<\/p>\n<\/li>\n

    5. \n

       Minsky, M. (1967). Computation: Finite and Infinite Machines. Englewood Cliffs, New Jersey: Prentice – Hall.<\/p>\n<\/li>\n

    6. \n

       Chomsky, N. (1956). “Three models for the description of language”. IRE Transactions on Information Theory. 2: 113\u2013124.<\/p>\n<\/li>\n

    7. \n

       Hopcroft, J. E.; Ullman, J. D. (1979). Introduction to Automata Theory, Languages, and Computation. Reading: Addison – Wesley.<\/p>\n<\/li>\n

    8. \n

       Holldobler, B.; Wilson, E. O. (1990). The Ants. Cambridge, Massachusetts: Belknap Press of Harvard University Press.<\/p>\n<\/li>\n

    9. \n

       Reynolds, C. W. (1987). “Flocks, herds, and schools: A distributed behavioral model”. Computer Graphics. 21: 25\u201334.<\/p>\n<\/li>\n

    10. \n

       Fama, E. F. (1991). “Efficient capital markets II”. Journal of Finance. 46: 1575\u20131617.<\/p>\n<\/li>\n

    11. \n

       Barnett, L.; Seth, A.K. (2023). “Dynamical independence: discovering emergent macroscopic processes in complex dynamical systems”. Physical Review E. 108 (1): 014304.<\/p>\n<\/li>\n

    12. \n

       Seth, A. K. (2008). “Measuring emergence via nonlinear granger”. Artificial Life XI: Proceedings of the Eleventh International Conference on the Synthesis and Simulation of Living Systems. 2008: 545\u2013552.<\/p>\n<\/li>\n

    13. \n

       Crutchfield, James P. (1994). “The Calculi of Emergence: Computation, Dynamics, and Induction”. Physica D: Nonlinear Phenomena. 75: 11\u201354.<\/p>\n<\/li>\n

    14. \n

       Shalizi, C. R.; Crutchfield, J. P. (2001). “Computational Mechanics: Pattern and Prediction, Structure and Simplicity”. Journal of Statistical Physics. 104 (3\/4): 817\u2013879.<\/p>\n<\/li>\n

    15. \n

       Rupe, Adam; Crutchfield, James P. (2024). “On principles of emergent organization”. Physics Reports. 1071: 1\u201347.<\/p>\n<\/li>\n

    16. \n

       Bennett, C. H. (1988). Pines, D. (ed.). “Dissipation, information, computational complexity, and the definition of organization”. Emerging Syntheses in the Sciences. Redwood City: Addison-Wesley.<\/p>\n<\/li>\n<\/ol>\n

      <\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

      \n
      \n

      \uff08\u53c2\u8003\u6587\u732e\u53ef\u4e0a\u4e0b\u6ed1\u52a8<\/strong>\u67e5\u770b\uff09<\/p>\n<\/section>\n<\/section>\n

      <\/p>\n

      <\/section>\n
      \n
      \n
      \n
      \n

      \u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u7b2c\u516d\u5b63<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

      <\/section>\n

      \u5728\u9713\u8679\u706f\u7684\u95ea\u70c1\u3001\u8681\u7fa4\u7684\u7cbe\u5bc6\u534f\u4f5c\u3001\u4eba\u7c7b\u610f\u8bc6\u7684\u8bde\u751f\u4e2d\uff0c\u9690\u85cf\u7740\u5fae\u89c2\u4e0e\u5b8f\u89c2\u4e4b\u95f4\u6df1\u523b\u7684\u56e0\u679c\u5173\u8054\u2014\u2014\u8fd9\u4e9b\u770b\u4f3c\u7b80\u5355\u7684\u4e2a\u4f53\u884c\u4e3a\uff0c\u5982\u4f55\u8de8\u8d8a\u5c3a\u5ea6\uff0c\u6d8c\u73b0\u51fa\u4ee4\u4eba\u60ca\u53f9\u7684\u590d\u6742\u73b0\u8c61\uff1f\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u4e3a\u6211\u4eec\u63ed\u793a\u4e86\u7b54\u6848\uff1a\u590d\u6742\u7cfb\u7edf\u7684\u5b8f\u89c2\u7279\u5f81\u65e0\u6cd5\u901a\u8fc7\u5fae\u89c2\u5143\u7d20\u7684\u7b80\u5355\u53e0\u52a0\u89e3\u91ca\uff0c\u800c\u662f\u6e90\u4e8e\u591a\u5c3a\u5ea6\u52a8\u6001\u4ea4\u4e92\u4e2d\u6d8c\u73b0\u7684\u56e0\u679c\u7ed3\u6784\u3002\u4ece\u5947\u5f02\u503c\u5206\u89e3\uff08SVD\uff09\u9a71\u52a8\u7684\u52a8\u6001\u53ef\u9006\u6027\u5206\u6790\uff0c\u5230\u56e0\u679c\u62bd\u8c61\u4e0e\u4fe1\u606f\u5206\u89e3\u7684\u91cf\u5316\u5de5\u5177\uff0c\u7814\u7a76\u8005\u4eec\u6b63\u9010\u6b65\u6784\u5efa\u8d77\u4e00\u5957\u8de8\u8d8a\u6570\u5b66\u3001\u7269\u7406\u4e0e\u4fe1\u606f\u79d1\u5b66\u7684\u7406\u8bba\u6846\u67b6\uff0c\u8bd5\u56fe\u89e3\u7801\u590d\u6742\u7cfb\u7edf\u7684\u201c\u6d8c\u73b0\u5bc6\u7801\u201d\u3002<\/span><\/p>\n

      <\/p>\n

      \u4e3a\u4e86\u7cfb\u7edf\u68b3\u7406\u56e0\u679c\u6d8c\u73b0\u6700\u65b0\u8fdb\u5c55\uff0c\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7cfb\u7edf\u79d1\u5b66\u5b66\u9662\u6559\u6388\u3001\u96c6\u667a\u4ff1\u4e50\u90e8\u521b\u59cb\u4eba\u5f20\u6c5f\u8001\u5e08\u9886\u8854\u53d1\u8d77\u300c\u56e0\u679c\u6d8c\u73b0\u7b2c\u516d\u5b63\u300d\u8bfb\u4e66\u4f1a<\/a>\uff0c\u7ec4\u7ec7\u5bf9\u672c\u8bdd\u9898\u611f\u5174\u8da3\u7684\u670b\u53cb\uff0c\u6df1\u5165\u7814\u8bfb\u76f8\u5173\u6587\u732e\uff0c\u6fc0\u53d1\u79d1\u7814\u7075\u611f\u3002<\/span><\/p>\n

      <\/p>\n

      \u8bfb\u4e66\u4f1a\u5c06\u4ece2025\u5e743\u670816\u65e5\u5f00\u59cb\uff0c\u6bcf\u5468\u65e5\u65e99:00-11:00\uff0c\u6301\u7eed\u65f6\u95f4\u9884\u8ba110\u5468\u5de6\u53f3\u3002\u6bcf\u5468\u8fdb\u884c\u7ebf\u4e0a\u4f1a\u8bae\uff0c\u4e0e\u4e3b\u8bb2\u4eba\u7b49\u793e\u533a\u6210\u5458\u5f53\u9762\u4ea4\u6d41\uff0c\u4e4b\u540e\u53ef\u4ee5\u83b7\u5f97\u89c6\u9891\u56de\u653e\u6301\u7eed\u5b66\u4e60\u3002\u8bda\u631a\u9080\u8bf7\u9886\u57df\u5185\u7814\u7a76\u8005\u3001\u5bfb\u6c42\u8de8\u9886\u57df\u878d\u5408\u7684\u7814\u7a76\u8005\u52a0\u5165\uff0c\u5171\u540c\u63a2\u8ba8\u3002<\/span><\/p>\n


      <\/span><\/p>\n

      \"\u56fe\u7247\"<\/span><\/a><\/section>\n
      \n


      <\/span><\/p>\n

      \u8be6\u60c5\u8bf7\u89c1\uff1a\u56e0\u679c\u6d8c\u73b0\u7b2c\u516d\u5b63\u2014\u2014\u52a8\u529b\u5b66\u3001\u56e0\u679c\u62bd\u8c61\u4e0e\u4fe1\u606f\u5206\u89e3<\/a><\/span><\/p>\n

      <\/p>\n<\/section>\n

      <\/p>\n

      \u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/strong><\/p>\n

      1. <\/strong>\u5947\u5f02\u503c\u5206\u89e3\uff08SVD\uff09\uff5c\u96c6\u667a\u767e\u79d1<\/a><\/strong><\/span><\/section>\n
      2. <\/strong>\u6d8c\u73b0\u7684\u8ba1\u7b97\u65b9\u6cd5\uff1a\u4ece\u8ba1\u7b97\u529b\u5b66\u5230\u5c42\u7ea7\u6d8c\u73b0<\/a><\/strong><\/span><\/section>\n
      3. <\/strong>\u56e0\u679c\u6d8c\u73b0\uff1a\u7528\u56e0\u679c\u91cf\u5316\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u6d8c\u73b0\uff5c\u96c6\u667a\u767e\u79d1<\/a><\/strong><\/span><\/section>\n
      4. <\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
      <\/strong>5.<\/strong> \u89e3\u9501\u96c6\u667a\u5168\u7ad9\u5185\u5bb9\uff0c\u5f00\u542f\u65b0\u5e74\u5b66\u4e60\u8ba1\u5212<\/a><\/strong><\/strong><\/strong><\/strong><\/span><\/strong><\/strong><\/section>\n

      6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/p>\n

      <\/p>\n

      <\/p>\n

      \u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/strong><\/span><\/strong><\/span><\/strong><\/p>\n<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

      \u5bfc\u8bed \u8ba1\u7b97\u529b\u5b66\uff08Computational Mechanics\uff09\u662f\u4e00\u5957\u7528\u4e8e\u91cf\u5316\u6d8c\u73b0\u7684\u6846\u67b6\u3002\u5b83\u4ee5\u4e00\u79cd\u8ba1\u7b97\u7684\u89c6\u89d2\uff0c\u7814\u7a76\u89c2\u5bdf\u8005\u5efa\u7acb\u7684\u6a21\u578b\u5728\u8bc6\u522b\u6d8c\u73b0\u65f6\uff0c\u6a21\u578b\u53d1\u751f\u7684\u53d8\u5316\u3002\u8ba1\u7b97\u529b\u5b66\u4ee5\u4fe1\u606f\u8bba\u548c\u751f\u7269\u8fdb\u5316\u7684\u601d\u60f3\u4e3a\u57fa\u7840\uff0c\u662f\u76ee\u524d\u6700\u65e9\u7684\u5bf9\u6d8c\u73b0\u7684\u5b9a\u91cf\u5316\u7814\u7a76\u3002\u5728\u5e94\u7528\u5f53\u4e2d\uff0c\u8be5\u7406\u8bba\u63d0\u51fa\u4e86\u5bf9\u590d\u6742\u6027\u5ea6\u91cf\u7684\u65b0\u6307\u6807\uff0c\u5373\u7edf\u8ba1\u590d\u6742\u5ea6\uff0c\u540c\u65f6\u8fd8\u63d0…<\/p>\n","protected":false},"author":1,"featured_media":56495,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/56588"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=56588"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/56588\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/56495"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=56588"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=56588"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=56588"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=56588"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}