{"id":61034,"date":"2025-06-19T22:32:32","date_gmt":"2025-06-19T14:32:32","guid":{"rendered":"https:\/\/swarma.org\/?p=61034"},"modified":"2025-06-19T22:32:32","modified_gmt":"2025-06-19T14:32:32","slug":"%e8%ae%a1%e7%ae%97%e5%8a%9b%e5%ad%a6%e3%80%81%e9%97%ad%e5%90%88%e5%9c%88%e4%b8%8e%e6%b6%8c%e7%8e%b0","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=61034","title":{"rendered":"\u8ba1\u7b97\u529b\u5b66\u3001\u95ed\u5408\u5708\u4e0e\u6d8c\u73b0"},"content":{"rendered":"
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\u4eba\u4eec\u4e60\u60ef\u4e8e\u4ece\u4e0d\u540c\u5c3a\u5ea6\u53bb\u63cf\u8ff0\u540c\u4e00\u4e2a\u5bf9\u8c61\u3002\u6bd4\u5982\u5bf9\u4e8e\u4e00\u4e2a\u4eba\u7c7b\u7fa4\u4f53\uff0c\u4f60\u65e2\u53ef\u4ee5\u4ece\u793e\u4f1a\u5b66\u7ecf\u6d4e\u5b66\u89d2\u5ea6\u89e3\u91ca\u8fd9\u4e2a\u7cfb\u7edf\u7684\u73b0\u8c61\uff0c\u4e5f\u53ef\u4ee5\u4ece\u751f\u7269\u5b66\u751f\u7406\u8fc7\u7a0b\u7684\u5c42\u6b21\u53bb\u63cf\u8ff0\u5b83\uff0c\u8fd8\u53ef\u4ee5\u4ece\u5206\u5b50\u5c3a\u5ea6\u7684\u7269\u7406\u5b66\u53bb\u63cf\u8ff0\u5b83\u3002\u6bd5\u7adf\u4eba\u7684\u7ec4\u6210\u6765\u81ea\u4e8e\u4e00\u4e2a\u4e2a\u5668\u5b98\u548c\u7ec6\u80de\uff0c\u800c\u6bcf\u4e00\u4e2a\u7ec6\u80de\u90fd\u6709\u5206\u5b50\u7ec4\u6210\u3002\u8fd9\u4e9b\u5c3a\u5ea6\u4e0a\u7684\u5404\u81ea\u89c4\u5f8b\u53ef\u4ee5\u72ec\u7acb\u6210\u7acb\uff0c\u7531\u6b64\u8bde\u751f\u4e86\u5404\u4e2a\u5b66\u79d1\u3002\u8fd9\u79cd\u5206\u5c42\u6b21\u7684\u73b0\u8c61\u4e00\u76f4\u88ab\u54f2\u5b66\u5bb6\u4eec\u7528\u56e0\u679c\u95ed\u5408\u6216\u56e0\u679c\u95ed\u5305\u7684\u6982\u5ff5\u8fdb\u884c\u8ba8\u8bba\u3002\u5728Fernando E. Rosas\u7b49\u4eba\u7684\u6700\u8fd1\u7814\u7a76\u5de5\u4f5c\u4e2d\uff0c\u8fd9\u79cd\u5c42\u6b21\u6d8c\u73b0\u7684\u73b0\u8c61\u53ef\u4ee5\u88ab\u5b9a\u91cf\u5316\u5730\u63cf\u8ff0\u3002\u501f\u52a9\u590d\u6742\u7cfb\u7edf\u6d8c\u73b0\u7406\u8bba\uff0c\u6211\u4eec\u53ef\u4ee5\u5bf9\u8fd9\u79cd\u795e\u5947\u7684\u73b0\u8c61\u786e\u7acb\u5171\u8bc6\uff0c\u5e76\u4e14\u83b7\u53d6\u66f4\u6df1\u523b\u7684\u6d1e\u89c1\u3002<\/span><\/span><\/strong><\/p>\n


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\u8bba\u6587\u9898\u76ee\uff1aSoftware in the natural world: A computational approach to hierarchical emergence<\/span><\/span><\/p>\n

\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/arxiv.org\/abs\/2402.09090<\/span><\/span><\/p>\n<\/blockquote>\n


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\u50cf\u8fd9\u6837\u7684\u7f16\u7a0b\u8bed\u8a00\u662f\u5728\u8f6f\u4ef6\u5c42\u6b21\u4e0a\u7f16\u5199\u548c\u8fd0\u884c\u7684\uff0c\u800c\u6211\u4eec\u77e5\u9053\u5b9e\u9645\u53d1\u751f\u7684\u53ea\u662f\u786c\u4ef6\u5c42\u6b21\u7684\u4e8c\u8fdb\u5236\u8fd0\u7b97\uff0c\u4f46\u6211\u4eec\u5728\u5199\u4ee3\u7801\u65f6\u4e0d\u4f1a\u53bb\u60f3\u90a3\u4e9b\u7e41\u6742\u7684\u4e8c\u8fdb\u5236\u8bed\u8a00\u3002\u5982\u679c\u4f60\u4e4b\u524d\u8bfb\u8fc7\u5173\u4e8e\u56e0\u679c\u6d8c\u73b0\u7684\u6587\u7ae0\uff0c\u4f1a\u53d1\u73b0\u76f8\u4f3c\u7684\u73b0\u8c61\uff1a\u6211\u4eec\u53ef\u4ee5\u7c7b\u6bd4\u786c\u4ef6\u662f\u7cfb\u7edf\u7684\u5fae\u89c2\u5c42\uff0c\u8f6f\u4ef6\u662f\u5b8f\u89c2\u5c42\u3002\u4ee5\u4e0a\u7684\u8ba8\u8bba\u8bf4\u660e\uff0c\u5b8f\u89c2\u5c42\u6b21\u4e0a\u7684\u52a8\u529b\u5b66\u548c\u56e0\u679c\u53ef\u4ee5\u5b8c\u5168\u8131\u79bb\u5fae\u89c2\u5c42\u7684\u4fe1\u606f\u6765\u8ba8\u8bba\u3002 <\/span><\/span><\/p>\n

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\u7814\u7a76\u56e0\u679c\u6d8c\u73b0\u7684\u5b66\u8005Fernando E. Rosas\u53ca\u5176\u5408\u4f5c\u8005\u8ba4\u4e3a[3]\uff0c\u9664\u4e86\u72ed\u4e49\u7684\u8ba1\u7b97\u673a\u5916\u5f88\u591a\u7cfb\u7edf\u5176\u5b9e\u90fd\u5177\u5907\u7c7b\u4f3c\u7684\u6027\u8d28\u3002\u5982\u679c\u4e00\u4e2a\u7cfb\u7edf\u6709\u8f93\u5165\u6709\u8f93\u51fa\uff0c\u5177\u5907\u8ba1\u7b97\u7684\u80fd\u529b\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u628a\u5b83\u6bd4\u4f5c\u4e00\u53f0\u673a\u5668\uff0c\u7136\u540e\u68c0\u9a8c\u4e00\u4e0b\u770b\u770b\u5b83\u662f\u5426\u5177\u6709\u80fd\u591f\u548c\u786c\u4ef6\u89e3\u8026\u7684\u8f6f\u4ef6\u5c42\uff0c\u6216\u8005\u8bf4\u8f6f\u4ef6\u6027\uff08software-ness\uff09\u3002Rosas\u7b49\u4eba\u8ba4\u4e3a\uff0c\u5177\u6709\u8fd9\u6837\u6027\u8d28\u7684\u7cfb\u7edf\u4fbf\u53d1\u751f\u4e86\u8ba1\u7b97\u89c6\u89d2\u4e0b\u7684\u6d8c\u73b0\u3002 <\/span><\/span><\/p>\n


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\u4fe1\u606f\u95ed\u5408\u7684\u6982\u5ff5\u5176\u5b9e\u5728\u4e4b\u524d\u7684\u7814\u7a76\u5de5\u4f5c\u4e2d\u5df2\u7ecf\u88ab\u63d0\u51fa\u8fc7\uff0c\u800c\u4e14\u6709\u5bf9\u5e94\u7684\u5f62\u5f0f\u5316\u8868\u8fbe\u3002\u5728Anil Seth\u56e2\u961f\u7684\u5de5\u4f5c\u4e2d\uff0c\u5b83\u53eb\u505a\u52a8\u529b\u5b66\u89e3\u8026[1]\u3002\u4e8c\u8005\u5728\u6570\u5b66\u8868\u8fbe\u4e0a\u662f\u76f8\u540c\u7684\uff0c\u7528\u4e92\u4fe1\u606f\u6216\u6761\u4ef6\u4e92\u4fe1\u606f\u6765\u5b9a\u4e49\uff1a<\/span><\/span><\/p>\n

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X\u548cZ\u5206\u522b\u662f\u5fae\u89c2\u4e0e\u5b8f\u89c2\u53d8\u91cf\u3002\u8bfb\u8005\u53ef\u53c2\u8003<\/span>\u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u7b2c\u4e8c\u5b63<\/span><\/a>23\u671f\u7684\u5185\u5bb9\uff08\u4e0b\u65b9\u626b\u7801\u76f4\u8fbe\uff09\u3002\u4ece\u53e6\u4e00\u4e2a\u89d2\u5ea6\u6765\u770b\uff0c\u8fd9\u5b9e\u9645\u4e0a\u662f\u6784\u6210\u4e86<\/span><\/span><\/span><\/span>\u7684\u9a6c\u5c14\u53ef\u592b\u94fe\uff0c\u5373\u63a7\u5236<\/span><\/span><\/span><\/span>\uff0c\u5f97\u5230<\/span><\/span><\/span><\/span>\u4e0e<\/span><\/span><\/span><\/span>\u72ec\u7acb\u3002 <\/span><\/span><\/p>\n

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\u4f46\u662f\u4fe1\u606f\u95ed\u5408\u7684\u63d0\u51fa\u4ec5\u662f\u4ece\u4e00\u4e2a\u89c2\u6d4b\u8005\u7684\u89c6\u89d2\u63d0\u51fa\u7684\uff0c\u5e76\u672a\u89e6\u53ca\u8be5\u6027\u8d28\u5b9e\u73b0\u7684\u5e95\u5c42\u539f\u7406\uff0c\u5373\u56e0\u679c\u673a\u5236\u3002\u4e3a\u6b64\uff0c\u4f5c\u8005\u4eec\u8fdb\u4e00\u6b65\u63d0\u51fa\u56e0\u679c\u95ed\u5408\uff08causal closure\uff09\u7684\u6982\u5ff5\uff0c\u4e0e\u4fe1\u606f\u95ed\u5408\u975e\u5e38\u76f8\u4f3c\u3002\u8fd8\u4ee5\u624b\u673a\u4e3a\u4f8b\uff0c\u4fe1\u606f\u95ed\u5408\u662f\u4f60\u4f5c\u4e3a\u65c1\u89c2\u8005\u770b\u522b\u4eba\u4f7f\u7528\u624b\u673a\uff0c\u53d1\u73b0\u8f6f\u4ef6\u7684\u8fd0\u884c\u53ef\u4ee5\u201c\u72ec\u7acb\u201d\u4e8e\u786c\u4ef6\u5c42\u3002\u800c\u56e0\u679c\u95ed\u5408\u5219\u662f\u628a\u4f60\u81ea\u5df1\u7f6e\u4e8e\u4f7f\u7528\u8005\u7684\u4f4d\u7f6e\u3002\u5f53\u4f60\u64cd\u4f5c\u624b\u673a\u65f6\uff0c\u5176\u5b9e\u662f\u5728\u65bd\u52a0\u5b8f\u89c2\u5c42\u6b21\u7684\u5e72\u9884\u3002\u800c\u8f6f\u4ef6\u8f93\u51fa\u7684\u7ed3\u679c\u53ea\u6765\u81ea\u4e8e\u8fd9\u5b8f\u89c2\u7684\u5e72\u9884\uff0c\u4e0e\u5e95\u5c42\u786c\u4ef6\u65e0\u5173\uff0c\u8fd9\u4fbf\u662f\u56e0\u679c\u95ed\u5408\u3002\u5982\u679c\u624b\u673a\u574f\u4e86\uff0c\u65e0\u8bba\u4f60\u600e\u4e48\u6309\u952e\u5b83\u90fd\u4e0d\u54cd\u5e94\uff0c\u90a3\u4e48\u4f60\u5c31\u4e0d\u5f97\u4e0d\u5230\u786c\u4ef6\u5c42\u53bb\u8ffd\u7a76\u5b83\u574f\u6389\u7684\u539f\u56e0\uff0c\u8fd9\u65f6\u5019\u574f\u6389\u7684\u624b\u673a\u5c31\u662f\u56e0\u679c\u4e0d\u95ed\u5408\u7684\u7cfb\u7edf\u3002<\/span><\/span><\/p>\n

\u73b0\u5728\u95ee\u9898\u6765\u4e86\uff0c\u6211\u4eec\u8981\u5982\u4f55\u5f62\u5f0f\u5316\u8868\u8fbe\u56e0\u679c\u95ed\u5408\u8fd9\u4e2a\u6982\u5ff5\uff1f\u65e9\u5728\u4e0a\u4e2a\u4e16\u7eaa80\u5e74\u4ee3\uff0c\u5723\u5854\u83f2\u5b66\u8005Crutchfield\u63d0\u51fa\u4e86\u8ba1\u7b97\u529b\u5b66\uff08Computational Mechanics\uff09\u8fd9\u4e00\u6574\u5957\u7406\u8bba\uff0c\u4ece\u8ba1\u7b97\u7684\u89c6\u89d2\u4e3a\u6d8c\u73b0\u73b0\u8c61\u8fdb\u884c\u4e86\u5efa\u6a21\u3002Rosas\u7b49\u4eba\u4fbf\u501f\u9274\u8ba1\u7b97\u529b\u5b66\u7684\u6838\u5fc3\u601d\u60f3\uff0c\u6765\u4e3a\u56e0\u679c\u95ed\u5408\u6784\u5efa\u7406\u8bba\u57fa\u7840\u3002\u5982\u679c\u8bfb\u8005\u60f3\u5168\u9762\u4e86\u89e3\u8ba1\u7b97\u529b\u5b66\u8fd9\u4e2a\u7406\u8bba\u6846\u67b6\uff0c\u53ef\u53c2\u8003\u96c6\u667a\u767e\u79d1\u8bcd\u6761\u3010<\/span>\u8ba1\u7b97\u529b\u5b66<\/span><\/a>\u3011\u3002\u4e0b\u9762\u662f\u5bf9\u76f8\u5173\u5185\u5bb9\u7684\u4e00\u4e2a\u7b80\u7565\u4ecb\u7ecd\u3002 <\/span><\/span><\/p>\n


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

\n
\n
\n
\n
\n

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

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

\u56e0\u679c\u6001\u548c\u03f5\u673a\u5668<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

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

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


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

\u5305\u62ec\u4eba\u7c7b\u5728\u5185\u7684\u667a\u80fd\u4f53\uff0c\u6bcf\u65f6\u6bcf\u523b\u90fd\u5728\u5bf9\u5468\u56f4\u73af\u5883\u89c2\u5bdf\uff0c\u5f97\u5230\u5927\u91cf\u7684\u89c2\u6d4b\u6570\u636e\uff0c\u4ee5\u65f6\u95f4\u5e8f\u5217\u7684\u65b9\u5f0f\u53ef\u4ee5\u5f62\u5f0f\u5316\u8868\u8fbe\u51fa\u6765\uff0c\u5982\u4e0b\u56fe\u4e2d\u7684<\/span><\/span><\/span><\/span>\u3002 <\/span><\/span><\/p>\n

<\/section>\n

\u4f46\u6211\u4eec\u89c2\u6d4b\u5230\u7684\u6570\u636e\u5e76\u4e0d\u4ee3\u8868\u4ea7\u751f\u6570\u636e\u7684\u673a\u5236\u672c\u8eab\u3002\u800c\u667a\u80fd\u4f53\u4e3a\u4e86\u751f\u5b58\uff0c\u5fc5\u987b\u5728\u81ea\u5df1\u7684\u5185\u90e8\uff08\u5927\u8111\u4e2d\uff09\u6784\u5efa\u7b80\u6d01\u7684\u673a\u5236\u6765\u9884\u6d4b\u89c2\u6d4b\u6570\u636e\u7684\u53d8\u5316\uff0c\u8fd9\u4fbf\u662f\u4e0a\u56fe\u4e2d\u7684<\/span><\/span><\/span><\/span>\u3002\u800c\u8ba1\u7b97\u529b\u5b66\u5047\u8bbe\uff0c\u8fdb\u5316\u7684\u538b\u529b\u4f7f\u5f97\u667a\u80fd\u4f53\u6784\u5efa\u7684\u9884\u6d4b\u673a\u5236\u8d8b\u5411\u4e8e\u4e00\u4e2a\u6700\u7406\u60f3\u7684\u72b6\u6001\u2014\u2014\u56e0\u679c\u6001\uff08Causal States\uff09\u3002 <\/span><\/span><\/p>\n

\u56e0\u679c\u6001\u662f\u6839\u636e\u9884\u6d4b\u7b49\u4ef7\u6027\u6765\u5b9a\u4e49\u7684\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u4e8c\u8fdb\u5236\u6570\u5b57\u4e32\u5206\u522b\u4ee3\u8868\u4e0d\u540c\u7684\u72b6\u6001\uff0c\u53f3\u4fa7\u7684\u9ed1\u8272\u7bad\u5934\u8868\u793a\u5b83\u4eec\u5bf9\u672a\u6765\u9884\u6d4b\u7684\u6982\u7387\u5206\u5e03\u3002<\/span><\/span><\/span><\/span>\u4e2d\u4e24\u4e2a\u72b6\u6001\u7684\u9884\u6d4b\u5206\u5e03\u5b8c\u5168\u76f8\u540c\uff0c\u6240\u4ee5\u5b83\u4eec\u5c5e\u4e8e\u540c\u4e00\u4e2a\u56e0\u679c\u6001\u3002\u800c<\/span><\/span><\/span><\/span>\u4e2d\u7684\u72b6\u6001\u5bf9\u672a\u6765\u7684\u9884\u6d4b\u4e0e<\/span><\/span><\/span><\/span>\u4e0d\u540c\uff0c\u6240\u4ee5<\/span><\/span><\/span><\/span>\u662f\u53e6\u4e00\u4e2a\u56e0\u679c\u6001\u3002 <\/span><\/span><\/p>\n

<\/section>\n

\u56e0\u679c\u6001\u5f7c\u6b64\u4e4b\u95f4\u6709\u5b83\u4eec\u81ea\u5df1\u7684\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u3002\u628a\u56e0\u679c\u6001\u548c\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u653e\u5728\u4e00\u8d77\uff0c\u4fbf\u6784\u6210\u4e86<\/span><\/span><\/span><\/span>\u673a\u5668\u3002\u5bf9\u4e8e\u63cf\u8ff0\u548c\u9884\u6d4b\u4e00\u7ec4\u89c2\u6d4b\u6570\u636e\u6765\u8bf4\uff0c<\/span><\/span><\/span><\/span>\u673a\u5668\u5c31\u662f\u6700\u7b80\u6d01\u548c\u6709\u6548\u7684\u673a\u5236\u6a21\u578b\uff0c\u4fdd\u7559\u4e86\u4e00\u4e2a\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\u6700\u6709\u7528\u7684\u90a3\u90e8\u5206\u4fe1\u606f\uff0c\u540c\u65f6\u53bb\u9664\u4e86\u5176\u4ed6\u5bf9\u9884\u6d4b\u65e0\u7528\u7684\u5197\u4f59\u4fe1\u606f\u3002 <\/span><\/span><\/p>\n

\u56e0\u679c\u6001\u548c<\/span><\/span><\/span><\/span>\u673a\u5668\u6709\u5f88\u591a\u975e\u5e38\u7406\u60f3\u7684\u6570\u5b66\u6027\u8d28\uff0c\u611f\u5174\u8da3\u7684\u670b\u53cb\u53ef\u4ee5\u53c2\u8003\u6587\u732e[2]\u548c<\/span>\u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u7b2c\u4e09\u5b63<\/span><\/a>\u7b2c5\u671f\u3002<\/span><\/span>
<\/span><\/p>\n

\"\u6d77\u62a5\u9884\u89c8\"<\/span><\/p>\n


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

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

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

\u03bd\u673a\u5668<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

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

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


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

 <\/span><\/span><\/span><\/span>\u673a\u5668\u548c\u56e0\u679c\u95ed\u5408\u53c8\u6709\u4ec0\u4e48\u5173\u7cfb\u5462\uff1f\u6211\u4eec\u6765\u770b\u4e0b\u56fe\uff0cX\u548cZ\u5206\u522b\u8868\u793a\u5fae\u89c2\u548c\u5b8f\u89c2\u8fc7\u7a0b\u3002\u5bf9\u4e8e\u8fd9\u4e24\u4e2a\u5c3a\u5ea6\uff0c\u6211\u4eec\u53ef\u4ee5\u5206\u522b\u6784\u5efa\u5173\u4e8e\u5b83\u4eec\u81ea\u8eab\u7684<\/span><\/span><\/span><\/span>\u673a\u5668\uff0c\u5176\u56e0\u679c\u6001\u4e3a<\/span><\/span><\/span><\/span>\u548c<\/span><\/span><\/span><\/span>\u3002\u5b83\u4eec\u5206\u522b\u662f\u5fae\u89c2\u9884\u6d4b\u5fae\u89c2\uff0c\u5b8f\u89c2\u9884\u6d4b\u5b8f\u89c2\u6700\u6709\u6548\u7684\u673a\u5236\u3002\u800c\u4f5c\u8005\u53c8\u5b9a\u4e49\u4e86<\/span><\/span><\/span><\/span>\u673a\u5668\uff0c\u5176\u56e0\u679c\u6001\u4e3a\u56fe\u4e2d\u7684<\/span><\/span><\/span><\/span>\u3002 <\/span><\/span><\/p>\n

<\/section>\n

\u4ece\u56fe\u4e2d\u7bad\u5934\u5173\u7cfb\u53ef\u4ee5\u770b\u51fa\uff0c<\/span><\/span><\/span><\/span>\u673a\u5668\u662f\u5bf9\u5fae\u89c2\u53d8\u91cf\u7684\u5212\u5206\uff0c\u76ee\u7684\u5219\u662f\u5bf9\u5b8f\u89c2\u7684\u672a\u6765\u8fdb\u884c\u9884\u6d4b\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b83\u662f\u6839\u636e\u5bf9\u5b8f\u89c2\u672a\u6765\u7684\u9884\u6d4b\u7b49\u4ef7\u6027\u5bf9\u5fae\u89c2\u72b6\u6001\u8fdb\u884c\u4e86\u5206\u7ec4\u3002\u4e0b\u9762\u4e24\u4e2a\u5f0f\u5b50\u5206\u522b\u662f<\/span><\/span><\/span><\/span>\u673a\u5668\u4e2d\u5173\u4e8e\u5212\u5206\u7684\u5b9a\u4e49\uff0c\u4ee5\u53ca<\/span><\/span><\/span><\/span>\u673a\u5668\u4e2d\u5bf9\u4e8e\u5212\u5206\u7684\u5b9a\u4e49\uff1a<\/span><\/span><\/p>\n

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

\u5f0f\u5b50\u4e2dL\u8868\u793a\u5e8f\u5217\u957f\u5ea6\uff0c\u53d8\u91cf\u4e0a\u7bad\u5934\u5f80\u5de6\u4ee3\u8868\u5386\u53f2\u72b6\u6001\uff0c\u5f80\u53f3\u4ee3\u8868\u672a\u6765\u72b6\u6001\u3002\u5b83\u4eec\u7684\u533a\u522b\u53ea\u662f\u5728\u4e8e\uff0c<\/span><\/span><\/span><\/span>\u673a\u5668\u662f\u5bf9\u540c\u4e00\u4e2a\u5c3a\u5ea6\u7684\u6700\u6709\u6548\u9884\u6d4b\u673a\u5236\uff0c<\/span><\/span><\/span><\/span>\u673a\u5668\u662f\u5bf9\u66f4\u5b8f\u89c2\u5c3a\u5ea6\u7684\u6700\u6709\u6548\u9884\u6d4b\u673a\u5236\u3002 <\/span><\/span><\/p>\n

\u63a5\u4e0b\u6765\u6211\u4eec\u5c31\u53ef\u4ee5\u7ed9\u51fa\u56e0\u679c\u95ed\u5408\u7684\u5b9a\u4e49\u4e86\u3002\u5bf9\u4e8e\u4e00\u4e2a\u7cfb\u7edf\u7684\u5b8f\u89c2\u8fc7\u7a0b\uff0c\u5982\u679c\u9884\u6d4b\u672a\u6765\u6240\u4f7f\u7528\u7684<\/span><\/span><\/span><\/span>\u673a\u5668\u548c<\/span><\/span><\/span><\/span>\u673a\u5668\u5b8c\u5168\u7b49\u4ef7\uff0c\u5373\u4e0a\u56fe\u4e2d<\/span><\/span><\/span><\/span>\u548c<\/span><\/span><\/span><\/span>\u76f8\u7b49\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u8bf4\u8be5\u5b8f\u89c2\u8fc7\u7a0b\u662f\u56e0\u679c\u95ed\u5408\u7684\u3002\u5176\u7269\u7406\u610f\u4e49\u4e3a\uff0c<\/span>\u5728\u5b8f\u89c2\u4e0a\u7684\u5e72\u9884\uff0c\u548c\u5fae\u89c2\u4e0a\u4e0e\u4e4b\u5bf9\u5e94\u7684\u5e72\u9884\uff0c\u4f5c\u7528\u5728\u5b8f\u89c2\u5c42\u9762\u4e0a\u4ea7\u751f\u7684\u7ed3\u679c\u5b8c\u5168\u76f8\u540c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u5b8f\u89c2\u7684\u7ed3\u679c\u89c6\u4e3a\u53ea\u6765\u81ea\u4e8e\u5b8f\u89c2\u7684\u5e72\u9884\uff0c\u4e0e\u5fae\u89c2\u65e0\u5173\u3002 <\/span><\/span><\/p>\n

\u4ece\u5b9a\u6027\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u4f3c\u4e4e\u56e0\u679c\u95ed\u5408\u548c\u4fe1\u606f\u95ed\u5408\u662f\u4e00\u6837\u7684\u3002\u5728\u7ed9\u51fa\u6570\u5b66\u5b9a\u4e49\u540e\uff0c\u4f5c\u8005\u5728\u6587\u7ae0\u4e2d\u4e25\u683c\u8bc1\u660e\u4e86\u4fe1\u606f\u95ed\u5408\u548c\u56e0\u679c\u95ed\u5408\u786e\u5b9e\u662f\u7b49\u4ef7\u7684\u3002\u4e0d\u8fc7\u8fd9\u4e0d\u610f\u5473\u7740\u4ee5\u4e0a\u8ba8\u8bba\u662f\u6ca1\u6709\u610f\u4e49\u7684\u3002\u4e00\u65b9\u9762\u5982\u524d\u6587\u6240\u8ff0\uff0c\u56e0\u679c\u95ed\u5408\u76f8\u6bd4\u4e8e\u4fe1\u606f\u95ed\u5408\u662f\u53e6\u4e00\u79cd\u5bf9\u7cfb\u7edf\u5b8f\u89c2\u8fc7\u7a0b\u66f4\u672c\u8d28\u7684\u63cf\u8ff0\uff1b\u53e6\u4e00\u65b9\u9762\uff0c\u5f53\u5b8f\u89c2\u8fc7\u7a0b\u56e0\u679c\u548c\u4fe1\u606f\u4e0d\u95ed\u5408\u7684\u65f6\u5019\uff0c\u4f5c\u8005\u8fd8\u8bc1\u660e\u4e86<\/span><\/span><\/span><\/span>\u673a\u5668\u603b\u6bd4<\/span><\/span><\/span><\/span>\u673a\u5668\u638c\u63e1\u66f4\u591a\u7684\u4fe1\u606f\uff0c\u662f\u4e00\u4e2a\u66f4\u5f3a\u6709\u529b\u7684\u8868\u5f81\u3002\u8bfb\u8005\u6ce8\u610f\uff0c\u8fd9\u91cc\u7684\u201c\u66f4\u5f3a\u201d\u5b9e\u9645\u4e0a\u6765\u81ea\u4e8e\u5fae\u89c2\u603b\u6bd4\u5b8f\u89c2\u6709\u66f4\u591a\u53ef\u80fd\u7684\u4fe1\u606f\uff0c\u8fd9\u4e0e\u5b8f\u89c2\u7684<\/span><\/span><\/span><\/span>\u673a\u5668\u5728\u53ea\u8003\u8651\u5b8f\u89c2\u5c3a\u5ea6\u81ea\u8eab\u4fe1\u606f\u65f6\u662f\u6700\u6709\u6548\u7684\u9884\u6d4b\u673a\u5236\u5e76\u4e0d\u77db\u76fe\u3002<\/span><\/span><\/p>\n


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

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<\/section>\n<\/section>\n<\/section>\n
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\u8ba1\u7b97\u95ed\u5408<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

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

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


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

\u4f5c\u8005\u4eec\u7684\u601d\u8003\u5230\u8fd9\u91cc\u8fd8\u6ca1\u6709\u7ed3\u675f\u3002\u5176\u5b9e\u4fe1\u606f\u95ed\u5408\u6216\u56e0\u679c\u95ed\u5408\u662f\u4e00\u4e2a\u6bd4\u8f83\u5f3a\u7684\u8981\u6c42\u3002\u5728\u5386\u53f2\u4e0a\uff0c\u6211\u4eec\u4e5f\u4e0d\u662f\u4e00\u8e74\u800c\u5c31\u53d1\u660e\u521b\u9020\u51fa\u4e86\u667a\u80fd\u624b\u673a\uff0c\u8fd9\u91cc\u9762\u6709\u5f88\u591a\u4e2d\u95f4\u5f62\u6001\u3002\u5728\u4eba\u7c7b\u53d1\u660e\u673a\u5668\u7684\u65e9\u671f\uff0c\u6211\u4eec\u4e00\u65b9\u9762\u5c1d\u8bd5\u642d\u5efa\u5b8f\u89c2\u7684\u7f16\u7801\u89c4\u5219\uff0c\u53e6\u4e00\u65b9\u9762\u6211\u4eec\u4e5f\u9700\u8981\u4e86\u89e3\u5fae\u89c2\u539f\u7406\u624d\u80fd\u66f4\u597d\u5730\u64cd\u4f5c\u673a\u5668\u3002\u5728\u8fd9\u4e2a\u9636\u6bb5\uff0c\u5bf9\u673a\u5668\u7cfb\u7edf\u7684\u7c97\u7c92\u5316\u4f9d\u7136\u6709\u597d\u574f\u4e4b\u5206\u3002\u5bf9\u4e8e\u4e00\u53f0\u673a\u5668\uff0c\u6211\u4eec\u80af\u5b9a\u5e0c\u671b\u5b83\u7684\u5b8f\u89c2\u7684\u8ba1\u7b97\u8fc7\u7a0b\u8981\u66f4\u52a0\u7684\u7b80\u6d01\uff0c\u4e5f\u5c31\u662f\u8bf4\u5b8f\u89c2\u7684<\/span><\/span><\/span><\/span>\u673a\u5668\u6700\u597d\u662f\u5fae\u89c2\u7684<\/span><\/span><\/span><\/span>\u673a\u5668\u7684\u4e00\u79cd\u7c97\u7c92\u5316\u3002 <\/span><\/span><\/p>\n

\u8fd9\u5c31\u662f\u8ba1\u7b97\u95ed\u5408\uff08Computational closure\uff09\u7684\u5b9a\u4e49\u3002\u96be\u9053\u5b8f\u89c2<\/span><\/span><\/span><\/span>\u673a\u5668\u8fd8\u53ef\u4ee5\u4e0d\u662f\u5fae\u89c2<\/span><\/span><\/span><\/span>\u673a\u5668\u7684\u7c97\u7c92\u5316\u5417\uff1f\u7c97\u7c92\u5316\u610f\u5473\u7740\u5b8f\u89c2\u53d8\u91cf\u662f\u5fae\u89c2\u53d8\u91cf\u7684\u5355\u5c04\u3002\u8fd9\u4e2a\u6620\u5c04\u8fc7\u7a0b\u53ef\u80fd\u5f15\u5165\u66f4\u591a\u7684\u566a\u97f3\uff0c\u5bfc\u81f4\u5b8f\u89c2\u8fc7\u7a0b\u7684\u56e0\u679c\u6001\u53cd\u800c\u6bd4\u5fae\u89c2\u7684\u8fd8\u8981\u591a\u3002\u6211\u4eec\u770b\u4e0b\u9762\u8fd9\u6837\u4e00\u4e2a\u4f8b\u5b50\uff1a <\/span><\/span><\/p>\n

\u8003\u8651\u4e00\u4e2a\u9a6c\u5c14\u53ef\u592b\u94fe <\/span><\/span><\/span><\/span>\uff0c\u6709\u4e09\u4e2a\u72b6\u6001<\/span><\/span><\/span><\/span>\u3001<\/span><\/span><\/span><\/span> \u548c <\/span><\/span><\/span><\/span>\u3002\u5047\u8bbe <\/span><\/span><\/span><\/span> \u548c <\/span><\/span><\/span><\/span> \u7684\u6240\u6709\u8f6c\u79fb\u6982\u7387\u5411\u91cf\u90fd\u76f8\u540c\u4e14\u4e3a\u6b63\u6570\u3002\u8fd9\u6837\uff0c\u5fae\u89c2<\/span><\/span><\/span><\/span>\u673a\u5668 <\/span><\/span><\/span><\/span> \u53ea\u6709\u4e24\u4e2a\u56e0\u679c\u6001\uff0c\u5206\u522b\u662f <\/span><\/span><\/span><\/span> \u548c <\/span><\/span><\/span><\/span>\u3002 <\/span><\/span><\/p>\n

\u73b0\u5728\u8fdb\u4e00\u6b65\u8bbe\u5b9a\uff0c<\/span><\/span><\/span><\/span> \u4e0d\u80fd\u8f6c\u79fb\u5230 <\/span><\/span><\/span><\/span>\uff0c\u800c\u4e14 <\/span><\/span><\/span><\/span> \u548c <\/span><\/span><\/span><\/span> \u7684\u8f6c\u79fb\u6982\u7387\u4e5f\u4e0d\u76f8\u540c\u3002\u5047\u8bbe\u6211\u4eec\u7684\u7c97\u7c92\u5316\u65b9\u6848\u4e3a\uff1a\u82e5 <\/span><\/span><\/span><\/span>\uff0c\u5219 <\/span><\/span><\/span><\/span>\uff1b\u82e5 <\/span><\/span><\/span><\/span> \u6216 <\/span><\/span><\/span><\/span>\uff0c\u5219 <\/span><\/span><\/span><\/span>\u3002 <\/span><\/span><\/p>\n

\u53ef\u4ee5\u8bc1\u660e\uff0c<\/span><\/span><\/span><\/span> \u4e0d\u662f\u9a6c\u5c14\u53ef\u592b\u7684\u3002\u7406\u7531\u662f\uff0c<\/span><\/span><\/span><\/span> \u8fde\u7eed\u5904\u4e8e <\/span><\/span><\/span><\/span> \u72b6\u6001\u7684\u65f6\u95f4\u8d8a\u957f\uff0c<\/span><\/span><\/span><\/span> \u7684\u6982\u7387\u5c31\u8d8a\u9ad8\uff08\u56e0\u4e3a <\/span><\/span><\/span><\/span> \u7684\u8f6c\u79fb\u88ab\u7981\u6b62\uff09\u3002\u7531\u4e8e <\/span><\/span><\/span><\/span> \u548c <\/span><\/span><\/span><\/span> \u8f6c\u79fb\u5230 <\/span><\/span><\/span><\/span> \u7684\u6982\u7387\u4e0d\u540c\uff0c\u56e0\u6b64 <\/span><\/span><\/span><\/span> \u7684<\/span><\/span><\/span><\/span>\u673a\u5668 <\/span><\/span><\/span><\/span> \u9700\u8981\u533a\u5206\u4ee5\u4e0d\u540c\u957f\u5ea6\u7684 <\/span><\/span><\/span><\/span> \u7ed3\u5c3e\u7684\u5386\u53f2\uff0c\u4f8b\u5982 <\/span><\/span><\/span><\/span>\u3002\u663e\u7136\uff0c<\/span><\/span><\/span><\/span> \u7684\u56e0\u679c\u6001\u591a\u4e8e <\/span><\/span><\/span><\/span> \u7684\u56e0\u679c\u6001\uff0c\u56e0\u6b64<\/span><\/span><\/span><\/span> \u4e0d\u53ef\u80fd\u662f<\/span><\/span><\/span><\/span>\u7684\u7c97\u7c92\u5316\u3002 <\/span><\/span><\/p>\n

\u6211\u4eec\u672c\u4ee5\u4e3a\uff0c\u628a\u5e95\u5c42\u7cfb\u7edf\u7528<\/span><\/span><\/span><\/span>\u673a\u5668\u63cf\u8ff0\u540e\uff0c\u5b8f\u89c2\u5c42\u7684\u03f5-\u673a\u53ef\u80fd\u53ea\u9700\u628a\u5e95\u5c42<\/span><\/span><\/span><\/span>\u673a\u5668\u7684\u72b6\u6001\u5408\u5e76\u5373\u53ef\u3002\u4f46\u4e8b\u5b9e\u8fdc\u975e\u5982\u6b64\u3002\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u539f\u59cb\u7cfb\u7edf\u67093\u4e2a\u72b6\u6001\uff0c\u4f46\u56e0\u4e3a<\/span><\/span><\/span><\/span>\u548c<\/span><\/span><\/span><\/span>\u770b\u8d77\u6765\u5b8c\u5168\u4e00\u6837\uff0c\u6240\u4ee5\u5fae\u89c2<\/span><\/span><\/span><\/span>\u673a\u5668\u53ea\u9700\u8981\u533a\u5206 <\/span><\/span><\/span><\/span> \u548c <\/span><\/span><\/span><\/span>\u4e24\u79cd\u72b6\u6001\u3002\u4f46\u5b8f\u89c2\u7684\u7c97\u7c92\u5316\u9009\u62e9\u5374\u662f\uff0c\u628a<\/span><\/span><\/span><\/span>\u548c<\/span><\/span><\/span><\/span>\u6620\u5c04\u5230\u4e00\u4e2a\u5b8f\u89c2\u72b6\u6001\u4e0a\u3002\u56e0\u4e3a\u5e95\u5c42\u52a8\u529b\u5b66\u7684\u7279\u6b8a\u6027\uff0c\u60f3\u9884\u6d4b\u4e0b\u4e00\u4e2a<\/span><\/span><\/span><\/span>\u4f55\u65f6\u51fa\u73b0\uff0c\u5b8f\u89c2\u03f5-\u673a\u9700\u8981\u8bb0\u4f4f\u6700\u8fd1\u8fde\u7eed\u51fa\u73b0\u4e86\u51e0\u4e2a<\/span><\/span><\/span><\/span>\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c<\/span>\u5b8f\u89c2\u884c\u4e3a\u5b9e\u9645\u4e0a\u589e\u52a0\u4e86\u8bb0\u5fc6\u957f\u5ea6<\/span>\uff0c\u9700\u8981\u65e0\u7a77\u591a\u4e2a\u4e0d\u540c\u7684\u56e0\u679c\u6001\uff0c\u800c\u4e0d\u4ec5\u4ec5\u662f\u7b80\u5355\u7684\u4e24\u79cd\u72b6\u6001\u3002\u6240\u4ee5\uff0c\u8fd9\u5e76\u4e0d\u662f\u4e00\u4e2a\u597d\u7684\u7c97\u7c92\u5316\u65b9\u6848\u3002 <\/span><\/span><\/p>\n

\u73b0\u5728\u6211\u4eec\u7528\u7a0d\u5fae\u62bd\u8c61\u4e00\u70b9\u7684\u56fe\u793a\u6765\u8bf4\u660e\u4e00\u822c\u60c5\u51b5\u4e0b\u7684\u8ba1\u7b97\u95ed\u5408\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c<\/span><\/span><\/span><\/span>\u548c<\/span><\/span><\/span><\/span>\u5206\u522b\u662f\u4e24\u4e2a\u7c97\u7c92\u5316\u6620\u5c04\u3002\u8ba1\u7b97\u95ed\u5408\u7684\u8981\u6c42\uff0c\u662f<\/span>\u5e0c\u671b\u4ece\u5fae\u89c2\u53d8\u91cf<\/span><\/span><\/span><\/span>\u5230\u5b8f\u89c2\u56e0\u679c\u6001<\/span><\/span><\/span><\/span>\u7684\u4e24\u6761\u6620\u5c04\u8def\u5f84\u662f\u53ef\u4ea4\u6362\u7684\uff0c\u5373<\/span><\/span><\/span><\/span>\u3002<\/span><\/span><\/p>\n

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

\u5982\u679c\u6ee1\u8db3\u8ba1\u7b97\u95ed\u5408\u7684\u8981\u6c42\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4ece\u8ba1\u7b97\u6a21\u578b\u7684\u89d2\u5ea6\u5bf9\u4e00\u4e2a\u7cfb\u7edf\u8fdb\u884c\u591a\u5c3a\u5ea6\u5efa\u6a21\uff0c\u5982\u4e0b\u56fe\u6240\u793a\u3002\u56fe\u4e2d\u7684\u6982\u7387\u5206\u5e03\u548c\u6709\u5411\u56fe\u8868\u793a\u7684\u90fd\u662f\u5404\u4e2a\u5c3a\u5ea6\u4e0a\u7684<\/span><\/span><\/span><\/span>\u673a\u5668\uff0c\u4e5f\u5c31\u662f\u5404\u4e2a\u5c3a\u5ea6\u4e0a\u7684\u6700\u4f73\u9884\u6d4b\u6a21\u578b\u3002<\/span>\u5728\u8003\u8651\u591a\u5c3a\u5ea6\u5efa\u6a21\u7684\u65f6\u5019\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5173\u6ce8\u5404\u4e2a\u5c3a\u5ea6<\/span><\/span><\/span><\/span>\u673a\u5668\u4e0a\u7684\u7c97\u7c92\u5316\u8fc7\u7a0b\u5373\u53ef\u3002 <\/span><\/span><\/p>\n

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


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<\/section>\n<\/section>\n<\/section>\n
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\u6848\u4f8b\u5206\u6790<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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

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


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

\u539f\u6587\u4e2d\u6709\u5f88\u591a\u66f4\u590d\u6742\u7684\u6848\u4f8b\u5206\u6790\uff0c\u56e0\u4e3a\u7bc7\u5e45\u6709\u9650\uff0c\u6211\u8fd9\u91cc\u4ec5\u4ecb\u7ecd\u6a21\u5757\u5316\u7f51\u7edc\u4e0a\u7684\u968f\u673a\u6e38\u8d70\u6848\u4f8b\u3002 <\/span><\/span><\/p>\n

\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u5047\u8bbe\u4e00\u4e2a\u7f51\u7edc\u7531\u597d\u51e0\u4e2a\u201c\u793e\u7fa4\u201d\u6216\u201c\u6a21\u5757\u201d\u7ec4\u6210\uff0c\u6bcf\u4e2a\u6a21\u5757\u5185\u90e8\u7684\u8fde\u63a5\u5f88\u5f3a\uff08\u5bb9\u6613\u4ece\u4e00\u4e2a\u8282\u70b9\u8df3\u5230\u53e6\u4e00\u4e2a\u8282\u70b9\uff09\uff0c\u6a21\u5757\u4e4b\u95f4\u5219\u8fde\u63a5\u5f88\u5f31\uff08\u4e00\u65e6\u8fdb\u4e86\u522b\u7684\u6a21\u5757\uff0c\u8981\u8df3\u51fa\u6765\u5f88\u96be\uff09\u3002\u6709\u4e00\u4e2a\u201c\u6e38\u8d70\u8005\u201d\uff08\u6bd4\u5982\u4e00\u4e2a\u9152\u9189\u7684\u4eba\uff09\uff0c\u6bcf\u4e00\u6b65\u4f1a\u968f\u673a\u51b3\u5b9a\u662f\u5426\u5728\u539f\u5730\u505c\u7559\u3001\u5728\u672c\u793e\u533a\u5185\u4e71\u901b\uff0c\u6216\u8005\u5076\u5c14\u8df3\u5230\u522b\u7684\u793e\u533a\u3002\u8fd9\u6837\u7684\u7f51\u7edc\u5728\u73b0\u5b9e\u4e2d\u5f88\u5e38\u89c1\uff0c\u6bd4\u5982\u793e\u4ea4\u7f51\u7edc\u4e2d\u7684\u5c0f\u5708\u5b50\u3001\u529f\u80fd\u5206\u533a\u7684\u4ea4\u901a\u7cfb\u7edf\u7b49\u3002<\/span><\/span><\/p>\n

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\u4ece\u5fae\u89c2\u5230\u5b8f\u89c2\uff0c\u6211\u4eec\u9996\u5148\u8fdb\u884c\u7684\u7c97\u7c92\u5316\u7b56\u7565\u662f\uff1a\u53ea\u5173\u6ce8\u201c\u6e38\u8d70\u8005\u5f53\u524d\u5728\u54ea\u4e2a\u6a21\u5757\/\u793e\u7fa4\u201d\uff0c\u4e0d\u5173\u5fc3\u4ed6\u5728\u6a21\u5757\u5185\u7684\u5177\u4f53\u4f4d\u7f6e\uff0c\u5982\u56fe\u4e2d\u7684A\u3001B\u3001C\u3001D\u3001E\u6240\u793a\u3002\u8fd9\u79cd\u7c97\u7c92\u5316\u6709\u4e2a\u91cd\u8981\u6027\u8d28\uff1a\u53ea\u8981\u4f60\u77e5\u9053\u73b0\u5728\u5728\u7b2c\u51e0\u4e2a\u793e\u533a\uff0c\u672a\u6765\u5728\u54ea\u4e2a\u793e\u533a\u4ec5\u4ec5\u53d6\u51b3\u4e8e\u73b0\u5728\u5728\u7684\u793e\u533a\uff0c\u800c\u4e0d\u53d6\u51b3\u4e8e\u5728\u8fd9\u4e2a\u793e\u533a\u91cc\u7684\u5177\u4f53\u70b9\u2014\u2014\u7c97\u7c92\u5316\u540e\u7684\u793e\u533a\u95f4\u8f6c\u79fb\u7684\u52a8\u6001\u662f\u56e0\u679c\u95ed\u5408\u7684\u3002 <\/span><\/span><\/p>\n

\u5728\u66f4\u5b8f\u89c2\u7684\u5c3a\u5ea6\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u53ea\u5173\u5fc3\u4ed6\u6240\u5728\u793e\u533a\u7684\u89c4\u6a21\uff0c\u800c\u4e0d\u662f\u5177\u4f53\u54ea\u4e00\u4e2a\u793e\u533a\u3002\u793e\u533aA\u3001B\u5206\u522b\u670925\u4e2a\u8282\u70b9\uff0cC\u3001D\u3001E\u5219\u5206\u522b\u67099\u4e2a\u8282\u70b9\u3002\u8fd9\u4fbf\u628a\u4ecb\u89c2\u5c3a\u5ea6\u4e0a\u76845\u4e2a\u53d8\u91cf\u7c97\u7c92\u5316\u5f97\u5230\u6700\u5b8f\u89c2\u7684\u4e24\u4e2a\u53d8\u91cf\u3002\u8fd9\u6837\u5f97\u5230\u7684\u5b8f\u89c2\u8fc7\u7a0b\u4e5f\u662f\u56e0\u679c\uff08\u4fe1\u606f\uff09\u95ed\u5408\u7684\u3002\u800c\u4e14\u6839\u636e\u4f5c\u8005\u5728\u6587\u4e2d\u8bc1\u660e\u7684\u5b9a\u7406\uff0c\u8fd9\u591a\u4e2a\u5c3a\u5ea6\u7684\u8fc7\u7a0b\u4e5f\u90fd\u662f\u8ba1\u7b97\u95ed\u5408\u7684\u3002\u4e09\u4e2a\u95ed\u5408\u8bf4\u660e\u6211\u4eec\u53ef\u4ee5\u5728\u4e0d\u8003\u8651\u5176\u4ed6\u5c3a\u5ea6\u7684\u60c5\u51b5\u4e0b\u5355\u72ec\u4e3a\u4e09\u4e2a\u5c3a\u5ea6\u4e0a\u7684\u53d8\u5316\u5efa\u6a21\uff0c\u6bd4\u5982\u5fae\u89c2\u4e0a\u7684\u968f\u673a\u6e38\u8d70\u52a8\u529b\u5b66\uff0c\u4ecb\u89c2\u4e0a\u793e\u533a\u95f4\u7684\u8f6c\u79fb\u52a8\u529b\u5b66\uff0c\u5b8f\u89c2\u4e0a\u4e0d\u540c\u89c4\u6a21\u793e\u533a\u95f4\u7684\u4ea4\u4e92\u89c4\u5f8b\u3002 <\/span><\/span><\/p>\n


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\u6982\u5ff5\u8fa8\u6790<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u5728\u5386\u53f2\u4e0a\uff0c\u5bf9\u4e8e\u9a6c\u5c14\u53ef\u592b\u7cfb\u7edf\u7684\u7c97\u7c92\u5316\uff0c\u5df2\u7ecf\u6709\u5b66\u8005\u63d0\u51fa\u6210\u5757\u6027\uff08Lumpability\uff09\u8fd9\u4e00\u6982\u5ff5\u6765\u7ea6\u675f\u7c97\u7c92\u5316\u51fd\u6570\u7684\u9009\u53d6\u3002\u6210\u5757\u6027\u548c\u95ed\u5408\u6027\u90fd\u662f\u5bf9\u7c97\u7c92\u5316\u9009\u53d6\u7684\u7ea6\u675f\u6761\u4ef6\uff0c\u6240\u4ee5\u6211\u4eec\u6765\u505a\u4e00\u4e2a\u6982\u5ff5\u7684\u68b3\u7406\u4e0e\u8fa8\u6790\u3002\u5bf9\u4e8e\u6210\u5757\u6027\u611f\u5174\u8da3\u7684\u8bfb\u8005\uff0c\u53ef\u8fdb\u4e00\u6b65\u901a\u8fc7\u96c6\u667a\u767e\u79d1\u8bcd\u6761\u3010\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u6210\u5757\u6027\u3011\u4e86\u89e3\u8fd9\u4e2a\u6982\u5ff5\u3002 \u5f3a\u6210\u5757\u6027\uff08Strong Lumpability\uff09\u662f\u6307\uff0c\u65e0\u8bba\u521d\u59cb\u5206\u5e03\u600e\u4e48\u9009\uff0c\u7c97\u7c92\u5316\u540e\u7684\u5b8f\u89c2\u8fc7\u7a0b\u90fd\u662f\u9a6c\u5c14\u53ef\u592b\u7684\uff0c\u8f6c\u79fb\u6982\u7387\u53ea\u7531\u5f53\u524d\u5b8f\u89c2\u72b6\u6001\u51b3\u5b9a\u3002\u4ece\u8fd9\u4e2a\u5b9a\u4e49\u4e0d\u96be\u770b\u51fa\uff0c\u5982\u679c\u4e00\u4e2a\u7c97\u7c92\u5316\u662f\u6ee1\u8db3\u5f3a\u6210\u5757\u6027\u7684\uff0c\u90a3\u4e48\u5b83\u5fc5\u7136\u662f\u56e0\u679c\u548c\u4fe1\u606f\u95ed\u5408\u7684\uff0c\u4e5f\u5c31\u5fc5\u7136\u662f\u8ba1\u7b97\u95ed\u5408\u7684\u3002<\/span><\/span><\/p>\n


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\u9a6c\u5c14\u53ef\u592b\u94fe\u8bcd\u6761<\/span><\/span><\/p>\n

\u5f31\u6210\u5757\u6027\uff08Weak Lumpability\uff09\u5219\u662f\u8bf4\uff0c\u53ea\u5728\u67d0\u4e9b\u521d\u59cb\u5206\u5e03\u6761\u4ef6\u4e0b\uff0c\u7c97\u7c92\u5316\u540e\u7684\u5b8f\u89c2\u8fc7\u7a0b\u662f\u9a6c\u5c14\u53ef\u592b\u7684\u3002\u5f3a\u5f31k\u9636\u6210\u5757\u6027\u4fbf\u662f\u5728\u524d\u9762\u5b9a\u4e49\u7684\u57fa\u7840\u4e0a\uff0c\u53ef\u4ee5\u653e\u5bbd\u8981\u6c42\uff0c\u8ba9\u5b8f\u89c2\u8fc7\u7a0b\u662fk\u9636\u9a6c\u5c14\u53ef\u592b\u8fc7\u7a0b\u5373\u53ef\u3002k\u8d8a\u5927\uff0c\u8981\u6c42\u8d8a\u5bbd\u677e\u3002\u4ece\u8bba\u6587[3]\u4e2d\u63d0\u4f9b\u7684\u793a\u610f\u56fe\u53ef\u4ee5\u770b\u51fa\uff0c\u9664\u4e86\u5f3a\u6210\u5757\u6027\u4ee5\u5916\uff0c\u95ed\u5408\u6027\u548c\u6210\u5757\u6027\u4e4b\u95f4\u6ca1\u6709\u5fc5\u7136\u7684\u5305\u542b\u6216\u88ab\u5305\u542b\u7684\u5173\u7cfb\u3002 <\/span><\/span><\/p>\n

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\u6210\u5757\u6027\u7684\u63d0\u51fa\u5bf9\u4e8e\u9a6c\u5c14\u53ef\u592b\u52a8\u529b\u7cfb\u7edf\u7684\u591a\u5c3a\u5ea6\u5efa\u6a21\u975e\u5e38\u5173\u952e\uff0c\u6bd4\u5982\u5728\u591a\u4e3b\u4f53\u5efa\u6a21\u4e2d\uff0c\u5e95\u5c42\u673a\u5236\u5f80\u5f80\u662f\u9a6c\u5c14\u53ef\u592b\u7684\uff0c\u6211\u4eec\u5e0c\u671b\u7c97\u7c92\u5316\u51fa\u6765\u7684\u5b8f\u89c2\u89c4\u5219\u4e5f\u80fd\u662f\u9a6c\u5c14\u53ef\u592b\u7684\u3002\u8fd9\u6837\u7814\u7a76\u8005\u53ef\u4ee5\u907f\u514d\u5728\u5fae\u89c2\u6a21\u578b\u4e0a\u9ad8\u6210\u672c\u7684\u6a21\u62df\uff0c\u53ef\u4ee5\u76f4\u63a5\u5728\u5b8f\u89c2\u5c3a\u5ea6\u4e0a\u8fdb\u884c\u8fed\u4ee3\u3002\u800c\u95ed\u5408\u6027\u5219\u66f4\u5173\u6ce8\u5b8f\u89c2\u7684\u5c3a\u5ea6\u662f\u5426\u80fd\u81ea\u6d3d\u3002\u5b83\u4eec\u7ea6\u675f\u7684\u89d2\u5ea6\u4e0d\u540c\uff0c\u4f46\u6700\u7ec8\u53ef\u4ee5\u6709\u4e00\u79cd\u6700\u7406\u60f3\u7684\u7c97\u7c92\u5316\u65b9\u5f0f\u540c\u65f6\u6ee1\u8db3\u6700\u9ad8\u8981\u6c42\u7684\u6210\u5757\u6027\u548c\u95ed\u5408\u6027\u3002 \u4e0b\u8868\u662f\u6587\u4e2d\u6d89\u53ca\u7684\u5173\u952e\u6982\u5ff5\u7684\u672f\u8bed\u8868\uff0c\u4f9b\u8bfb\u8005\u53c2\u8003\uff1a<\/span><\/span><\/p>\n

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\u8bb2\u5ea7\u63a8\u8350<\/span><\/span><\/span><\/p>\n


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\u8bba\u6587\u4e00\u4f5c\u662f\u8428\u585e\u514b\u65af\u5927\u5b66\u8bb2\u5e08Fernando Rosas\uff0c\u4ed6\u7684\u5b66\u4e60\u548c\u7814\u7a76\u7ecf\u5386\u975e\u5e38\u4e30\u5bcc\uff0c\u672c\u79d1\u5148\u540e\u83b7\u5f97\u97f3\u4e50\u7406\u8bba\u4e0e\u4f5c\u66f2\u3001\u6570\u5b66\u5b66\u58eb\u3002\u4ed6\u6709\u975e\u5e38\u660e\u786e\u7684\u79d1\u5b66\u76ee\u6807\uff1a\u63ed\u793a\u9a71\u52a8\u5206\u5e03\u5f0f\u591a\u667a\u80fd\u4f53\u7cfb\u7edf\u8ba1\u7b97\u7684\u8ff7\u4eba\u539f\u5219\uff1a\u5b83\u4eec\u5982\u4f55\u5b9e\u73b0\u6574\u4f53\u5927\u4e8e\u90e8\u5206\u4e4b\u548c\uff0c\u5171\u540c\u6267\u884c\u5355\u4e2a\u4e2a\u4f53\u65e0\u6cd5\u5b9e\u73b0\u7684\u4efb\u52a1\uff0c\u751a\u81f3\u4ea7\u751f\u9884\u5148\u672a\u5b9a\u4e49\u7684\u65b0\u7279\u6027\u3002\u96c6\u667a\u4ff1\u4e50\u90e8\u66fe\u9080\u8bf7\u4ed6\u6765\u505a\u8fc7\u5206\u4eab\uff0c\u626b\u7801\u5373\u53ef\u89c2\u770b\u3002<\/span><\/span><\/p>\n


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\u53c2\u8003\u6587\u732e<\/span><\/span><\/h1>\n

[1] L. Barnett and A. K. Seth, \u201cDynamical independence: discovering emergent macroscopic processes in complex dynamical systems,\u201d Physical Review E, vol. 108, no. 1, p. 014304, 2023.<\/span><\/span><\/p>\n

[2] J. P. Crutchfield, \u201cThe calculi of emergence: computation, dynamics and induction,\u201d Physica D: Nonlinear Phenomena, vol. 75, no. 1-3, pp. 11\u201354, 1994.<\/span><\/span><\/p>\n

[3] F. E. Rosas, et al. “Software in the natural world: A computational approach to hierarchical emergence.” arXiv preprint arXiv:2402.09090, 2024.<\/span><\/span><\/p>\n


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


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


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


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1. \u57fa\u4e8e\u6709\u6548\u4fe1\u606f\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\uff5c\u96c6\u667a\u767e\u79d1<\/span><\/a><\/span><\/strong>
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2.\u56e0\u679c\u6d8c\u73b0\u4e0e\u201c\u65f6\u95f4\u5012\u6d41\u201d\uff1a\u57fa\u4e8e\u53ef\u9006\u6027\u7684\u56e0\u679c\u6d8c\u73b0\u65b0\u7406\u8bba\uff5c\u96c6\u667a\u79d1\u5b66\u7814\u7a76\u4e2d\u5fc3\u6700\u65b0\u6210\u679c<\/span><\/a><\/span><\/strong>
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3.\u590d\u6742\u7f51\u7edc\u4e2d\u7684\u56e0\u679c\u6d8c\u73b0\uff5c\u96c6\u667a\u767e\u79d1<\/span><\/a><\/span><\/strong><\/section>\n
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6. <\/span><\/strong>\u63a2\u7d22\u8005\u8ba1\u5212 | \u96c6\u667a\u4ff1\u4e50\u90e82025\u5185\u5bb9\u56e2\u961f\u62db\u52df\uff08\u5168\u804c&\u517c\u804c\uff09<\/a><\/span><\/strong><\/span><\/p>\n


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