{"id":64256,"date":"2025-09-06T17:28:39","date_gmt":"2025-09-06T09:28:39","guid":{"rendered":"https:\/\/swarma.org\/?p=64256"},"modified":"2025-09-06T17:28:39","modified_gmt":"2025-09-06T09:28:39","slug":"%e4%bb%8e%e5%8f%af%e8%ae%a1%e7%ae%97%e6%80%a7%e7%90%86%e8%ae%ba%e7%90%86%e8%a7%a3%e6%a6%82%e7%8e%87%e7%9a%84%e6%9c%ac%e8%b4%a8","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=64256","title":{"rendered":"\u4ece\u53ef\u8ba1\u7b97\u6027\u7406\u8bba\u7406\u89e3\u6982\u7387\u7684\u672c\u8d28"},"content":{"rendered":"
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<\/strong>Kolmogorov\u4f7f\u7528\u4e86\u4e09\u6761\u516c\u7406\u5960\u5b9a\u4e86\u5f53\u4eca\u6982\u7387\u8bba\u7684\u57fa\u7840\u3002\u7136\u800c\u636e\u4f20\uff0c\u4ed6\u672c\u4eba\u5bf9\u6b64\u5e76\u4e0d\u6ee1\u610f\u3002\u672c\u6587\u5c06\u4ece\u53ef\u8ba1\u7b97\u6027\u7406\u8bba\u7684\u89d2\u5ea6\u5411\u60a8\u4ecb\u7ecd\u8d85\u8d8aKolmogorov\u516c\u7406\u7684\u5bf9\u4e8e\u6982\u7387\u8bba\u7684\u9c9c\u4e3a\u4eba\u77e5\u7684\u5168\u65b0\u7406\u89e3\u3002<\/span><\/span><\/strong><\/p>\n


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\u5173\u952e\u8bcd\uff1a\u6982\u7387\u8bba\u3001\u968f\u673a\u6027\u3001\u56fe\u7075\u505c\u673a\u3001Martin-L\u00f6f\u968f\u673a\u6027\u3001\u53ef\u8ba1\u7b97\u6027<\/span><\/strong><\/strong><\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\"\u56fe\u7247\"<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\u7f57\u6d69\u6e90\uff08\u5bbe\u5915\u6cd5\u5c3c\u4e9a\u5dde\u7acb\u5927\u5b66\u5728\u8bfb\u535a\u58eb\uff09\u4e28\u4f5c\u8005<\/span><\/span><\/section>\n<\/section>\n


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\u4e07\u80fd\u7684\u4e0a\u5e1d\u53ef\u4ee5\u89e3\u51fa\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\u5417<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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


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\u4e0a\u5e1d\u662f\u4e07\u80fd\u7684\u5417\uff1f\u5927\u6982\u4e0d\u662f\u5427\u3002\u54f2\u5b66\u5bb6\u7ed9\u51fa\u4e86\u8fd9\u6837\u7684\u8bba\u8ff0\u3002\u5982\u679c\u4e0a\u5e1d\u662f\u4e07\u80fd\u7684\uff0c\u90a3\u4ed6\u5e94\u8be5\u80fd\u521b\u9020\u4e00\u4e2a\u81ea\u5df1\u4e5f\u4e3e\u4e0d\u8d77\u6765\u7684\u77f3\u5934\u3002\u4f46\u5982\u679c\u4ed6\u81ea\u5df1\u4e5f\u4e3e\u4e0d\u8d77\u6765\u8fd9\u5757\u77f3\u5934\uff0c\u4ed6\u8fd8\u662f\u4e07\u80fd\u7684\u5417\uff1f\u6216\u8bb8\u60a8\u4f1a\u89c9\u5f97\u54f2\u5b66\u5bb6\u7684\u8fd9\u4e2a\u8be1\u8fa9\u8352\u8bde\u4e0d\u7ecf\uff0c\u4f46\u5982\u679c\u6211\u6362\u4e00\u4e2a\u95ee\u6cd5\uff0c\u60a8\u4f1a\u7acb\u9a6c\u610f\u8bc6\u5230\u5176\u4e2d\u7684\u4ef7\u503c\u3002<\/span><\/span><\/p>\n

\u6211\u4eec\u5199\u7a0b\u5e8f\u65f6\u90fd\u975e\u5e38\u8ba8\u538c\u7a0b\u5e8f\u9677\u5165\u6b7b\u5faa\u73af\uff0c\u90a3\u4e48\u662f\u5426\u5b58\u5728\u8fd9\u6837\u4e00\u4e2a\u5168\u77e5\u5168\u80fd\u7684\u7a0b\u5e8f \uff0c\u6211\u4eec\u8f93\u5165\u4e00\u4e2a\u7a0b\u5e8f\u6e90\u4ee3\u7801\u7684\u5b57\u7b26\u4e32 \uff0c\u4ee5\u53ca\u6253\u7b97\u5582\u7ed9\u8be5\u7a0b\u5e8f\u7684\u8f93\u5165\u5b57\u7b26\u4e32\uff0c\u5b83\u53ef\u4ee5\u81ea\u52a8\u5224\u65ad\u6e90\u7801\u6240\u63cf\u8ff0\u7684\u7a0b\u5e8f\u5728\u8f93\u5165\u5b57\u7b26\u4e32\u4e0a\u662f\u5426\u4f1a\u9677\u5165\u6b7b\u5faa\u73af\u3002\u5982\u679c\u5047\u8bbe\u8fd9\u6837\u7684\u7a0b\u5e8f\u5b58\u5728\uff0c\u901a\u8fc7\u7c7b\u4f3c\u4e8e\u4e0a\u9762\u5173\u4e8e\u4e07\u80fd\u4e0a\u5e1d\u7684\u8ba8\u8bba\uff0c\u6211\u4eec\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u63a8\u51fa\u77db\u76fe\uff0c\u4ece\u800c\u8bc1\u4f2a\u8fd9\u4e2a\u547d\u9898\u3002<\/span><\/span><\/p>\n

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\u56fe\u7075\u505c\u673a\u95ee\u9898\u7684\u63a8\u7406\u8fc7\u7a0b\uff1a<\/span><\/span><\/span><\/p>\n

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  1. \n

    \u5047\u8bbe\u5b58\u5728\u8fd9\u6837\u4e00\u4e2a\u5168\u77e5\u5168\u80fd\u7684\u7a0b\u5e8f H\uff0c\u5b83\u80fd\u5224\u65ad\u4efb\u610f\u4e00\u4e2a\u7a0b\u5e8f P \u548c\u8f93\u5165 I\uff0cP \u5728\u8f93\u5165 I \u65f6\u662f\u5426\u4f1a\u505c\u673a\uff08\u4e0d\u4f1a\u6b7b\u5faa\u73af\uff09\u3002<\/span><\/span><\/p>\n<\/li>\n

      \n
    1. \n

        if H(P,I) == “\u4f1a\u505c\u673a”:<\/span><\/span><\/p>\n

        return “\u662f” # \u4e0d\u4f1a\u6b7b\u5faa\u73af<\/span><\/span><\/p>\n

        else:<\/span><\/span><\/p>\n

        return “\u5426” # \u6b7b\u5faa\u73af<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n

    2. \n

      \u6784\u9020\u4e00\u4e2a\u65b0\u7a0b\u5e8f D\uff0c\u5b83\u7684\u884c\u4e3a\u5982\u4e0b\uff1a<\/span><\/span><\/p>\n

      <\/span><\/li>\n

        <\/ul>\n
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        • \n

          D \u63a5\u53d7\u4e00\u4e2a\u7a0b\u5e8f Q \u4f5c\u4e3a\u8f93\u5165\u3002<\/span><\/p>\n<\/li>\n

        • \n

          D(Q) \u7684\u903b\u8f91\uff1a<\/span><\/p>\n<\/li>\n<\/ul>\n<\/ol>\n

            \n
          • \n

            \u7528 H(Q, Q) \u5224\u65ad Q \u5728\u8f93\u5165 Q \u65f6\u662f\u5426\u4f1a\u505c\u673a\u3002<\/span><\/span><\/p>\n<\/li>\n

          • \n

            \u5982\u679c H(Q, Q) \u8bf4\u201c\u4f1a\u505c\u673a\u201d\uff0c\u5219\u8ba9 D(Q) \u8fdb\u5165\u6b7b\u5faa\u73af\u3002<\/span><\/span><\/p>\n<\/li>\n

          • \n

            \u5982\u679c H(Q, Q) \u8bf4\u201c\u4e0d\u4f1a\u505c\u673a\u201d\uff0c\u5219\u8ba9 D(Q) \u7acb\u523b\u505c\u673a\u3002<\/span><\/span><\/p>\n<\/li>\n<\/ul>\n

                 def D(Q):<\/span><\/span><\/p>\n

                    if H(Q, Q) == “\u4f1a\u505c\u673a”:<\/span><\/span><\/p>\n

                        while True:  # \u6b7b\u5faa\u73af<\/span><\/span><\/p>\n

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

                    else:<\/span><\/span><\/p>\n

                        return 0  # \u7acb\u523b\u505c\u673a<\/span><\/span>
            <\/span><\/span><\/p>\n

            3. \u8ba9 D \u8f93\u5165\u81ea\u5df1 D(D)<\/span><\/span><\/p>\n

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              • \n

                \u5982\u679c H(D, D) \u8bf4\u201c\u4f1a\u505c\u673a\u201d\uff0c\u90a3\u4e48\u6839\u636e D \u7684\u5b9a\u4e49\uff0cD(D) \u4f1a\u6b7b\u5faa\u73af\uff08\u77db\u76fe\uff09\u3002<\/span><\/span><\/p>\n<\/li>\n

              • \n

                \u5982\u679c H(D, D) \u8bf4\u201c\u4e0d\u4f1a\u505c\u673a\u201d\uff0c\u90a3\u4e48\u6839\u636e D \u7684\u5b9a\u4e49\uff0cD(D) \u4f1a\u7acb\u523b\u505c\u673a\uff08\u77db\u76fe\uff09\u3002<\/span><\/span><\/p>\n<\/li>\n

              • \n

                \u4e5f\u5c31\u662f\u8bf4\uff0c\u65e0\u8bba H \u600e\u4e48\u5224\u65ad\uff0c\u90fd\u4f1a\u4ea7\u751f\u77db\u76fe\u3002<\/span><\/span><\/p>\n<\/li>\n<\/ul>\n<\/ol>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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


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

                \u201c\u5224\u65ad\u7a0b\u5e8f\u662f\u5426\u9677\u5165\u6b7b\u5faa\u73af\u201d\u5c31\u662f\u5927\u540d\u9f0e\u9f0e\u7684\u505c\u673a\u95ee\u9898\uff0c\u8fd9\u4e2a\u5168\u77e5\u5168\u80fd\u7684\u7a0b\u5e8f\u5e76\u4e0d\u5b58\u5728\u5c31\u662f\u4eba\u4eec\u5e38\u8bf4\u7684\u505c\u673a\u95ee\u9898\u4e0d\u53ef\u5224\u5b9a\u3002\u4f46\u7a0d\u5fae\u4e86\u89e3\u8fc7\u6570\u5b66\u53f2\u7684\u8bfb\u8005\u5f88\u5feb\u4fbf\u80fd\u610f\u8bc6\u5230\uff0c\u8fd9\u5c31\u662f\u5f15\u8d77\u7b2c\u4e09\u6b21\u6570\u5b66\u5371\u673a\u7684\u7f57\u7d20\u6096\u8bba\u7684\u53d8\u4f53\uff0c\u800c\u8fd9\u4e0e\u54e5\u5fb7\u5c14\u4e0d\u5b8c\u5907\u6027\u5b9a\u7406\u4e5f\u6709\u5343\u4e1d\u4e07\u7f15\u7684\u8054\u7cfb\u3002\u4e0a\u9762\u5173\u4e8e\u505c\u673a\u95ee\u9898\u7684\u8bba\u8ff0\u5e76\u6ca1\u6709\u4f7f\u7528\u4efb\u4f55\u5177\u4f53\u7684\u6784\u9020\uff0c\u4f46\u5374\u6e05\u695a\u5730\u8868\u660e\u4e86\u4e00\u4e2a\u4e8b\u5b9e\uff0c\u5373\u4fbf\u8ba1\u7b97\u673a\u89e3\u51b3\u4e86\u5f53\u4eca\u65e0\u6570\u7684\u96be\u9898\uff0c\u521b\u9020\u4e86\u65e0\u5c3d\u7684\u8d22\u5bcc\uff0c\u603b\u6709\u4e00\u4e9b\u95ee\u9898\u662f\u6c38\u8fdc\u6ca1\u6709\u529e\u6cd5\u4f7f\u7528\u8ba1\u7b97\u673a\u89e3\u7b54\u7684\uff0c\u91cf\u5b50\u8ba1\u7b97\u673a\u4e5f\u4e0d\u884c\u3002\u6211\u4eec\u79f0\u8fd9\u7c7b\u95ee\u9898\u662f\u4e0d\u53ef\u8ba1\u7b97\u7684\u3002\u4f5c\u8005\u5728\u540e\u6587\u5c06\u4f1a\u6307\u51fa\uff0c\u6211\u4eec\u80fd\u591f\u7cbe\u786e\u8ba1\u7b97\u7684\u95ee\u9898\u5176\u5b9e\u5c11\u5f97\u53ef\u601c\u3002<\/span><\/span><\/p>\n

                \u4e8b\u5b9e\u4e0a\uff0c\u5982\u679c\u8fd9\u6837\u4e00\u4e2a\u5168\u77e5\u5168\u80fd\u7684\u7a0b\u5e8f\u771f\u7684\u5b58\u5728\uff0c\u5b83\u53ef\u4ee5\u8f7b\u677e\u5730\u56de\u7b54\u5f53\u4eca\u56f0\u6270\u65e0\u6570\u6570\u5b66\u5bb6\u7684\u96be\u9898\u3002\u4f8b\u5982\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\uff1a<\/span><\/span>\u4efb\u4e00\u5927\u4e8e2\u7684\u5076\u6570\u90fd\u53ef\u5199\u6210\u4e24\u4e2a\u7d20\u6570\u4e4b\u548c\u3002<\/span><\/span><\/strong><\/span><\/p>\n

                \u6211\u4eec\u53ea\u9700\u8981\u5199\u4e00\u4e2a\u7a0b\u5e8f\uff0c\u5176\u4e2d\u4f7f\u7528while\u5faa\u73af\u4f9d\u6b21\u679a\u4e3e\u5927\u4e8e2\u7684\u6240\u6709\u5076\u6570\uff0c\u5728\u5faa\u73af\u4f53\u4e2d\u4f9d\u6b21\u5c1d\u8bd5\u6240\u6709\u4e0d\u5927\u4e8e\u5f53\u524d\u5076\u6570\u7684\u7d20\u6570\u7ec4\u5408\uff0c\u770b\u770b\u5176\u4e2d\u662f\u5426\u6709\u4e00\u4e2a\u7ec4\u5408\u80fd\u6ee1\u8db3\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\u7684\u8981\u6c42\u3002\u5982\u679c\u67d0\u4e2a\u5076\u6570\u4e0d\u80fd\u6ee1\u8db3\u8981\u6c42\uff0c\u4f7f\u7528break\u8bed\u53e5\u7ec8\u6b62while\u5faa\u73af\u7136\u540e\u8f93\u51fa0\uff0c\u53cd\u4e4b\u5c31\u4e00\u76f4\u8ba1\u7b97\u4e0b\u53bb\u3002<\/span><\/span><\/p>\n

                \u82e5\u8fd9\u6837\u7684\u5168\u77e5\u5168\u80fd\u7684\u7a0b\u5e8f\u771f\u7684\u5b58\u5728\uff0c\u6211\u4eec\u53ea\u9700\u8981\u7528\u5b83\u5224\u65ad\u4e00\u4e0b\u4e0a\u4e00\u6bb5\u4e2d\u6240\u63cf\u8ff0\u7684\u7a0b\u5e8f\u662f\u5426\u4f1a\u9677\u5165\u6b7b\u5faa\u73af\u4fbf\u53ef\u4ee5\u8f7b\u800c\u6613\u4e3e\u5730\u77e5\u9053\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\u662f\u5426\u6b63\u786e\u3002\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\u81f3\u4eca\u4ecd\u672a\u88ab\u5b8c\u5168\u8bc1\u660e\u7684\u4e8b\u5b9e\u4e5f\u4ece\u4fa7\u9762\u5370\u8bc1\u4e86\u8fd9\u6837\u7684\u5168\u77e5\u5168\u80fd\u7684\u7a0b\u5e8f\u5e76\u4e0d\u5b58\u5728\uff0c\u4e0d\u53ef\u8ba1\u7b97\u7684\u95ee\u9898\u662f\u5f88\u591a\u7684\u3002\u4f46\u4e0d\u53ef\u8ba1\u7b97\u5e76\u4e0d\u610f\u5473\u7740\u6211\u4eec\u65e0\u80fd\u4e3a\u529b\uff0c<\/span><\/span>\u5728Martin-L\u00f6f\u968f\u673a\u6027\u7684\u89c2\u70b9\u4e0b\uff0c\u6b63\u662f\u4ece\u4e0d\u53ef\u8ba1\u7b97\u7684\u5c40\u9650\u6027\u4e2d\u6d8c\u73b0\u51fa\u4e86\u6982\u7387\u3002<\/span><\/span><\/strong><\/span><\/p>\n


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

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

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                <\/section>\n<\/section>\n<\/section>\n
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                \u6570\u5b66\u4e0a\u4e00\u4e2a\u7a0b\u5e8f\u957f\u5565\u6837<\/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

                <\/section>\n

                \u56fe\u7075\u57281936\u5e74\u63d0\u51fa\u4e86\u8ba1\u7b97\u673a\u7684\u7406\u8bba\u6a21\u578b\u2014\u2014\u56fe\u7075\u673a\u3002\u4e0a\u56fe\u4fbf\u662f\u56fe\u7075\u673a\u7684\u793a\u610f\u56fe\u3002\u65e0\u7a77\u957f\u7684\u7eb8\u5e26\u4e0a\uff0c\u6bcf\u4e00\u683c\u53ef\u4ee5\u6253\u70b9\u4e5f\u53ef\u4ee5\u7559\u7a7a\uff0c\u6709\u4e00\u4e2a\u8bfb\u53d6\u5199\u5165\u5934\u5728\u7eb8\u5e26\u4e0a\u79fb\u52a8\uff0c\u5e76\u4fee\u6539\u7eb8\u5e26\u4e0a\u7684\u6570\u636e\u3002\u8bfb\u53d6\u5199\u5165\u5934\u6709\u5f88\u591a\u4e0d\u540c\u7684\u72b6\u6001\uff0c\u4ee5\u53ca\u4e00\u7cfb\u5217\u7684\u6307\u4ee4\u3002\u4f8b\u5982\uff0c\u5728\u4e0a\u56fe\u4e2d\uff0c(qi, _ , qj , * , \u2190)\u6307\u4ee4\u7684\u542b\u4e49\u662f\uff0c\u82e5\u8bfb\u53d6\u5199\u5165\u5934\u5f53\u524d\u662f\u201cqi\u201d\uff0c\u5f53\u524d\u8bfb\u5230\u4e86\u7a7a\u683c\u201c_\u201d\uff0c\u90a3\u4e48\u5c06\u5f53\u524d\u72b6\u6001\u6539\u4e3a\u201cqj\u201d\uff0c\u5728\u5f53\u524d\u7a7a\u683c\u4e2d\u5199\u5165\u201c*\u201d\uff0c\u6700\u540e\u5411\u5de6\u624b\u79fb\u52a8\u3002\u800c\u5728\u56fe\u7247\u6240\u8868\u793a\u7684\u4f8b\u5b50\u4e2d\uff0c\u8bfb\u53d6\u5199\u5165\u5934\u7684\u5f53\u524d\u72b6\u6001\u662f\u201cqk\u201d\uff0c\u8bfb\u53d6\u5230\u7684\u4fe1\u606f\u662f\u201c*\u201d\uff0c\u4e8e\u662f\u5339\u914d\u5230\u7b2c\u4e8c\u6761\u6307\u4ee4\uff0c\u5c06\u5f53\u524d\u72b6\u6001\u6539\u4e3a\u201cqh\u201d\uff0c\u64e6\u9664\u5f53\u524d\u683c\u5b50\u4e2d\u7684\u201c*\u201d\uff0c\u6700\u540e\u5411\u53f3\u79fb\u52a8\u3002\u8bfb\u53d6\u5199\u5165\u5934\u6709\u4e00\u4e2a\u6700\u7ec8\u72b6\u6001\uff0c\u5f53\u8fbe\u5230\u6700\u7ec8\u72b6\u6001\u540e\u5b83\u505c\u6b62\u5de5\u4f5c\uff0c\u6b64\u65f6\u6211\u4eec\u79f0\u56fe\u7075\u673a\u505c\u673a\uff0c\u8868\u793a\u8ba1\u7b97\u5b8c\u6210\uff0c\u800c\u7eb8\u5e26\u4e0a\u7684\u4fe1\u606f\u5c31\u662f\u8ba1\u7b97\u7684\u7ed3\u679c\u3002<\/span><\/span><\/p>\n

                \u56fe\u7075\u673a\u523b\u753b\u4e86\u4eba\u7c7b\u548c\u8ba1\u7b97\u673a\u7684\u8ba1\u7b97\u8fc7\u7a0b\uff0c\u662f\u4e00\u4e2a\u76f8\u5f53\u6210\u529f\u7684\u6a21\u578b\u3002\u4f46\u82e5\u60f3\u8981\u7814\u7a76\u5230\u5e95\u4ec0\u4e48\u95ee\u9898\u662f\u53ef\u8ba1\u7b97\u7684\uff0c\u4ec0\u4e48\u662f\u4e0d\u53ef\u8ba1\u7b97\u7684\uff0c\u76f4\u63a5\u6784\u9020\u56fe\u7075\u673a\u5199\u51fa\u6307\u4ee4\u8fd8\u662f\u592a\u9ebb\u70e6\u4e86\u3002\u56de\u60f3\u6211\u4eec\u5728\u5b9e\u9645\u7f16\u7a0b\u4e2d\u662f\u5982\u4f55\u64cd\u4f5c\u7684\uff0c\u6211\u4eec\u628a\u673a\u5668\u8bed\u8a00\u5c01\u88c5\u6210\u6c47\u7f16\u8bed\u8a00\uff0c\u53c8\u628a\u6c47\u7f16\u8bed\u8a00\u5c01\u88c5\u6210\u5176\u4ed6\u9ad8\u7ea7\u8bed\u8a00\uff0c\u901a\u8fc7\u4ee3\u7801\u5e93\u7684\u590d\u7528\u7b80\u5316\u6211\u4eec\u7684\u601d\u7ef4\u8fc7\u7a0b\u3002<\/span><\/span>\u4e8e\u662f\u6570\u5b66\u5bb6\u5c06\u56fe\u7075\u673a\u53ef\u4ee5\u5b9e\u73b0\u7684\u57fa\u672c\u64cd\u4f5c\u5c01\u88c5\u6210\u4e86\u5982\u4e0b\u76845\u4e2aapi<\/span><\/span><\/strong>\u3002\u8003\u8651\u6ee1\u8db3\u5982\u4e0b\u516c\u7406\u7684\u3001\u8f93\u5165\u662f\u6709\u9650\u4f4d\u81ea\u7136\u6570\u3001\u8f93\u51fa\u662f\u4e00\u4e2a\u81ea\u7136\u6570\u7684\u51fd\u6570\u7684\u6700\u5c0f\u96c6\u5408 C\u3002\u5b83\u4eec\u6ee1\u8db3\uff1a<\/span><\/span><\/span><\/p>\n

                  \n
                1. \n

                  \u81ea\u589e\u51fd\u6570\u5728C\u4e2d\u3002\u5373C\u4e2d\u5b58\u5728\u4e00\u4e2a\u51fd\u6570s, s(n)=n+1\u3002<\/span><\/span><\/p>\n<\/li>\n

                2. \n

                  \u6240\u6709\u7684\u5e38\u6570\u51fd\u6570\u5728C\u4e2d\u3002\u5373\u5bf9\u4e8e\u4efb\u610f\u7684m\uff0c\u90fd\u5b58\u5728\u4e00\u4e2a\u51fd\u6570cm, cm(x1, \u2026, xk)=m\uff0ccm\u5728\u51fd\u6570\u96c6\u5408C\u4e2d\u3002<\/span><\/span><\/p>\n<\/li>\n

                3. \n

                  \u6295\u5f71\u51fd\u6570\u5728C\u4e2d\u3002\u5373\u5bf9\u4e8e\u4efb\u610f\u7684\u6b63\u6574\u6570k\u548c\u4e0d\u5927\u4e8ek\u7684\u6b63\u6574\u6570i\uff0c\u5230\u7b2ci\u4f4d\u7684\u6295\u5f71pi(x1, \u2026 , xk)=xi \u5728C\u4e2d\u3002<\/span><\/span><\/p>\n<\/li>\n

                4. \n

                  \u51fd\u6570\u7684\u590d\u5408\u5728C\u4e2d\u3002\u5373\uff0c\u82e5g1, \u2026 gk \u548ch\u5728C\u4e2d\uff0c\u90a3\u4e48h(g1, \u2026 , gk)\u4e5f\u5728C\u4e2d\u3002<\/span><\/span><\/p>\n<\/li>\n

                5. \n

                  \u9012\u5f52\u51fd\u6570\u5728C\u4e2d\u3002\u5373\uff0c\u82e5g\u548ch\u5728C\u4e2d\uff0cg\u7684\u8f93\u5165\u4e3ak\u5143\u81ea\u7136\u6570\u6570\u7ec4\uff0ch\u7684\u8f93\u5165\u4e3ak+2\u5143\u81ea\u7136\u6570\u6570\u7ec4\uff0c\u5219\u5728C\u4e2d\u5b58\u5728\u51fd\u6570f\uff0c\u6ee1\u8db3f(0, x1, \u2026 , xk)=g(x1, \u2026 xk), \u4e14f(n+1, x1, \u2026 xk)=h(n, x1, \u2026 xk, f(n, x1, \u2026 xk))\u3002<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n

                  \u6570\u5b66\u5bb6\u4eec\u628a\u8fd9\u6837\u6700\u5c0f\u7684\u51fd\u6570\u96c6\u5408C\u53eb\u505a<\/span><\/span>\u539f\u59cb\u9012\u5f52\u51fd\u6570\uff08primitive recursive function\uff09<\/span><\/span><\/strong>\uff0c\u4e5f\u5c31\u662f\u4f7f\u7528\u8fd9\u4e94\u4e2aapi\u53ef\u4ee5\u7ec4\u5408\u51fa\u7684\u6240\u6709\u8fd0\u7b97\u7684\u5168\u4f53<\/span><\/span>\u3002<\/span><\/span><\/strong>\u8fd9\u4e94\u4e2a\u201c\u57fa\u7840api\u201d\u6216\u8005\u4e94\u6761\u516c\u7406\u770b\u4f3c\u5e73\u5e73\u65e0\u5947\uff0c\u4f46\u662f\u5343\u4e07\u4e0d\u8981\u56e0\u6b64\u5c0f\u770b\u4e86\u539f\u59cb\u9012\u5f52\u51fd\u6570\uff0c\u4e8b\u5b9e\u4e0a\uff0c\u901a\u8fc7\u539f\u59cb\u9012\u5f52\u51fd\u6570\u6211\u4eec\u53ef\u4ee5\u8868\u8fbe\u51fa\u4efb\u4f55\u4e0d\u4f7f\u7528while\u5faa\u73af\u7684\u7b97\u6cd5\u3002\u82e5\u60a8\u4e0d\u4fe1\uff0c\u60a8\u53ef\u4ee5\u81ea\u5df1\u52a8\u624b\u8bd5\u8bd5\u3002<\/span><\/span><\/span><\/p>\n

                  \u901a\u8fc7\u9012\u5f52\u51fd\u6570\uff0c\u6211\u4eec\u53ef\u4ee5\u8868\u8fbe\u51fa\u52a0\u6cd5\uff0c\u6709\u4e86\u52a0\u6cd5\uff0c\u4f7f\u7528\u9012\u5f52\u4fbf\u6709\u4e86\u4e58\u6cd5\u3002\u901a\u8fc7\u9012\u5f52\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u5b9a\u4e49\u51cf\u6cd5\uff0c\u53ea\u4e0d\u8fc7a-b\u5728b\u6bd4a\u5927\u65f6\u8f93\u51fa0\u3002\u901a\u8fc7\u9012\u5f52\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u5b9a\u4e49\u4e00\u4e2a\u51fd\u6570\u03c3\uff0c\u5b83\u5728\u4efb\u610f\u975e\u96f6\u81ea\u7136\u6570\u4e0a\u8f93\u51fa1\uff0c\u800c\u57280\u4e0a\u8f93\u51fa0\uff0c\u4e8e\u662f\u53ea\u9700\u8981\u8ba1\u7b97\u03c3(a-b)\uff0c\u4fbf\u53ef\u4ee5\u6bd4\u8f83a\u548cb\u7684\u5927\u5c0f\u3002\u4ece\u800c\u7c7b\u4f3c\u5730\u53ef\u4ee5\u5b9a\u4e49\u5e03\u5c14\u8fd0\u7b97\u3002\u800c\u5982\u679cf\u662f\u4e00\u4e2a\u5224\u65ad\u51fd\u6570\uff0c\u5f53\u6761\u4ef6\u6ee1\u8db3\u65f6\u8f93\u51fa1\uff0c\u53cd\u4e4b\u8f93\u51fa0\uff0c\u4f7f\u7528\u4e58\u6cd5\uff0cf*g+(1-f)*h\uff0c\u4fbf\u662f\u4e00\u6761if-else\u8bed\u53e5\uff0c\u5f53f\u7684\u6761\u4ef6\u6ee1\u8db3\u65f6\u8be5\u8868\u8fbe\u5f0f\u8f93\u51fa\u51fd\u6570g\u7684\u8ba1\u7b97\u7ed3\u679c\uff0c\u53cd\u4e4b\u5219\u8f93\u51fah\u7684\u8ba1\u7b97\u7ed3\u679c\u3002\u540c\u65f6\u901a\u8fc7\u9012\u5f52\u6211\u4eec\u8fd8\u53ef\u4ee5\u5b9a\u4e49do\u5faa\u73af\u3002<\/span><\/span><\/p>\n

                  \u770b\u5230\u8fd9\u91cc\u60a8\u6216\u8bb8\u4f1a\u95ee\uff0c\u539f\u59cb\u9012\u5f52\u51fd\u6570\u786e\u5b9e\u6709\u5f88\u5f3a\u7684\u8868\u8fbe\u80fd\u529b\uff0c\u4f46\u662f\u5404\u79cd\u5217\u8868\u64cd\u4f5c\u5b83\u80fd\u505a\u5230\u5417\uff1f\u7b54\u6848\u662f\u80fd\uff01\u901a\u8fc7\u539f\u59cb\u9012\u5f52\u51fd\u6570\uff0c\u6211\u4eec\u53ef\u4ee5\u8868\u793a\u51fa\u5e26\u4f59\u6570\u7684\u9664\u6cd5\uff0c\u4ece\u800c\u53ef\u4ee5\u901a\u8fc7\u9664\u6cd5\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002\u6211\u4eec\u628a\u5217\u8868\u7684\u5404\u4e2a\u5143\u7d20\u85cf\u5728\u81ea\u7136\u6570\u7684\u56e0\u6570\u4e2d\u5373\u53ef\u3002\u4f8b\u59822^5*3^8*5^1*7^10\uff0c\u5c31\u8868\u793a\u4e00\u4e2a(5, 8, 1, 10)\u7684\u52a8\u6001\u5217\u8868\u3002<\/span><\/span><\/p>\n

                  \u81f3\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u80af\u5b9a\uff0c<\/span><\/span>\u6240\u6709\u4e0d\u4f7f\u7528while\u5faa\u73af\u7684\u7b97\u6cd5\u90fd\u53ef\u4ee5\u7528\u4e00\u4e2a\u539f\u59cb\u9012\u5f52\u51fd\u6570\u6765\u8868\u793a<\/span><\/span><\/strong>\uff0c\u540c\u65f6\u56e0\u4e3a\u6ca1\u6709\u4f7f\u7528while\u5faa\u73af\uff0c\u539f\u59cb\u9012\u5f52\u51fd\u6570\u90fd\u4f1a\u5728\u6709\u9650\u6b65\u4e4b\u5185\u505c\u6b62\u5e76\u7ed9\u51fa\u786e\u5b9a\u7684\u7ed3\u679c\uff0c<\/span><\/span>\u6240\u4ee5\u539f\u59cb\u9012\u5f52\u51fd\u6570\u90fd\u662f\u53ef\u8ba1\u7b97\u7684<\/span><\/span><\/strong>\uff08\u4f46\u5e76\u975e\u6240\u6709\u53ef\u8ba1\u7b97\u51fd\u6570\u90fd\u662f\u539f\u59cb\u9012\u5f52\u51fd\u6570\uff0c\u56e0\u4e3a\u67d0\u4e9b\u4f7f\u7528\u4e86while\u5faa\u73af\u7684\u7b97\u6cd5\u4e5f\u53ef\u4ee5\u7ed9\u51fa\u786e\u5b9a\u7684\u7ed3\u679c\uff09\u3002\u6ca1\u6709while\u5faa\u73af\uff0c\u6211\u4eec\u7684api\u8fd8\u662f\u4e0d\u591f\u5f3a\u5927\u3002\u90a3\u4e48\uff0cwhile\u5faa\u73af\u5462\uff1f\u5176\u5b9e\u6211\u4eec\u53ea\u9700\u8981\u518d\u5c01\u88c5\u4e00\u4e2aapi\u6216\u8005\u8bf4\u5728\u96c6\u5408 C\u4e2d\u518d\u52a0\u4e00\u6761\u516c\u7406\uff1a<\/span><\/span><\/span><\/p>\n

                    \n
                  1. \n

                    \u82e5\u4e00\u4e2ak+1\u4f4d\u8f93\u5165\u7684\u51fd\u6570\u03b8\u5728C\u4e2d\uff0c\u90a3\u4e48\u5728C\u4e2d\u6709\u4e00\u4e2a\u51fd\u6570\u03c8(x1, \u2026 , xk)\uff0c\u82e5\u03b8(x1, \u2026 xk, i) \u5728i<n\u65f6\u90fd\u6709\u786e\u5b9a\u7684\u8f93\u51fa0\uff0c\u800c\u5728i=n\u65f6\u6709\u786e\u5b9a\u7684\u8f93\u51fa1\uff0c\u5219\u8ba9\u03c8\u8f93\u51fan\uff0c\u8868\u793a\u4e3a\u03c8(x1, \u2026 , xk)\u2193=n\uff0c\u53cd\u4e4b\u03c8\u6ca1\u6709\u8f93\u51fa\uff0c\u8868\u793a\u4e3a\u03c8(x1, \u2026 , xk)\u2191\u3002<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n

                    \u4e8e\u662f\u8fd9\u6837\uff0c\u6211\u4eec\u4fbf\u523b\u753b\u4e86while\u5faa\u73af\u3002\u8fd9\u4e2a\u65b0\u7684\u51fd\u6570\u96c6\u5408\u6bd4\u539f\u59cb\u9012\u5f52\u51fd\u6570\u7684\u96c6\u5408\u66f4\u5927\uff0c\u6211\u4eec\u79f0\u5b83\u662f<\/span><\/span>\u03bc-\u9012\u5f52\u51fd\u6570\uff08\u03bc-recursive\uff09<\/span><\/span><\/strong>\u7531\u4e8e\u8fd9\u4e9b\u51fd\u6570\u53ea\u5728\u81ea\u7136\u6570\u7684\u4e00\u90e8\u5206\u4e0a\u6709\u786e\u5b9a\u7684\u8f93\u51fa\uff0c\u5b83\u4eec\u4e5f\u88ab\u79f0\u4f5c<\/span><\/span>\u90e8\u5206\u53ef\u8ba1\u7b97\u51fd\u6570\uff08partial computable\uff09<\/span><\/span><\/strong>\u3002<\/span><\/span><\/span><\/p>\n

                    \u53ef\u4ee5\u8bc1\u660e\u90e8\u5206\u53ef\u8ba1\u7b97\u51fd\u6570\u7684\u5168\u4f53\u5c31\u662f\u4f7f\u7528\u56fe\u7075\u673a\u53ef\u4ee5\u8ba1\u7b97\u7684\u51fd\u6570\u7684\u5168\u4f53\u3002\u6570\u5b66\u4e0a\u8981\u8bc1\u660e\u8fd9\u4e00\u70b9\uff0c\u4e00\u65b9\u9762\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5177\u4f53\u7684\u6784\u9020\u8bc1\u660e\u53ef\u4ee5\u88ab\u56fe\u7075\u673a\u8ba1\u7b97\u7684\u6240\u6709\u51fd\u6570\u6784\u6210\u7684\u96c6\u5408\u786e\u5b9e\u6ee1\u8db3\u8fd9\u91cc1~6\u7684\u6240\u6709\u516c\u7406\uff0c\u8fd9\u5e76\u4e0d\u56f0\u96be\u3002\u800c\u53e6\u4e00\u65b9\u9762\uff0c\u6211\u4eec\u9700\u8981\u8bf4\u660e\u4f7f\u7528\u90e8\u5206\u53ef\u8ba1\u7b97\u51fd\u6570\u786e\u5b9e\u53ef\u4ee5\u6a21\u62df\u6240\u6709\u56fe\u7075\u673a\u7684\u884c\u4e3a\u3002<\/span><\/span><\/p>\n

                    \u4e3a\u6b64\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u56fe\u7075\u673a\u8fdb\u884c\u7f16\u7801\u3002\u4e00\u6761\u5f62\u5982\u201c(qi, _ , qj , * , \u2190)\u201d\u7684\u56fe\u7075\u673a\u6307\u4ee4\u53ef\u4ee5\u770b\u6210\u4e00\u4e2a\u5217\u8868\uff0c\u901a\u8fc7\u4e0a\u9762\u7684\u8ba8\u8bba\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e00\u4e2a\u81ea\u7136\u6570\u6765\u7f16\u7801\u8fd9\u4e00\u6761\u6307\u4ee4\u3002\u800c\u56fe\u7075\u673a\u7684\u6240\u6709\u6307\u4ee4\u4fbf\u53ef\u4ee5\u8868\u8fbe\u4e3a\u4e00\u4e2a\u81ea\u7136\u6570\u5217\u8868\uff0c\u800c\u8fd9\u4e2a\u5217\u8868\u53c8\u53ef\u4ee5\u7f16\u7801\u4e3a\u4e00\u4e2a\u81ea\u7136\u6570\uff0c\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u7528\u4e00\u4e2a\u81ea\u7136\u6570\u6765\u8868\u793a\u4e00\u4e2a\u56fe\u7075\u673a\uff0c\u8fd9\u4fbf\u662f\u54e5\u5fb7\u5c14\u6570\u3002\u4e0d\u540c\u56fe\u7075\u673a\u7684\u54e5\u5fb7\u5c14\u6570\u4e00\u5b9a\u4e0d\u76f8\u540c\uff0c\u4e8e\u662f\u6211\u4eec\u5c06\u56fe\u7075\u673a\u6309\u7167\u54e5\u5fb7\u5c14\u6570\u4ece\u5c0f\u5230\u5927\u6392\u5217\u8d77\u6765\uff0c\u4f9d\u6b21\u7f16\u53f7\uff0c\u8fd9\u5c31\u662f\u56fe\u7075\u673a\u7f16\u53f7\u3002<\/span><\/span><\/p>\n

                    \u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u8fd9\u6837\u4e00\u4e2a\u539f\u59cb\u9012\u5f52\u51fd\u6570\u03c6(e, t, x1, \u2026 , xk)\u6765\u6a21\u62df\u56fe\u7075\u673a\u8fd0\u884ct\u6b65\u540e\u7684\u72b6\u6001\uff0c\u5176\u4e2de\u4e3a\u56fe\u7075\u673a\u7f16\u53f7\uff0c\u03c6\u4ecee\u4e2d\u89e3\u7801\u51fa\u56fe\u7075\u673a\u7684\u5168\u90e8\u6307\u4ee4\uff0c\u7528\u81ea\u7136\u6570\u7f16\u7801\u7684\u5217\u8868\u6765\u6a21\u62df\u7eb8\u5e26\uff0c\u5c06(x1, \u2026 , xk)\u4f5c\u4e3a\u7f16\u53f7\u662fe\u7684\u56fe\u7075\u673a\u7684\u8f93\u5165\uff0c\u6a21\u62df\u8be5\u56fe\u7075\u673a\u8fd0\u884ct\u6b65\uff0c\u6700\u540e\u8f93\u51fa\u8868\u8fbe\u56fe\u7075\u673a\u72b6\u6001\u4ee5\u53ca\u7eb8\u5e26\u4fe1\u606f\u7684\u591a\u7ef4\u5217\u8868\u3002\u7531\u4e8e\u8fd9\u91cc\u7684\u6bcf\u4e00\u6b65\u90fd\u662f\u53ef\u4ee5\u88ab\u660e\u786e\u8ba1\u7b97\u7684\uff0c\u4e0d\u9700\u8981\u4f7f\u7528while\u5faa\u73af\uff0c\u6240\u4ee5\u03c6\u5b9e\u9645\u4e0a\u662f\u4e00\u4e2a\u539f\u59cb\u9012\u5f52\u51fd\u6570\u3002\u6700\u540e\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u4e00\u4e2a\u90e8\u5206\u53ef\u8ba1\u7b97\u51fd\u6570\u03a6(e, x1, \u2026 , xk)\uff0c\u5b83\u4f7f\u7528while\u5faa\u73af\u4ee4\u03c6(e, t, x1, \u2026 , xk)\u4e2d\u7684t\u53d6\u904d1, 2, 3, 4, 5, \u2026 \u76f4\u5230\u7f16\u53f7\u662fe\u7684\u56fe\u7075\u673a\u5728\u8f93\u5165(x1, \u2026 , xk)\u4e0a\u505c\u673a\uff0c\u6700\u540e\u8f93\u51fa\u7eb8\u5e26\u4e0a\u7684\u7ed3\u679c\u3002\u4e8e\u662f\u03a6(e, x1, \u2026 , xk)\uff0c\u4f5c\u4e3a\u4e00\u4e2a(x1, \u2026 , xk)\u4e0a\u7684\u51fd\u6570\uff0c\u4fbf\u5b8c\u5168\u6a21\u62df\u4e86\u7f16\u53f7\u4e3ae\u7684\u56fe\u7075\u673a\u7684\u884c\u4e3a\u3002\u540c\u65f6\u53ef\u4ee5\u770b\u51fa\u03a6\u786e\u5b9e\u662f\u4e00\u4e2a\u90e8\u5206\u53ef\u8ba1\u7b97\u51fd\u6570\u3002<\/span><\/span><\/p>\n

                    \u81f3\u6b64\uff0c\u6211\u4eec\u4fbf\u53ef\u4ee5\u5f97\u51fa\u7ed3\u8bba\uff0c<\/span><\/span>\u90e8\u5206\u53ef\u8ba1\u7b97\u51fd\u6570\u7684\u5168\u4f53\u5c31\u662f\u4f7f\u7528\u56fe\u7075\u673a\u53ef\u4ee5\u8ba1\u7b97\u7684\u51fd\u6570\u7684\u5168\u4f53<\/span><\/span><\/strong>\u3002\u8fd9\u4e5f\u4e0e\u6211\u4eec\u7684\u76f4\u89c2\u611f\u53d7\u5b8c\u5168\u4e00\u81f4\uff0c<\/span><\/span>\u56e0\u4e3a\u90e8\u5206\u53ef\u8ba1\u7b97\u51fd\u6570\u53ef\u4ee5\u8868\u8fbe\u6240\u6709\u6211\u4eec\u53ef\u80fd\u9047\u5230\u7684\u7f16\u7a0b\u8bed\u53e5\u3002<\/span><\/span><\/strong><\/span><\/p>\n

                    \u5bf9\u5e94\u51fd\u6570\u03a6\uff0c\u4e5f\u4e00\u5b9a\u5b58\u5728\u4e00\u4e2a\u56fe\u7075\u673a\uff0c\u5b83\u53ef\u4ee5\u50cf\u03a6\u4e00\u6837\u6a21\u62df\u4efb\u4f55\u56fe\u7075\u673a\u7684\u8ba1\u7b97\u8fc7\u7a0b\uff0c\u4e8e\u662f\u6211\u4eec\u628a\u03a6\u79f0\u4f5c<\/span><\/span>\u901a\u7528\u56fe\u7075\u673a\uff08universal Turing machine\uff09<\/span><\/span><\/strong>\uff0c\u5b83\u5c31\u662f\u6211\u4eec\u6bcf\u5929\u4f7f\u7528\u7684\u7535\u8111\uff0c\u800c\u5176\u4ed6\u56fe\u7075\u673a\u4fbf\u662f\u7535\u8111\u4e0a\u8fd0\u884c\u7684\u7a0b\u5e8f\u6216\u8005\u5b9e\u73b0\u786e\u5b9a\u529f\u80fd\u7684\u82af\u7247\uff0c\u56fe\u7075\u673a\u7f16\u53f7\u4fbf\u662f\u7a0b\u5e8f\u7684\u6e90\u7801\u3002<\/span><\/span>\u540c\u65f6\uff0c\u8bc1\u660e\u4e00\u4e2a\u7cfb\u7edf\u6709\u4e0d\u4e9a\u4e8e\u56fe\u7075\u673a\u7684\u8ba1\u7b97\u80fd\u529b\uff0c\u6211\u4eec\u53ea\u9700\u8981\u8bf4\u660e\u5b83\u80fd\u8ba1\u7b97\u7684\u51fd\u6570\u6ee1\u8db3\u4e0a\u8ff06\u6761\u516c\u7406\u5373\u53ef<\/span><\/span><\/strong>\uff0c<\/span><\/span><\/strong>\u5373\u7cfb\u7edf\u7684\u5e95\u5c42\u786e\u5b9e\u53ef\u4ee5\u5b9e\u73b0\u8fd96\u4e2aapi\u3002<\/span><\/span><\/span><\/p>\n


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

                    \n
                    \n
                    \n
                    \n
                    \n

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

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

                    Kolmogorov \u7684\u5fc3\u7ed3<\/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

                    <\/section>\n

                    \u56fe\u7075\u673a\u53ef\u4ee5\u88ab\u7f16\u53f7\u672c\u8eab\u5c31\u662f\u4e00\u4ef6\u6781\u5176\u4e0d\u5e73\u51e1\u7684\u4e8b\u60c5\uff0c\u8fd9\u8bf4\u660e\u56fe\u7075\u673a\u548c\u81ea\u7136\u6570\u4e00\u6837\u591a\u3002\u81ea\u7136\u6570\u6709\u65e0\u7a77\u591a\u4e2a\uff0c\u6211\u4eec\u53ef\u4ee5\u5199\u7684\u7a0b\u5e8f\uff0c\u4e5f\u5c31\u662f\u56fe\u7075\u673a\u4e5f\u662f\u65e0\u7a77\u591a\u4e2a\uff0c\u8fd9\u6ca1\u6709\u4ec0\u4e48\u95ee\u9898\u3002\u7136\u800c\uff0c\u6240\u6709\u7684\u65e0\u7a77\u90fd\u662f\u4e00\u6837\u591a\u7684\u5417\uff1f<\/span><\/span><\/p>\n

                    \u5047\u5982\u75310\u548c1\u7ec4\u6210\u7684\u65e0\u7a77\u5e8f\u5217\u548c\u81ea\u7136\u6570\u4e00\u6837\u591a\uff0c\u4e5f\u5c31\u662f\u8bf4\u53ef\u4ee5\u50cf\u81ea\u7136\u6570\u4e00\u6837\u4e00\u4e2a\u4e00\u4e2a\u6392\u5217\u51fa\u6765\uff0c\u90a3\u4e48\u6211\u53ea\u9700\u8981\u50cf\u4e0a\u56fe\u4e00\u6837\uff0c\u53d6\u4e00\u4e2a\u5e8f\u5217\uff0c\u5b83\u7684\u7b2ci\u4f4d\u548c\u6392\u5217\u51fa\u7684\u7b2ci\u4e2a\u65e0\u7a77\u5e8f\u5217\u7684\u7b2ci\u4f4d\u4e0d\u4e00\u6837\uff0c\u90a3\u4e48\u8fd9\u4e2a\u6784\u9020\u51fa\u7684\u65e0\u7a77\u5e8f\u5217\u4e00\u5b9a\u548c\u6392\u5217\u51fa\u7684\u6240\u6709\u65e0\u7a77\u5e8f\u5217\u4e0d\u540c\u3002\u8fd9\u5c31\u8bf4\u660e\u75310\u548c1\u7ec4\u6210\u7684\u65e0\u7a77\u5e8f\u5217\u4e00\u5b9a\u662f\u4e0d\u80fd\u88ab\u50cf\u81ea\u7136\u6570\u4e00\u6837\u6392\u5217\u51fa\u6765\u7684\uff0c\u4e5f\u5c31\u662f\u8bf4\u5b83\u4eec\u6bd4\u81ea\u7136\u6570\u66f4\u591a\u3002<\/span><\/span><\/p>\n

                    \u4e8b\u5b9e\u4e0a\uff0c\u8981\u7406\u89e3\u65e0\u7a77\u6709\u5927\u6709\u5c0f\u5e76\u4e0d\u56f0\u96be\u3002\u5b9e\u6570\u548c\u81ea\u7136\u6570\u8c01\u66f4\u591a\uff1f\u5f53\u7136\u662f\u5b9e\u6570\u3002\u6211\u4eec\u7528\u6982\u7387\u7684\u89d2\u5ea6\u6765\u8003\u8651\u597d\u4e86\uff0c\u6211\u4eec\u53ea\u9700\u8981\u8003\u8651\u81ea\u7136\u6570\u96c6\u5408\u7684\u201c\u957f\u5ea6\u201d\u548c\u5b9e\u8f74\u7684\u957f\u5ea6\u7684\u6bd4\u503c\u3002\u5bf9\u4e8e\u81ea\u7136\u6570n\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u5b83\u5305\u88f9\u5728\u4e00\u4e2a\u533a\u95f4(n-\u03b5\/2^n, n+\u03b5\/2^n)\u4e2d\uff0c\u7136\u540e\u628a\u8fd9\u4e9b\u533a\u95f4\u52a0\u8d77\u6765\uff0c\u7ed3\u679c\u662f \u03b5(2+1+1\/2+1\/4+1\/8+1\/16+\u2026)=4 \u03b5\u3002\u4e5f\u5c31\u662f\u8bf4\u201c\u81ea\u7136\u6570\u96c6\u5408\u7684\u957f\u5ea6\u201d\u4e00\u5b9a\u662f\u5c0f\u4e8e4\u03b5\u7684\u3002\u7136\u800c\u03b5\u53ef\u4ee5\u4efb\u610f\u5730\u5c0f\uff0c\u4f8b\u59820.0001\u5df2\u7ecf\u591f\u5c0f\u4e86\uff0c\u4f46\u662f\u6211\u53ef\u4ee5\u8ba94\u03b5\u53d60.000000001\uff0c\u53ea\u8981\u662f\u4e2a\u6b63\u6570\u5c31\u884c\u3002\u4e8e\u662f\u201c\u81ea\u7136\u6570\u96c6\u5408\u7684\u957f\u5ea6\u201d\u4e00\u5b9a\u662f0\uff0c\u5426\u5219\u6211\u76844\u03b5\u53ef\u4ee5\u66f4\u5c0f\uff0c\u4ece\u800c\u5f97\u5230\u77db\u76fe\u3002<\/span><\/span><\/p>\n

                    \u4e0a\u9762\u8fd9\u4e2a\u8ba8\u8bba\u770b\u4f3c\u6beb\u65e0\u610f\u4e49\uff0c\u56e0\u4e3a\u81ea\u7136\u6570\u662f\u70b9\uff0c\u800c\u5b9e\u6570\u662f\u7ebf\uff0c\u70b9\u8868\u793a\u7684\u6570\u600e\u4e48\u53ef\u80fd\u6bd4\u7ebf\u8868\u793a\u7684\u6570\u66f4\u591a\u3002\u4f46\u4e8b\u5b9e\u4e0a\uff0c\u7531\u4e8e\u6709\u7406\u6570\u90fd\u53ef\u4ee5\u5199\u6210\u5206\u6570p\/q\u7684\u5f62\u5f0f\uff0c\u5176\u4e2dp\u548cq\u90fd\u662f\u6574\u6570\uff0c[0,1]\u533a\u95f4\u4e2d\u7684\u6709\u7406\u6570\u4e00\u5b9a\u662f\u53ef\u4ee5\u88ab\u4e00\u4e2a\u4e00\u4e2a\u6392\u5217\u51fa\u6765\u7684\u3002\u4e0a\u8ff0\u8ba8\u8bba\u53ef\u4ee5\u5b8c\u5168\u79fb\u690d\u5230[0,1]\u533a\u95f4\u4e2d\u7684\u6709\u7406\u6570\u4e0e[0,1]\u533a\u95f4\u4e2d\u7684\u5b9e\u6570\u4e0a\u3002\u4e5f\u5c31\u662f\u8bf4\u5728[0,1]\u533a\u95f4\u4e2d\u968f\u4fbf\u6311\u4e00\u4e2a\u70b9\uff0c\u9009\u5230\u6709\u7406\u6570\u7684\u6982\u7387\u662f0\uff01<\/span><\/span><\/p>\n

                    \u90a3\u8fd9\u548c\u6211\u4eec\u7684\u56fe\u7075\u673a\u53c8\u6709\u4ec0\u4e48\u5173\u7cfb\u5462\uff1f\u4e8b\u5b9e\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u4e8c\u8fdb\u5236\u5c0f\u6570\u6765\u8868\u793a[0,1]\u533a\u95f4\u4e2d\u7684\u70b9\uff0c\u6bcf\u4e00\u4e2a\u70b9\u90fd\u5bf9\u5e94\u7740\u4e00\u4e2a\u75310\u548c1\u7ec4\u6210\u7684\u65e0\u7a77\u5e8f\u5217\u3002\u800c\u56fe\u7075\u673a\u548c\u81ea\u7136\u6570\u4e00\u6837\u591a\uff0c\u4e5f\u5c31\u662f\u8bf4\u548c[0,1]\u533a\u95f4\u4e0a\u7684\u6709\u7406\u6570\u4e00\u6837\u591a\uff0c\u90a3\u4e48\u63a8\u8bba\u4fbf\u662f\u5728\u6240\u6709\u75310\u548c1\u7ec4\u6210\u7684\u65e0\u7a77\u5e8f\u5217\u4e2d\uff0c\u62bd\u5230\u80fd\u88ab\u56fe\u7075\u673a\u201c\u8ba1\u7b97\u201d\u6216\u8005\u8bf4\u201c\u9884\u6d4b\u201d\u7684\u65e0\u7a77\u5e8f\u5217\u7684\u6982\u7387\u662f0\u3002<\/span><\/span><\/p>\n

                    \u60f3\u5230\u8fd9\u91cc\u4e0d\u514d\u60b2\u4ece\u5fc3\u6765\uff0c\u539f\u6765\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u7684\u95ee\u9898\u662f\u5982\u6b64\u4e4b\u5c11\uff0c\u8fde\u6ca7\u6d77\u4e00\u7c9f\u90fd\u6bd4\u4e0d\u4e0a\u3002<\/span><\/span><\/strong>\u56e0\u4e3a\u81f3\u5c11\u90a3\u4e00\u7c9f\u8fd8\u6709\u4f53\u79ef\uff0c\u800c\u6211\u4eec\u53ef\u4ee5\u201c\u8ba1\u7b97\u201d\u7684\u65e0\u7a77\u5e8f\u5217\u5728\u6240\u6709\u65e0\u7a77\u5e8f\u5217\u9762\u524d\u5c31\u662f\u4e2a0\u3002\u4f46\u518d\u4ed4\u7ec6\u60f3\u60f3\uff0c\u96be\u9053\u4e8b\u5b9e\u4e0d\u5c31\u5e94\u8be5\u5982\u6b64\u5417\uff1f\u5047\u5982\u8bf4\u6709\u4e00\u4e2a\u7cfb\u7edf\u968f\u673a\u4e14\u5747\u5300\u5730\u4e0d\u505c\u4ea7\u751f\u6570\u5b570\u548c1\uff0c\u5b83\u4ea7\u751f\u76840\u548c1\u4e00\u5b9a\u662f\u6df7\u4e71\u800c\u4e0d\u53ef\u9884\u6d4b\u7684\uff0c\u6240\u4ee5\u201c\u5b83\u4ea7\u751f\u76840\u548c1\u5177\u6709\u7279\u5b9a\u6a21\u5f0f\u201d\u4e00\u5b9a\u662f\u4e00\u4e2a\u4e0d\u53ef\u80fd\u4e8b\u4ef6\uff0c\u201c\u5177\u6709\u7279\u5b9a\u6a21\u5f0f\u201d\u4e0d\u5c31\u662f\u610f\u5473\u7740\u80fd\u88ab\u56fe\u7075\u673a\u201c\u8ba1\u7b97\u201d\u5417\uff1f\u7531\u6b64\uff0c<\/span><\/span>\u6211\u4eec\u83b7\u5f97\u4e86\u5bf9\u4e8e\u968f\u673a\u6027\u4e0e\u6982\u7387\u8bba\u66f4\u52a0\u6df1\u523b\u4e0e\u672c\u8d28\u7684\u7406\u89e3\uff0c\u5373\u5b8c\u5168\u4e0d\u80fd\u88ab\u4efb\u4f55\u56fe\u7075\u673a\u201c\u9884\u6d4b\u201d\u76840\u548c1\u7ec4\u6210\u7684\u65e0\u7a77\u5e8f\u5217\u53ef\u4ee5\u88ab\u8ba4\u4e3a\u662f\u968f\u673a\u7684\u3002<\/span><\/span><\/strong>\u4e8b\u5b9e\u4e0a\u6570\u5b66\u5bb6\u8fd8\u8bc1\u660e\u4e86\uff0c\u8fd9\u6837\u7684\u65e0\u7a77\u5e8f\u5217\u6ee1\u8db3\u201c\u5927\u6570\u5b9a\u5f8b\u201d\uff0c\u5373\u82e5\u6211\u4eec\u7edf\u8ba1\u8be5\u5e8f\u5217\u4e2d0\u548c1\u51fa\u73b0\u7684\u9891\u7387\uff0c\u4f1a\u53d1\u73b0\u5b83\u4e00\u5b9a\u6536\u655b\u4e8e1\/2<\/span>\uff08\u8bf7\u6ce8\u610f\u8fd9\u91cc\u4e0d\u662f\u51e0\u4e4e\u5904\u5904\u6536\u655b\uff0c\u800c\u662f\u4e00\u5b9a\u6536\u655b\u4e8e1\/2\uff09<\/span>\u3002<\/span><\/span><\/span><\/p>\n

                    \u636e\u4f20Kolmogorov\u672c\u4eba\u5bf9\u4ed6\u521b\u7acb\u7684\u6982\u7387\u8bba\u5e76\u4e0d\u6ee1\u610f\uff0cKolmogorov\u89c9\u5f97\u4e00\u4e2a\u5ba2\u89c2\u5b58\u5728\u7684\u3001\u56fa\u5b9a\u4e0d\u53d8\u7684\u6982\u7387\u672c\u5c31\u662f\u4e00\u4e2a\u975e\u5e38\u5947\u602a\u7684\u8bbe\u5b9a\u3002\u867d\u7136\u5728\u521d\u4e2d\u3001\u9ad8\u4e2d\u3001\u4ee5\u53ca\u51e0\u4e4e\u6240\u6709\u5927\u5b66\u7684\u8bfe\u5802\u4e0a\uff0c\u201c\u968f\u673a\u5e8f\u5217\u201d\u8fd9\u79cd\u8bcd\u8bed\u4e00\u65e6\u8bf4\u51fa\u53e3\uff0c\u4efb\u8bfe\u8001\u5e08\u5927\u6982\u4f1a\u89c9\u5f97\u8fd9\u4e2a\u5b66\u751f\u6839\u672c\u6ca1\u6709\u5165\u95e8\uff0c\u8fde\u4ec0\u4e48\u662f\u6982\u7387\u90fd\u4e0d\u6e05\u695a\u3002\u4f46\u662f\u5728\u4ed6\u773c\u91cc\u4ee5\u53ca\u5927\u591a\u6570\u4eba\u6734\u7d20\u7684\u89c2\u5ff5\u91cc\uff0c01110110001000011010\u5c31\u662f\u6bd401010101010101010101\u66f4\u52a0\u968f\u673a\u3002\u6700\u7ec8\u4ed6\u7684\u5b66\u751fMartin-L\u00f6f\u5c06\u8fd9\u6837\u7684\u60f3\u6cd5\u53d1\u5c55\u6210\u4e00\u5957\u5b8c\u6574\u7684\u7406\u8bba\uff0c\u5f62\u6210\u4e86\u4e00\u79cd\u6709\u522b\u4e8e\u9891\u7387\u8bba\u5b66\u6d3e\u548c\u8d1d\u53f6\u65af\u5b66\u6d3e\u7684\u7b2c\u4e09\u79cd\u5bf9\u6982\u7387\u4e0e\u968f\u673a\u6027\u7684\u89c2\u70b9\uff0cMartin-L\u00f6f\u968f\u673a\u6027\u3002<\/span><\/span><\/p>\n

                    Martin-L\u00f6f \u968f\u673a\u6027\u89e3\u51b3\u4e86\u201c\u4ec0\u4e48\u6837\u7684\u5e8f\u5217\u624d\u662f\u771f\u6b63\u7684\u968f\u673a\u201d\u7684\u95ee\u9898\uff0c\u5c31\u662f\u7528\u201c\u901a\u8fc7\u6240\u6709\u53ef\u8ba1\u7b97\u7684\u968f\u673a\u6027\u68c0\u9a8c\u201d\u6765\u5b9a\u4e49\u771f\u6b63\u7684\u968f\u673a\u5e8f\u5217\u3002\u5b83\u662f\u7b97\u6cd5\u4fe1\u606f\u8bba\u4e2d\u6700\u4e25\u683c\u3001\u6700\u5e38\u7528\u7684\u201c\u968f\u673a\u6027\u201d\u5b9a\u4e49\u4e4b\u4e00\u3002\u5982\u679c\u8bf4\u4e00\u4e2a\u5e8f\u5217\u662f Martin-L\u00f6f \u968f\u673a\u7684\uff0c\u7b49\u4ef7\u4e8e\u5b83\u7684\u6240\u6709\u524d\u7f00\u7684 Kolmogorov \u590d\u6742\u5ea6\u90fd\u5f88\u9ad8<\/span>\uff08\u4e0d\u53ef\u6709\u6548\u538b\u7f29\uff09<\/span>\u3002<\/span><\/span><\/p>\n


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

                    \n
                    \n
                    \n
                    \n
                    \n

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

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

                    \u7ed3\u8bed<\/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\u9610\u91ca\u4e86\u901a\u8fc7\u8ba1\u7b97\u673a\u53ef\u4ee5\u8ba1\u7b97\u7684\u51fd\u6570\u5168\u4f53\u5176\u5b9e\u5c31\u662f\u90e8\u5206\u53ef\u8ba1\u7b97\u51fd\u6570\uff0c\u8bc1\u660e\u4e00\u4e2a\u7cfb\u7edf\u6709\u4e0d\u4e9a\u4e8e\u56fe\u7075\u673a\u7684\u8ba1\u7b97\u80fd\u529b\u53ea\u9700\u8981\u8bf4\u660e\u5b83\u6ee1\u8db36\u6761\u516c\u7406\u5373\u53ef\u3002\u800c\u56fe\u7075\u673a\u53ef\u4ee5\u88ab\u7f16\u53f7\u7684\u4e8b\u5b9e\u8868\u660e\uff0c\u5b58\u5728\u5927\u91cf\u7684\u95ee\u9898\u90fd\u662f\u4e0d\u53ef\u88ab\u8ba1\u7b97\u7684\u3002\u8fd9\u672c\u8d28\u4e0a\u662f\u4eba\u7c7b\u548c\u8ba1\u7b97\u673a\u53ea\u80fd\u5904\u7406\u6709\u9650\u7684\u3001\u79bb\u6563\u7684\u4fe1\u606f\u7684\u4f53\u73b0\u3002\u5728Martin-L\u00f6f\u968f\u673a\u6027\u7684\u89c2\u70b9\u4e0b\uff0c\u6b63\u662f\u4ece\u8fd9\u79cd\u5c40\u9650\u6027\u4e2d\u6d8c\u73b0\u51fa\u4e86\u6982\u7387\u3002<\/span><\/span><\/span><\/p>\n

                    \n
                    \n
                    \n
                    \n

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

                    \u5723\u5854\u83f2\u8bfe\u7a0b<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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

                    \u672c\u8bfe\u7a0b\u63a2\u8ba8\u8ba1\u7b97\u590d\u6742\u6027\uff0c\u6db5\u76d6\u641c\u7d22\u7b97\u6cd5\u3001\u89e3\u56fe\u3001\u7ea6\u7b80\u548c\u666e\u9002\u6027\u7b49\u4e3b\u9898\u3002\u6211\u4eec\u63a2\u8ba8\u7684\u95ee\u9898\u6db5\u76d6\u8303\u56f4\u5e7f\u6cdb\uff0c\u4ece\u7b80\u5355\uff08\u591a\u9879\u5f0f\u65f6\u95f4\uff09\u5230\u56f0\u96be\uff08NP \u5b8c\u5168\uff09\u518d\u5230\u4e0d\u53ef\u80fd\uff08\u4e0d\u53ef\u5224\u5b9a\uff09\u3002<\/span><\/p>\n

                    \u8bfe\u7a0b\u4e3b\u8bb2\u4eba Cristopher Moore \u662f\u5723\u83f2\u7814\u7a76\u6240\u7684\u5e38\u9a7b\u6559\u6388\u3002\u4ed6\u62e5\u6709\u897f\u5317\u5927\u5b66\u7269\u7406\u5b66\u3001\u6570\u5b66\u548c\u7efc\u5408\u79d1\u5b66\u5b66\u58eb\u5b66\u4f4d\uff0c\u4ee5\u53ca\u5eb7\u5948\u5c14\u5927\u5b66\u7269\u7406\u5b66\u535a\u58eb\u5b66\u4f4d\u3002\u4ed6\u64b0\u5199\u4e86 150 \u7bc7\u5173\u4e8e\u7269\u7406\u5b66\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u4ea4\u53c9\u9886\u57df\u7684\u8bba\u6587\uff0c\u6db5\u76d6\u91cf\u5b50\u8ba1\u7b97\u3001NP \u5b8c\u5168\u95ee\u9898\u4e2d\u7684\u76f8\u53d8\u3001\u793e\u4ea4\u7f51\u7edc\u7406\u8bba\u53ca\u5176\u7ed3\u6784\u5206\u6790\u7684\u6709\u6548\u7b97\u6cd5\u7b49\uff0c\u4e0eStephen Smale \u5408\u8457\u4e86\u725b\u6d25\u5927\u5b66\u51fa\u7248\u793e\u51fa\u7248\u7684\u300a\u8ba1\u7b97\u7684\u672c\u8d28\u300b\u3002<\/span><\/p>\n


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

                    <\/section>\n

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

                    <\/span><\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
                    \u63a8\u8350\u9605\u8bfb<\/span><\/span><\/strong><\/strong><\/strong><\/section>\n
                    <\/strong><\/section>\n
                    1. \u4eba\u5de5\u667a\u80fd\u5982\u4f55\u63b7\u9ab0\u5b50\u2014\u2014\u4e09\u79cd\u6982\u7387\u7406\u8bba<\/span><\/a><\/span><\/strong>
                    <\/span><\/strong><\/span><\/section>\n
                    2. \u4ec0\u4e48\u662f\u6982\u7387\u56fe\u6a21\u578b\uff1a\u8868\u793a\u3001\u63a8\u7406\u4e0e\u5b66\u4e60 | \u96c6\u667a\u767e\u79d1 | \u96c6\u667a\u767e\u79d1<\/span><\/a><\/span><\/strong>
                    <\/span><\/strong><\/span><\/section>\n
                    3. \u73b0\u4ee3\u6982\u7387\u8bba\u4e4b\u7236\uff1a\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7684\u201c\u968f\u673a\u201d\u4eba\u751f<\/span><\/a><\/span><\/strong><\/section>\n
                    <\/strong><\/section>\n
                    4. <\/span>\u6d8c\u73b0\u52a8\u529b\u5b66\u5982\u4f55\u7528\u6765\u5206\u6790\u590d\u6742\u7cfb\u7edf\uff1f | \u65b0\u8bfe\u4e0a\u7ebf<\/span><\/a><\/span><\/strong><\/span>
                    <\/span><\/strong><\/strong><\/span><\/section>\n
                    <\/strong>5. <\/span><\/strong>\u96c6\u667a\u5b66\u56ed\u7cbe\u54c1\u8bfe\u7a0b\u514d\u8d39\u5f00\u653e\uff0c\u89e3\u9501\u7cfb\u7edf\u79d1\u5b66\u4e0e AI \u65b0\u4e16\u754c<\/span><\/a><\/span><\/strong><\/section>\n

                    6. \u9ad8\u8003\u5206\u6570\u53ea\u662f\u5f20\u5165\u573a\u5238\uff0c\u4f60\u7684\u79d1\u7814\u5192\u9669\u5728\u8fd9\u91cc\u542f\u822a\uff01<\/span><\/a><\/span><\/strong><\/p>\n

                    7. <\/span><\/span><\/strong><\/strong><\/span>\u91cd\u6574\u5316\u7fa4\u4e0e\u975e\u7ebf\u6027\u7269\u7406\uff0c\u5bfb\u627e\u590d\u6742\u7cfb\u7edf\u8de8\u5c3a\u5ea6\u7684\u5206\u6790\u65b9\u6cd5\u4e28\u65b0\u8bfe\u53d1\u5e03<\/a><\/span><\/strong><\/strong><\/strong><\/strong><\/span><\/p>\n


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


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

                    \u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfe\u7a0b<\/span><\/span><\/section>\n<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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