{"id":50869,"date":"2024-06-12T21:41:57","date_gmt":"2024-06-12T13:41:57","guid":{"rendered":"https:\/\/swarma.org\/?p=50869"},"modified":"2024-06-12T21:41:57","modified_gmt":"2024-06-12T13:41:57","slug":"%e8%ae%a1%e7%ae%97%e5%a4%8d%e6%9d%82%e6%80%a7%e7%90%86%e8%ae%ba50%e5%b9%b4%ef%bc%9a%e4%bb%8ep%e4%b8%8enp%e9%97%ae%e9%a2%98%e5%88%b0%e5%85%83%e5%a4%8d%e6%9d%82%e6%80%a7","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=50869","title":{"rendered":"\u8ba1\u7b97\u590d\u6742\u6027\u7406\u8bba50\u5e74\uff1a\u4eceP\u4e0eNP\u95ee\u9898\u5230\u5143\u590d\u6742\u6027"},"content":{"rendered":"
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\u6587\u7ae0\u9898\u76ee\uff1aComplexity Theory\u2019s 50-Year Journey to the Limits of Knowledge<\/span><\/p>\n

\u6587\u7ae0\u94fe\u63a5\uff1ahttps:\/\/www.quantamagazine.org\/complexity-theorys-50-year-journey-to-the-limits-of-knowledge-20230817\/<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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2007\u5e74\u79cb\u5b63\u5b66\u671f\uff0cMarco Carmosino \u5728\u8bfb\u5927\u4e8c\uff0c\u6b63\u8003\u8651\u4ece\u5927\u5b66\u9000\u5b66\u53bb\u8bbe\u8ba1\u7535\u5b50\u6e38\u620f\u3002\u5f00\u5b66\u7b2c\u4e00\u5468\uff0c\u4ed6\u786c\u7740\u5934\u76ae\u53bb\u53c2\u52a0\u9a6c\u585e\u8bf8\u585e\u5927\u5b66\u963f\u9ed8\u65af\u7279\u5206\u6821\u8ba1\u7b97\u673a\u79d1\u5b66\u4e13\u4e1a\u5fc5\u4fee\u7684\u6570\u5b66\u8bfe\u3002\u7136\u540e\u6559\u6388\u63d0\u51fa\u4e86\u4e00\u4e2a\u6539\u53d8\u4ed6\u4e00\u751f\u7684\u7b80\u5355\u95ee\u9898\uff1a\u4f60\u600e\u4e48\u77e5\u9053\u6570\u5b66\u771f\u7684\u6709\u7528\uff1f<\/strong><\/span><\/p>\n


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Carmosino \u73b0\u5728\u6210\u4e3a\u4e86IBM\u7684\u7406\u8bba\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\uff0c\u4ed6\u56de\u5fc6\u5f53\u65f6\u573a\u666f\u8bf4\uff0c\u201c\u8fd9\u4e2a\u95ee\u9898\u8ba9\u6211\u5750\u76f4\u8d77\u6765\uff0c\u5e76\u96c6\u4e2d\u6ce8\u610f\u529b\u201d\u3002\u4ed6\u540e\u6765\u62a5\u540d\u4e86\u4e00\u4e2a\u5173\u4e8e\u5e93\u5c14\u7279\u00b7\u54e5\u5fb7\u5c14<\/span>\uff08Kurt G\u00f6del\uff09<\/span>\u5de5\u4f5c\u7684\u9009\u4fee\u7814\u8ba8\u4f1a\u3002\u54e5\u5fb7\u5c14\u5173\u4e8e\u81ea\u6307\u8bba\u8bc1\u7684\u5de5\u4f5c\u4ee4\u4eba\u773c\u82b1\u7f2d\u4e71\uff0c\u65e2\u66b4\u9732\u4e86\u6570\u5b66\u63a8\u7406\u7684\u5c40\u9650\u6027\uff0c\u8fd8\u4e3a\u672a\u6765\u6240\u6709\u5173\u4e8e\u8ba1\u7b97\u57fa\u672c\u6781\u9650\u7684\u5de5\u4f5c\u5960\u5b9a\u4e86\u57fa\u7840\u3002Carmosino \u4ece\u4e2d\u53d7\u76ca\u532a\u6d45\u3002\u4ed6\u8bf4\u9053\uff1a\u201c\u6211\u5b8c\u5168\u542c\u4e0d\u61c2\uff0c\u4f46\u6211\u77e5\u9053\u8fd9\u5c31\u662f\u6211\u60f3\u5e72\u7684\u3002\u201d<\/span><\/p>\n


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\u5982\u4eca\uff0c\u5373\u4f7f\u662f\u7ecf\u9a8c\u4e30\u5bcc\u7684\u7814\u7a76\u4eba\u5458\u5728\u9762\u5bf9\u7406\u8bba\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u7684\u6838\u5fc3\u5f00\u653e\u95ee\u9898\u2014\u2014\u5373P\u4e0eNP\u95ee\u9898\u2014\u2014\u65f6\uff0c\u4e5f\u4f1a\u53d1\u73b0\u7406\u89e3\u6b20\u7f3a\u3002\u8fd9\u4e2a\u95ee\u9898\u672c\u8d28\u4e0a\u5728\u95ee\uff1a\u90a3\u4e9b\u957f\u671f\u4ee5\u6765\u88ab\u8ba4\u4e3a\u96be\u4ee5\u8ba1\u7b97\u7684\u95ee\u9898\u662f\u5426\u53ef\u4ee5<\/span>\uff08\u901a\u8fc7\u6211\u4eec\u5c1a\u672a\u53d1\u73b0\u7684\u79d8\u5bc6\u6377\u5f84\uff09<\/span>\u8f7b\u677e\u89e3\u51b3\uff1f\u6216\u8005\uff0c\u5c31\u50cf\u7edd\u5927\u591a\u6570\u7814\u7a76\u8005\u6000\u7591\u7684\u90a3\u6837\uff0c\u4ed6\u4eec\u7684\u786e\u5c31\u662f\u5f88\u96be\u3002\u5173\u952e\u5728\u4e8e\u53ef\u77e5\u4e8b\u7269\u7684\u672c\u8d28\u3002<\/span><\/p>\n


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\u5c3d\u7ba1\u7814\u7a76\u8005\u4eec\u5728\u8ba1\u7b97\u590d\u6742\u6027\u7406\u8bba<\/strong><\/span>\uff08computational complexity theory\uff09<\/span>\u2014\u2014\u7814\u7a76\u4e0d\u540c\u95ee\u9898\u7684\u672c\u8d28\u56f0\u96be\u2014\u2014\u9886\u57df\u8015\u8018\u6570\u5341\u5e74\uff0c\u4f46P\u4e0eNP\u95ee\u9898\u4ecd\u8ba9\u4eba\u6478\u4e0d\u7740\u5934\u8111\uff0c\u751a\u81f3\u4e0d\u77e5\u9053\u8bc1\u660e\u8be5\u4ece\u4f55\u5f00\u59cb\u3002Michael Sipser \u662f\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u8d44\u6df1\u590d\u6742\u6027\u7406\u8bba\u5b66\u5bb6\uff0c\u572820\u4e16\u7eaa80\u5e74\u4ee3\u601d\u8003\u8fd9\u4e2a\u95ee\u9898\u591a\u5e74\u3002\u4ed6\u5f62\u5bb9\u8fd9\u79cd\u63a2\u7d22\u5c31\u50cf\u201c\u6ca1\u6709\u8def\u7ebf\u56fe\uff0c\u8d70\u8fdb\u8352\u91ce\u3002\u201d<\/span><\/p>\n


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\u8bc1\u660e\u8ba1\u7b97\u95ee\u9898\u96be\u4ee5\u89e3\u51b3\u672c\u8eab\u4f3c\u4e4e\u5c31\u5f88\u8270\u5de8\u3002\u4f46\u4e3a\u4ec0\u4e48\u8fd9\u4e48\u96be\u5462\uff1f\u5230\u5e95\u96be\u6210\u4ec0\u4e48\u6837\u5462\uff1fCarmosino \u548c\u5176\u4ed6\u5143\u590d\u6742\u6027<\/strong><\/span>\uff08meta-complexity\uff09<\/span>\u5b50\u9886\u57df\u7684\u7814\u7a76\u8005\u4eec\u5c06\u6b64\u7c7b\u95ee\u9898\u91cd\u65b0\u8868\u8ff0\u4e3a\u8ba1\u7b97\u95ee\u9898\uff0c\u901a\u8fc7\u590d\u6742\u6027\u7406\u8bba\u7684\u89c6\u89d2\u89c2\u5bdf\u590d\u6742\u6027\u7406\u8bba\u672c\u8eab<\/strong>\u6765\u63a8\u52a8\u8be5\u9886\u57df\u5411\u524d\u53d1\u5c55\u3002\u201c\u4f60\u53ef\u80fd\u4f1a\u60f3\uff0c\u2018\u597d\u5427\uff0c\u8fd9\u633a\u9177\u7684\u3002\u4e5f\u8bb8\u590d\u6742\u6027\u7406\u8bba\u5bb6\u4eec\u75af\u4e86\u3002\u2019\u201d Rahul Ilango \u5982\u662f\u8bf4\uff0c\u4ed6\u6700\u8fd1\u5728\u8be5\u9886\u57df\u53d6\u5f97\u4e86\u4e00\u4e9b\u4ee4\u4eba\u5174\u594b\u7684\u6210\u679c\u3002<\/span><\/p>\n


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\u7814\u7a76\u8005\u4eec\u901a\u8fc7\u7814\u7a76\u8fd9\u4e9b\u95ee\u9898\u53d1\u73b0\uff0c\u8bc1\u660e\u8ba1\u7b97\u96be\u5ea6\u7684\u96be\u5ea6\u4e0e\u4e00\u4e9b\u770b\u4f3c\u65e0\u5173\u7684\u95ee\u9898\u5bc6\u5207\u76f8\u5173\u3002\u5728\u770b\u4f3c\u968f\u673a\u7684\u6570\u636e\u4e2d\u53d1\u73b0\u9690\u85cf\u7684\u6a21\u5f0f\u6709\u591a\u96be\uff1f\u5982\u679c\u771f\u6b63\u7684\u56f0\u96be\u95ee\u9898\u786e\u5b9e\u5b58\u5728\uff0c\u90a3\u4e48\u5b83\u4eec\u7a76\u7adf\u6709\u591a\u5c11\uff1f\u201c\u5f88\u660e\u663e\uff0c\u5143\u590d\u6742\u6027\u63a5\u8fd1\u4e8b\u7269\u7684\u6838\u5fc3\u3002\u201d Scott Aaronson \u5982\u662f\u8bf4\uff0c\u4ed6\u662f\u5fb7\u514b\u8428\u65af\u5927\u5b66\u5965\u65af\u6c40\u5206\u6821\u7684\u590d\u6742\u6027\u7406\u8bba\u5b66\u5bb6\u3002<\/span><\/p>\n


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\u4eceP\u4e0eNP\u95ee\u9898\u8f6c\u53d8\u5230\u5143\u590d\u6742\u6027\u7684\u8def\uff0c\u7814\u7a76\u8005\u4eec\u8d70\u5f97\u6f2b\u957f\u800c\u66f2\u6298\u3002\u65c5\u7a0b\u5e76\u4e0d\u8f7b\u677e\uff0c\u8def\u4e0a\u5c3d\u662f\u9519\u8bef\u7684\u5206\u5c94\u548c\u8def\u969c\uff0c\u4e14\u5f80\u590d\u5faa\u73af\u3002\u7136\u800c\uff0c\u5bf9\u4e8e\u5143\u590d\u6742\u6027\u7684\u7814\u7a76\u4eba\u5458\u4eec\u6765\u8bf4\uff0c\u8e0f\u5165\u672a\u77e5\u7684\u65c5\u7a0b\u672c\u8eab\u5c31\u662f\u5956\u52b1\u3002\u52a0\u62ff\u5927\u897f\u8499\u00b7\u5f17\u96f7\u6cfd\u5927\u5b66<\/span>\uff08Simon Fraser University\uff09<\/span>\u7684\u590d\u6742\u6027\u7406\u8bba\u5bb6 Valentine Kabanets \u8bf4\uff0c\u4ece\u63d0\u51fa\u770b\u4f3c\u7b80\u5355\u7684\u95ee\u9898\u5f00\u59cb\uff0c\u201c\u884c\u81f3\u4f55\u5904\uff0c\u4e0d\u77e5\u9053\u3002\u201d<\/span><\/p>\n


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P\u4e0eNP\u95ee\u9898<\/span>\uff08P versus NP problem\uff09<\/span>\u7684\u540d\u79f0\u5e73\u5e73\u65e0\u5947\uff0c\u662f\u56e0\u4e3a\u590d\u6742\u6027\u7406\u8bba\u5b66\u5bb6\u4e60\u60ef\u7528\u6697\u793a\u7eb3\u65af\u8fbe\u514b\u80a1\u7968\u4ee3\u7801\u7684\u6807\u7b7e\u5c06\u8ba1\u7b97\u95ee\u9898\u5206\u7c7b\u4e3a\u5e7f\u6cdb\u7684\u201c\u590d\u6742\u6027\u7c7b\u522b\u201d\u3002\u8ba1\u7b97\u95ee\u9898\u53ef\u4ee5\u88ab\u7b97\u6cd5<\/span>\uff08\u4e00\u8fde\u4e32\u7cbe\u786e\u7684\u6307\u4ee4\uff09<\/span>\u89e3\u51b3\u3002\u4f46\u4e0d\u662f\u6240\u6709\u7684\u7b97\u6cd5\u90fd\u540c\u6837\u6709\u6548\uff0c\u7b97\u6cd5\u4e4b\u95f4\u7684\u5dee\u5f02\u6697\u793a\u4e86\u4e0d\u540c\u7c7b\u522b\u95ee\u9898\u4e4b\u95f4\u7684\u6839\u672c\u5dee\u522b\u3002\u590d\u6742\u6027\u7406\u8bba\u5b66\u5bb6\u9762\u4e34\u7684\u6311\u6218\u5c31\u662f\uff0c\u5c06\u8fd9\u4e9b\u201c\u6697\u793a\u7ebf\u7d22\u201d\u8f6c\u5316\u6210\u5728\u590d\u6742\u6027\u7c7b\u522b\u4e4b\u95f4\u5173\u7cfb\u7684\u4e25\u683c\u5b9a\u7406\u3002<\/span><\/p>\n


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Kabanets \u8bf4\uff1a\u201c\u8fd9\u4e9b\u5173\u7cfb\u53cd\u6620\u51fa\u7684\u4e1c\u897f\u8fdc\u8d85\u4efb\u4f55\u7279\u5b9a\u6280\u672f\uff0c\u662f\u5173\u4e8e\u8ba1\u7b97\u7684\u6c38\u6052\u771f\u7406\uff0c\u5c31\u50cf\u53d1\u73b0\u5b87\u5b99\u6cd5\u5219\u4e00\u6837\u3002\u201d<\/span><\/p>\n


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\u590d\u6742\u6027\u7c7b\u522b\u7684\u6570\u76ee\u4e0d\u65ad\u589e\u957f\uff0c\u6210\u767e\u4e0a\u5343\uff0c\u201cP\u201d\u548c\u201cNP\u201d\u662f\u5176\u4e2d\u4e24\u4e2a\u6700\u91cd\u8981\u7684\u6210\u5458\u3002\u7b80\u5355\u6765\u8bf4\uff0c\u201cP\u201d\u662f\u4e00\u7c7b\u6613\u4e8e\u89e3\u51b3\u7684\u95ee\u9898\uff0c\u6bd4\u5982\u6309\u5b57\u6bcd\u987a\u5e8f\u6392\u5e8f\u3002\u201cNP\u201d\u7c7b\u95ee\u9898\u5219\u6613\u4e8e\u9a8c\u8bc1\u89e3\u51b3\u65b9\u6848\uff0c\u4f8b\u5982\u6570\u72ec\u8c1c\u9898\u3002\u7531\u4e8e\u6240\u6709\u6613\u4e8e\u89e3\u51b3\u7684\u95ee\u9898\u90fd\u6613\u4e8e\u88ab\u9a8c\u8bc1\uff0c\u56e0\u6b64\u201cP\u201d\u7c7b\u95ee\u9898\u4ece\u5c5e\u4e8e\u201cNP\u201d\u7c7b\u3002\u4f46\u6709\u4e9b\u201cNP\u201d\u7c7b\u95ee\u9898\u770b\u8d77\u6765\u5f88\u96be\u89e3\u51b3\u2014\u2014\u5982\u679c\u6ca1\u6709\u9884\u5148\u5c1d\u8bd5\uff0c\u4f60\u5c31\u4e0d\u80fd\u7acb\u9a6c\u51ed\u76f4\u89c9\u7ed9\u51fa\u6570\u72ec\u95ee\u9898\u7684\u7b54\u6848\u3002\u8fd9\u79cd\u663e\u89c1\u7684\u56f0\u96be\u662f\u5e7b\u89c9\u5417\uff1f\u2014\u2014\u6211\u4eec\u80fd\u5426\u627e\u5230\u7b80\u5355\u7684\u6280\u5de7\u8f7b\u6613\u89e3\u51b3\u6240\u6709\u201cNP\u201d\u7c7b\u95ee\u9898\uff1f<\/strong><\/span><\/p>\n


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P\u4e0eNP\u95ee\u9898\u3002\uff5c\u6765\u6e90\uff1aSamuel Velasco\/Quanta Magazine<\/em><\/span><\/section>\n


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\u5982\u679c\u53ef\u4ee5\uff0c\u90a3\u4e48 P=NP \uff1a\u8fd9\u4e24\u4e2a\u95ee\u9898\u5c31\u662f\u7b49\u4ef7\u7684\u3002\u5982\u679c\u662f\u8fd9\u6837\u7684\u8bdd\uff0c\u90a3\u4e48\u6211\u4eec\u4e00\u5b9a\u80fd\u627e\u5230\u67d0\u79cd\u65b9\u6cd5\u8f7b\u6613\u89e3\u51b3\u5927\u91cf\u7684\u6570\u72ec\u8c1c\u9898\u3001\u8f7b\u6613\u4f18\u5316\u5168\u7403\u822a\u8fd0\u8def\u7ebf\u3001\u7834\u89e3\u6700\u5148\u8fdb\u7684\u5bc6\u7801\u4ee5\u53ca\u81ea\u52a8\u5316\u8bc1\u660e\u6570\u5b66\u5b9a\u7406\u3002\u5982\u679c P \u2260 NP\uff0c\u90a3\u4e48\u8bb8\u591a\u539f\u5219\u4e0a\u53ef\u4ee5\u89e3\u51b3\u7684\u8ba1\u7b97\u95ee\u9898\u5c06\u6c38\u8fdc\u65e0\u6cd5\u89e3\u51b3\u3002<\/span><\/p>\n


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\u5728P\u4e0eNP\u95ee\u9898\u63d0\u51fa\u4e4b\u524d\uff0c\u5b9e\u9645\u4e0a\u53ef\u4ee5\u8bf4\u662f\u65e9\u5728\u73b0\u4ee3\u8ba1\u7b97\u673a\u79d1\u5b66\u5f00\u59cb\u4e4b\u524d\uff0c\u7814\u7a76\u8005\u4eec\u5c31\u62c5\u5fc3\u5f62\u5f0f\u6570\u5b66\u63a8\u7406<\/span>\uff08formal mathematical reasoning\uff09<\/span>\u7684\u5c40\u9650\u6027\u30021921\u5e74\uff0c\u6570\u5b66\u5bb6\u6234\u7ef4\u00b7\u5e0c\u5c14\u4f2f\u7279<\/span>\uff08David Hilbert\uff09<\/span>\u629b\u51fa\u4e86\u4e00\u4e2a\u7814\u7a76\u8ba1\u5212\uff0c\u65e8\u5728\u786e\u4fdd\u6570\u5b66\u7684\u7edd\u5bf9\u786e\u5b9a\u6027\u3002\u4ed6\u5e0c\u671b\u80fd\u4ece\u4e00\u4e9b\u7b80\u5355\u7684\u5047\u8bbe<\/span>\uff08\u5373\u516c\u7406\uff0caxioms\uff09<\/span>\u5f00\u59cb\uff0c\u5bfc\u51fa\u4e00\u4e2a\u7b26\u5408\u4e09\u4e2a\u5173\u952e\u6761\u4ef6\u7684\u7edf\u4e00\u6570\u5b66\u7406\u8bba\u3002<\/span><\/p>\n


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\u5e0c\u5c14\u4f2f\u7279\u7684\u7b2c\u4e00\u4e2a\u6761\u4ef6\u662f\u4e00\u81f4<\/strong>\u6027<\/strong><\/span>\uff08consistency\uff09<\/span>\uff0c\u8fd9\u662f\u6570\u5b66\u4f53\u7cfb\u4e0d\u5b58\u5728\u77db\u76fe\u7684\u57fa\u672c\u6761\u4ef6\uff1a\u5982\u679c\u53ef\u4ee5\u4ece\u540c\u4e00\u4e2a\u516c\u7406\u51fa\u53d1\u8bc1\u660e\u4e24\u4e2a\u77db\u76fe\u7684\u8bba\u8ff0\uff0c\u90a3\u4e48\u6574\u4e2a\u7406\u8bba\u4f53\u7cfb\u5c06\u65e0\u53ef\u6551\u836f\u3002\u4f46\u4e00\u4e2a\u6ca1\u6709\u77db\u76fe\u7684\u7406\u8bba\u4f53\u7cfb\u5176\u638c\u63a7\u8303\u56f4\u5c31\u53d7\u9650\u3002\u8fd9\u5c31\u662f\u5e0c\u5c14\u4f2f\u7279\u63d0\u51fa\u7b2c\u4e8c\u4e2a\u6761\u4ef6\u2014\u2014\u5b8c\u5907\u6027<\/strong><\/span>\uff08completeness\uff09<\/span>\u7684\u52a8\u673a\uff1a\u4ed6\u8981\u6c42\u6240\u6709\u6570\u5b66\u547d\u9898\u90fd\u53ef\u8bc1\u660e\u771f\u4f2a\u3002\u4ed6\u7684\u7b2c\u4e09\u4e2a\u6761\u4ef6\u662f\u53ef\u5224\u5b9a\u6027<\/strong><\/span>\uff08decidability\uff09<\/span>\uff0c\u8981\u6c42\u6709\u660e\u786e\u7684\u673a\u5236\u7a0b\u5e8f\u786e\u5b9a\u4efb\u4f55\u6570\u5b66\u547d\u9898\u7684\u771f\u5047\u3002\u5e0c\u5c14\u4f2f\u7279\u57281930\u5e74\u7684\u4e00\u6b21\u4f1a\u8bae\u4e0a\u5ba3\u79f0\uff1a\u201c\u6211\u4eec\u7684\u53e3\u53f7\u662f\u2018\u6211\u4eec\u5fc5\u987b\u77e5\u9053\uff0c\u6211\u4eec\u7ec8\u4f1a\u77e5\u9053\u2019\u201d\u3002<\/span><\/p>\n


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\u4ec5\u4ec5\u4e00\u5e74\u540e\uff0c\u54e5\u5fb7\u5c14\u5c31\u7ed9\u5e0c\u5c14\u4f2f\u7279\u7684\u68a6\u60f3\u5e26\u6765\u4e86\u7b2c\u4e00\u6b21\u6253\u51fb\u3002\u4ed6\u8bc1\u660e\u50cf\u201c\u8fd9\u4e2a\u547d\u9898\u4e0d\u53ef\u8bc1\u201d\u8fd9\u6837\u81ea\u76f8\u77db\u76fe\u7684\u8bba\u8ff0\u53ef\u4ee5\u4ece\u4efb\u610f\u4e00\u7ec4\u516c\u7406\u4e2d\u63a8\u5bfc\u51fa\u6765\u3002\u5982\u679c\u8fd9\u6837\u7684\u547d\u9898\u786e\u5b9e\u65e0\u6cd5\u88ab\u8bc1\u660e\uff0c\u90a3\u4e48\u8fd9\u4e2a\u7406\u8bba\u5c31\u662f\u4e0d\u5b8c\u6574\u7684\uff0c\u4f46\u5982\u679c\u5b83\u53ef\u4ee5\u88ab\u8bc1\u660e\uff0c\u90a3\u4e48\u8fd9\u4e2a\u7406\u8bba\u4f53\u7cfb\u5c31\u662f\u4e0d\u4e00\u81f4\u7684\u2014\u2014\u66f4\u7cdf\u4e86\u3002\u5728\u540c\u4e00\u7bc7\u8bba\u6587\u4e2d\uff0c\u54e5\u5fb7\u5c14\u8fd8\u8bc1\u660e\uff0c\u6ca1\u6709\u4efb\u4f55\u6570\u5b66\u7406\u8bba\u80fd\u8bc1\u660e\u5176\u81ea\u8eab\u7684\u4e00\u81f4\u6027\u3002<\/span><\/p>\n


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20\u4e16\u7eaa20\u5e74\u4ee3\uff0c\u5927\u536b\u00b7\u5e0c\u5c14\u4f2f\u7279\uff08David Hilbert\uff0c\u5de6\uff09\u60f3\u628a\u6570\u5b66\u5efa\u7acb\u5728\u66f4\u575a\u5b9e\u7684\u57fa\u7840\u4e0a\u3002\u5e93\u5c14\u7279\u00b7\u54e5\u5fb7\u5c14\uff08Kurt G\u00f6del\uff0c\u4e2d\uff09\u548c\u827e\u4f26\u00b7\u56fe\u7075\uff08Alan Turing\uff09\u540e\u6765\u8bc1\u660e\u5e0c\u5c14\u4f2f\u7279\u7684\u68a6\u60f3\u662f\u4e0d\u53ef\u80fd\u7684\u3002\uff5c\u6765\u6e90\uff1aUniversity of G\u00f6ttingen (left); Kurt G\u00f6del Papers, the Shelby White and Leon Levy Archives Center, Institute for Advanced Study; GL Archive\/Alamy Stock Photo<\/span><\/section>\n


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\u7814\u7a76\u8005\u4eec\u4ecd\u5bf9\u672a\u6765\u7684\u6570\u5b66\u7406\u8bba\u62b1\u6709\u5e0c\u671b\uff0c\u5c3d\u7ba1\u5b83\u4e0d\u4e00\u5b9a\u5b8c\u5907\uff0c\u4f46\u4ecd\u53ef\u80fd\u662f\u53ef\u5224\u5b9a\u7684\u3002\u4e5f\u8bb8\u4ed6\u4eec\u53ef\u4ee5\u5f00\u53d1\u4e00\u5957\u7a0b\u5e8f\uff0c\u8bc6\u522b\u6240\u6709\u53ef\u8bc1\u660e\u7684\u547d\u9898\uff0c\u5c31\u80fd\u907f\u5f00\u50cf\u54e5\u5fb7\u5c14\u8fd9\u6837\u607c\u4eba\u7684\u547d\u9898\u3002\u95ee\u9898\u662f\u6ca1\u4eba\u77e5\u9053\u600e\u4e48\u63a8\u7406\u8fd9\u4e9b\u5047\u8bbe\u7684\u7a0b\u5e8f\u3002<\/span><\/p>\n


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1936\u5e74\uff0c\u56fe\u7075<\/span>\uff08Alan Turing\uff09<\/span>23\u5c81\uff0c\u5728\u8bfb\u7814\u7a76\u751f\u3002\u4ed6\u7528\u5f53\u65f6\u8fd8\u4e0d\u719f\u6089\u7684\u8ba1\u7b97\u673a\u8bed\u8a00\u91cd\u65b0\u8868\u8ff0\u4e86\u5e0c\u5c14\u4f2f\u7279\u7684\u53ef\u5224\u5b9a\u6027\u6761\u4ef6\uff0c\u5e76\u7ed9\u4e86\u5b83\u81f4\u547d\u4e00\u51fb\u3002\u56fe\u7075\u521b\u9020\u4e86\u4e00\u4e2a\u6570\u5b66\u6a21\u578b<\/span>\uff08\u73b0\u5728\u53eb\u56fe\u7075\u673a\uff09<\/span>\uff0c\u53ef\u4ee5\u8868\u793a\u6240\u6709\u53ef\u80fd\u7684\u7b97\u6cd5\uff0c\u5e76\u8868\u660e\uff0c\u5982\u679c\u5e0c\u5c14\u4f2f\u7279\u7684\u7a0b\u5e8f\u5b58\u5728\uff0c\u90a3\u4e48\u5b83\u5c06\u4e5f\u9002\u5408\u8fd9\u4e2a\u6a21\u578b\u3002\u7136\u540e\u4ed6\u501f\u9274\u54e5\u5fb7\u5c14\u7684\u81ea\u6307\u65b9\u6cd5\u8bc1\u660e\uff0c\u4e0d\u53ef\u5224\u5b9a\u7684\u7a0b\u5e8f\u2014\u2014\u6216\u8005\u7b49\u4ef7\u5730\uff0c\u4e0d\u53ef\u8ba1\u7b97\u7684\u95ee\u9898\u662f\u5b58\u5728\u7684\uff0c\u4efb\u4f55\u7b97\u6cd5\u90fd\u4e0d\u80fd\u89e3\u51b3\u3002<\/span><\/p>\n


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\u5e0c\u5c14\u4f2f\u7279\u7684\u8ba1\u5212\u5931\u8d25\u4e86\uff1a\u53ef\u8bc1\u660e\u548c\u53ef\u8ba1\u7b97\u7684\u5185\u5bb9\u5c06\u6c38\u8fdc\u5b58\u5728\u57fa\u672c\u9650\u5236\u3002\u4f46\u968f\u7740\u8ba1\u7b97\u673a\u4ece\u62bd\u8c61\u7684\u7406\u8bba\u6f14\u53d8\u6210\u771f\u5b9e\u7684\u673a\u5668\uff0c\u7814\u7a76\u8005\u4eec\u610f\u8bc6\u5230\uff0c\u56fe\u7075\u5c06\u95ee\u9898\u7b80\u5355\u533a\u5206\u4e3a\u53ef\u89e3\u51b3\u548c\u4e0d\u53ef\u89e3\u51b3\uff0c\u4e3a\u540e\u4e16\u7559\u4e0b\u8bb8\u591a\u672a\u89e3\u4e4b\u8c1c\u3002\u523020\u4e16\u7eaa60\u5e74\u4ee3\uff0c\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u5df2\u7ecf\u53d1\u5c55\u51fa\u89e3\u51b3\u67d0\u4e9b\u95ee\u9898\u7684\u5feb\u901f\u7b97\u6cd5\uff0c\u4f46\u5bf9\u4e8e\u5176\u4ed6\u95ee\u9898\uff0c\u552f\u4e00\u5df2\u77e5\u7684\u7b97\u6cd5\u6162\u5f97\u8ba9\u4eba\u96be\u4ee5\u63a5\u53d7\u3002\u5982\u679c\u95ee\u9898\u4e0d\u6b62\u662f\u8fd9\u4e9b\u95ee\u9898\u80fd\u5426\u89e3\u51b3\uff0c\u8fd8\u6709\u8fd9\u4e9b\u95ee\u9898\u89e3\u51b3\u8d77\u6765\u6709\u591a\u56f0\u96be\u5462\uff1fCarmosino \u8bf4\uff1a\u201c\u4e30\u5bcc\u7684\u7406\u8bba\u51fa\u73b0\u4e86\uff0c\u4f46\u6211\u4eec\u4e0d\u518d\u77e5\u9053\u7b54\u6848\u3002\u201d<\/span><\/p>\n


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\u4e0d\u540c\u7684\u8def\u5f84<\/span><\/strong><\/span><\/h3>\n

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\u600e\u4e48\u5f62\u8c61\u5730\u8868\u793a\u5173\u4e8e\u201c\u96be\u5ea6\u201d\u7684\u95ee\u9898\u5982\u4f55\u8ba9\u4eba\u5934\u75bc\u5462\uff1f\u8ba9\u6211\u4eec\u5728\u56fe<\/span>\uff08graph\uff09<\/span>\u4e0a\u8ba8\u8bba\u3002\u8282\u70b9<\/span>\uff08node\uff09<\/span>\u548c\u8fde\u8fb9<\/span>\uff08egde\uff09<\/span>\u7ec4\u6210\u7f51\u7edc\uff0c\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u4eec\u7528\u7f51\u7edc\u6a21\u62df\u4ece\u91cf\u5b50\u8ba1\u7b97<\/span>\uff08quantum computation\uff09<\/span>\u5230\u4ea4\u901a\u6d41\u7b49\u4f17\u591a\u95ee\u9898\u3002<\/span><\/p>\n


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\u54c8\u5bc6\u987f\u8def\u5f84\uff08Hamiltonian path\uff09\uff0c\u8def\u5f84\u7ecf\u8fc7\u6bcf\u4e2a\u8282\u70b9\uff0c\u4e14\u53ea\u7ecf\u8fc7\u4e00\u6b21\u3002\uff5c\u6765\u6e90\uff1aSamuel Velasco\/<\/span><\/span>Quanta Magazine<\/span><\/em><\/section>\n


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\u7ed9\u4f60\u4e00\u4e2a\u56fe\uff0c\u8ba9\u4f60\u627e\u5230\u56fe\u4e0a\u7684\u54c8\u5bc6\u987f\u8def\u5f84<\/strong><\/span>\uff08Hamiltonian path\uff0c\u8def\u5f84\u7ecf\u8fc7\u6bcf\u4e2a\u8282\u70b9\uff0c\u4e14\u53ea\u7ecf\u8fc7\u4e00\u6b21\uff09<\/span>\u3002\u8fd9\u4e2a\u95ee\u9898\u7406\u5e94\u662f\u53ef\u4ee5\u89e3\u51b3\u7684\uff0c\u56e0\u4e3a\u6240\u6709\u8def\u5f84\u6570\u91cf\u6709\u9650\uff0c\u5373\u4fbf\u522b\u65e0\u4ed6\u6cd5\uff0c\u4e5f\u53ef\u4ee5\u68c0\u67e5\u6bcf\u6761\u8def\u5f84\u662f\u5426\u7b26\u5408\u8981\u6c42\u3002\u5982\u679c\u56fe\u4e0a\u53ea\u6709\u51e0\u4e2a\u8282\u70b9\u90a3\u5c31\u597d\u529e\u4e86\uff0c\u4f46\u5bf9\u4e8e\u7a0d\u5fae\u5927\u4e00\u70b9\u7684\u56fe\uff0c\u603b\u8def\u5f84\u6570\u5c31\u4f1a\u6025\u5267\u4e0a\u5347\u4ee5\u81f3\u5931\u63a7\uff0c\u8fd9\u4e2a\u7b97\u6cd5\u5b9e\u9645\u4e0a\u5c31\u5931\u6548\u4e86\u3002<\/span><\/p>\n


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\u8fd8\u6709\u66f4\u590d\u6742\u7684\u54c8\u5bc6\u987f\u8def\u5f84\u7b97\u6cd5\uff0c\u4f46\u7b97\u6cd5\u89e3\u51b3\u95ee\u9898\u6240\u9700\u7684\u65f6\u95f4\u603b\u662f\u968f\u7740\u56fe\u7684\u5927\u5c0f\u5448\u6307\u6570\u589e\u957f\u3002\u52a0\u5dde\u5927\u5b66\u5723\u8fed\u6208\u5206\u6821<\/span>\uff08University of California, San Diego\uff09<\/span>\u7684\u590d\u6742\u6027\u7406\u8bba\u5b66\u5bb6 Russell Impagliazzo \u8bf4\uff1a\u201c\u56fe\u4e0d\u9700\u8981\u7279\u522b\u5927\uff0c\u4f46\u5373\u4f7f\u662f\u6700\u597d\u7684\u7b97\u6cd5\u7814\u7a76\u8005\u4e5f\u65e0\u6cd5\u5728 [\u4efb\u4f55\u5408\u7406\u7684\u65f6\u95f4\u5185] \u627e\u5230\u8def\u5f84\uff0c\u6211\u8bf4\u7684 [\u5408\u7406\u7684\u65f6\u95f4] \u662f\u6307 [\u5728\u5b87\u5b99\u7ec8\u7ed3\u4e4b\u524d]\u3002\u201d<\/span><\/p>\n


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\u54c8\u5bc6\u987f\u8def\u5f84\u95ee\u9898\u8fd8\u6709\u53e6\u4e00\u4e2a\u6709\u8da3\u7684\u6027\u8d28\u3002\u5982\u679c\u6709\u4eba\u58f0\u79f0\u5728\u7279\u5b9a\u56fe\u4e0a\u627e\u5230\u4e86\u4e00\u6761\u54c8\u5bc6\u987f\u8def\u5f84\uff0c\u5373\u4f7f\u8fd9\u4e2a\u56fe\u975e\u5e38\u5927\uff0c\u4f60\u4e5f\u53ef\u4ee5\u5feb\u901f\u5730\u68c0\u67e5\u5b83\u7684\u89e3\u662f\u5426\u6b63\u786e\u3002\u6240\u9700\u8981\u505a\u7684\u4ec5\u662f\u6cbf\u7740\u8def\u5f84\u9010\u4e00\u52fe\u9009\u8282\u70b9\uff0c\u5e76\u68c0\u67e5\u786e\u4fdd\u6ca1\u6709\u52fe\u9009\u4efb\u4f55\u8282\u70b9\u4e24\u6b21\u3002\u5982\u679c\u6700\u540e\u6ca1\u6709\u8282\u70b9\u4e22\u5931\uff0c\u90a3\u4e48\u8fd9\u6761\u8def\u5f84\u5c31\u662f\u54c8\u5bc6\u987f\u8def\u5f84\u3002<\/span><\/p>\n


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\u68c0\u67e5\u7b97\u6cd5\u6240\u9700\u7684\u65f6\u95f4\u4e0e\u56fe\u7684\u5927\u5c0f\u6210\u6b63\u6bd4\uff0c\u6211\u4eec\u5c06\u5176\u5f52\u5165\u591a\u9879\u5f0f\u7b97\u6cd5\u7c7b\u522b\uff0c\u5176\u8fd0\u884c\u65f6\u95f4\u968f\u7740\u56fe\u5927\u5c0f\u7684\u591a\u9879\u5f0f\u51fd\u6570\u800c\u589e\u52a0\u3002\u591a\u9879\u5f0f\u589e\u957f\u6bd4\u6307\u6570\u589e\u957f\u66f4\u6e29\u548c\uff0c\u56e0\u6b64\u591a\u9879\u5f0f\u7b97\u6cd5\u5373\u4f7f\u5728\u5f88\u5927\u7684\u56fe\u4e0a\u4e5f\u662f\u53ef\u884c\u7684\u3002Carmosino \u8bf4\uff1a\u201c\u8fd9\u5927\u5927\u63d0\u9ad8\u4e86\u6548\u7387\u3002\u201d<\/span><\/p>\n


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\u54c8\u5bc6\u987f\u8def\u5f84\u95ee\u9898\u5177\u6709\u660e\u663e\u7684\u4e0d\u5bf9\u79f0\u6027<\/span>\uff08asymmetry\uff09<\/span>\uff1a\u53ef\u4ee5\u7528\u591a\u9879\u5f0f\u7b97\u6cd5\u5feb\u901f\u9a8c\u8bc1\u89e3\uff0c\u4f46\u6c42\u89e3\u5219\u53ea\u80fd\u7528\u7f13\u6162\u7684\u6307\u6570\u7b97\u6cd5<\/strong>\u3002\u8fd9\u79cd\u4e0d\u5bf9\u79f0\u6027\u4e5f\u5e76\u4e0d\u610f\u5916\u2014\u2014\u6b23\u8d4f\u827a\u672f\u54c1\u603b\u6bd4\u521b\u4f5c\u66f4\u5bb9\u6613\uff0c\u9a8c\u8bc1\u6570\u5b66\u5b9a\u7406\u603b\u6bd4\u8bc1\u660e\u8981\u5bb9\u6613\uff0c\u4f46\u5e76\u975e\u6240\u6709\u7684\u8ba1\u7b97\u95ee\u9898\u90fd\u5177\u6709\u8fd9\u6837\u7684\u4e0d\u5bf9\u79f0\u7279\u5f81\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6709\u4e00\u4e2a\u4e0e\u5bfb\u627e\u54c8\u5bc6\u987f\u8def\u5f84\u975e\u5e38\u76f8\u4f3c\u7684\u95ee\u9898\uff0c\u5176\u96be\u5ea6\u5374\u622a\u7136\u4e0d\u540c\u3002<\/span><\/p>\n


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\u6307\u6570\u7b97\u6cd5\u4e0e\u591a\u9879\u5f0f\u7b97\u6cd5\u5bf9\u6bd4\u3002\u5e76\u975e\u6240\u6709\u95ee\u9898\u7684\u590d\u6742\u6027\u90fd\u4ee5\u540c\u6837\u7684\u901f\u5ea6\u589e\u957f\u3002\uff5c\u6765\u6e90\uff1aPaul Chaikin\/<\/span><\/span>Quanta Magazine<\/span><\/em><\/section>\n

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

\u5047\u8bbe\u518d\u7ed9\u4f60\u4e00\u5f20\u56fe\uff0c\u73b0\u5728\u8981\u6c42\u4f60\u627e\u5230\u6b27\u62c9\u8def\u5f84<\/strong><\/span>\uff08Eulerian path\uff09<\/span>\uff0c\u5373\u7ecf\u8fc7\u6bcf\u6761\u8fb9\u6070\u597d\u4e00\u6b21\u7684\u8def\u5f84\u3002\u540c\u6837\u7684\uff0c\u53ef\u4ee5\u7528\u591a\u9879\u5f0f\u7b97\u6cd5\u9a8c\u8bc1\u89e3\uff0c\u4f46\u5bf9\u4e8e\u6c42\u89e3\u6b27\u62c9\u95ee\u9898\uff0c\u4e5f\u5b58\u5728\u591a\u9879\u5f0f\u7b97\u6cd5\uff0c\u8fd9\u4e2a\u95ee\u9898\u5c31\u4e0d\u5b58\u5728\u4e0d\u5bf9\u79f0\u3002\u5728\u590d\u6742\u6027\u7406\u8bba\u4e2d\uff0c\u67d0\u4e9b\u8def\u5f84\u4f3c\u4e4e\u4f1a\u6bd4\u5176\u4ed6\u8def\u5f84\u66f4\u597d\u627e\u3002<\/span><\/p>\n


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<\/p>\n

\u6b27\u62c9\u8def\u5f84\uff08Eulerian path\uff09\uff0c\u7ecf\u8fc7\u6bcf\u6761\u8fb9\u6070\u597d\u4e00\u6b21\u7684\u8def\u5f84\u3002\uff5c\u6765\u6e90\uff1aSamuel Velasco\/<\/span><\/span>Quanta Magazine<\/span><\/em><\/section>\n


<\/em><\/p>\n

\u54c8\u5bc6\u987f\u8def\u5f84\u95ee\u9898\u548c\u6b27\u62c9\u8def\u5f84\u95ee\u9898\u90fd\u5c5e\u4e8e\u590d\u6742\u5ea6\u7c7b\u522b NP\uff0cNP \u95ee\u9898\u7684\u5b9a\u4e49\u662f\u6240\u6709\u53ef\u4ee5\u7528\u591a\u9879\u5f0f\u7b97\u6cd5\u68c0\u9a8c\u89e3\u7684\u95ee\u9898\u3002\u6b27\u62c9\u8def\u5f84\u95ee\u9898\u4e5f\u5c5e\u4e8eP\u7c7b\uff0c\u56e0\u4e3a\u53ef\u4ee5\u7528\u591a\u9879\u5f0f\u7b97\u6cd5\u6c42\u89e3\u3002\u4f46\u663e\u7136\uff0c\u54c8\u5bc6\u987f\u8def\u5f84\u95ee\u9898\u4e0d\u662f\u8fd9\u6837\u7684\u3002\u4e3a\u4ec0\u4e48\u8fd9\u4e24\u4e2a\u56fe\u95ee\u9898\u8868\u9762\u4e0a\u5982\u6b64\u76f8\u4f3c\uff0c\u5374\u6709\u5982\u6b64\u663e\u8457\u7684\u4e0d\u540c\uff1f\u8fd9\u5c31\u662fP\u4e0eNP\u95ee\u9898\u7684\u672c\u8d28\u3002<\/span><\/p>\n


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

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

\u4e24\u4e2a\u76f8\u4f3c\u7684\u95ee\u9898\u53ef\u80fd\u5177\u6709\u622a\u7136\u4e0d\u540c\u7684\u590d\u6742\u6027\u3002\uff5c\u6765\u6e90\uff1aPaul Chaikin\/Quanta Magazine<\/em><\/span><\/section>\n


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

\u201c\u666e\u904d\u201d\u95ee\u9898<\/span><\/strong><\/span><\/h3>\n

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

\u8d77\u521d\uff0c\u590d\u6742\u6027\u7c7b\u522b\u4f3c\u4e4e\u662f\u4e3a\u4e86\u5206\u7c7b\u51fa\u76f8\u4f3c\u4f46\u4e0d\u76f4\u63a5\u76f8\u5173\u7684\u95ee\u9898\u2014\u2014\u6ca1\u6709\u4eba\u6000\u7591\u8fc7\u5bfb\u627e\u54c8\u5bc6\u987f\u8def\u5f84\u4e0e\u5176\u4ed6\u56f0\u96be\u8ba1\u7b97\u95ee\u9898\u4e4b\u95f4\u6709\u4ec0\u4e48\u5173\u7cfb\u3002\u76f4\u52301971\u5e74\uff0c\u590d\u6742\u6027\u7406\u8bba\u5b66\u5bb6 Stephen Cook \u5728\u7f8e\u56fd\u83b7\u53d6\u7ec8\u8eab\u6559\u804c\u53d7\u632b\u540e\uff0c\u642c\u5230\u591a\u4f26\u591a\u5927\u5b66\uff0c\u4e00\u5e74\u5185\u5c31\u53d1\u8868\u4e86\u4e00\u4e2a\u975e\u51e1\u7684\u7ed3\u679c\u3002\u4ed6\u53d1\u73b0\u4e86\u4e00\u4e2a\u795e\u5947\u7684\u7279\u5b9a<\/strong>NP<\/strong>\u95ee\u9898\uff1a\u5982\u679c\u5b58\u5728\u4e00\u4e2a\u591a\u9879\u5f0f\u7b97\u6cd5\u53ef\u4ee5\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u90a3\u4e48\u5b83\u4e5f\u53ef\u4ee5\u89e3\u51b3NP\u4e2d\u7684\u5176\u4ed6\u6240\u6709\u95ee\u9898<\/strong>\u3002Cook \u53d1\u73b0\u7684\u8fd9\u4e2a\u201c\u666e\u904d\u201d\u95ee\u9898\u4f3c\u4e4e\u662f\u4e00\u6839\u5355\u72ec\u7684\u67f1\u5b50\uff0c\u652f\u6491\u7740\u770b\u4f3c\u56f0\u96be\u95ee\u9898\u7684\u7c7b\u522b\uff0c\u5c06\u5b83\u4eec\u4e0e\u5730\u9762\u7684\u7b80\u5355\u95ee\u9898\u5206\u5f00\u3002\u4e00\u65e6\u89e3\u51b3\u4e86\u8fd9\u4e2a\u95ee\u9898\uff0cNP\u4e2d\u7684\u5176\u4f59\u95ee\u9898\u5c31\u4f1a\u53d8\u5f97\u7b80\u5355\u3002<\/span><\/p>\n


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

Cook \u6000\u7591\u4ed6\u7684\u201c\u666e\u904d\u201d\u95ee\u9898\u6ca1\u6709\u5feb\u7684\u7b97\u6cd5\uff0c\u4ed6\u5728\u8bba\u6587\u4e2d\u4e5f\u8868\u8fbe\u4e86\u8fd9\u79cd\u6000\u7591\uff0c\u5e76\u8865\u5145\u9053\uff1a\u201c\u6211\u89c9\u5f97\u503c\u5f97\u82b1\u8d39\u5927\u91cf\u7cbe\u529b\u6765\u8bc1\u660e\u8fd9\u4e2a\u731c\u60f3\u3002\u201d\u540e\u6765\u8bc1\u660e\uff0c \u201c\u5927\u91cf\u7cbe\u529b\u201d\u7684\u8868\u8ff0\u8fd8\u662f\u4fdd\u5b88\u4e86\u3002<\/span><\/p>\n


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

<\/p>\n

Stephen Cook\u3001Leonid Levin \u548c Richard Karp \u572820\u4e16\u7eaa70\u5e74\u4ee3\u521d\u5171\u540c\u63d0\u51fa\u4e86P\u4e0eNP\u95ee\u9898\u3002\uff5c\u6765\u6e90\uff1aBBVA Foundation<\/span><\/section>\n


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

\u5927\u7ea6\u5728\u540c\u65f6\uff0c\u82cf\u8054\u7684\u672c\u79d1\u751f Leonid Levin \u8bc1\u660e\u4e86\u4e00\u4e2a\u7c7b\u4f3c\u7684\u7ed3\u679c\uff0c\u4ed6\u786e\u5b9a\u4e86\u591a\u4e2a\u4e0d\u540c\u7684\u666e\u904d\u95ee\u9898\u3002\u6b64\u5916\uff0c\u7f8e\u56fd\u590d\u6742\u6027\u7406\u8bba\u5bb6 Richard Karp \u8bc1\u660e\uff0cCook \u548c Levin \u6240\u786e\u5b9a\u7684\u666e\u904d\u6027\u5c5e\u6027\u672c\u8eab\u51e0\u4e4e\u666e\u904d\u5b58\u5728<\/span>\uff08\u5c3d\u7ba1 Karp \u548c\u5e93\u514b\u76f4\u5230\u591a\u5e74\u540e\u624d\u5f97\u77e5 Levin \u7684\u5de5\u4f5c\uff09<\/span>\u3002\u51e0\u4e4e\u6240\u6709\u6ca1\u6709\u5df2\u77e5\u591a\u9879\u5f0f\u7b97\u6cd5\u7684<\/strong>NP<\/strong>\u95ee\u9898\uff0c\u5373\u51e0\u4e4e\u6240\u6709\u770b\u4f3c\u56f0\u96be\u7684\u5bb9\u6613<\/strong>\u9a8c\u8bc1<\/strong>\u7684\u95ee\u9898\u90fd\u5177\u6709\u76f8\u540c\u7684\u6027\u8d28\uff0c\u8fd9\u88ab\u79f0\u4e3a<\/strong>NP\u5b8c\u5168\u95ee\u9898<\/strong><\/span>\uff08NP-completeness\uff09<\/span>\u3002\u8fd9\u610f\u5473\u7740\u6240\u6709NP\u5b8c\u5168\u95ee\u9898<\/span>\uff08\u5305\u62ec\u54c8\u5bc6\u987f\u8def\u5f84\u95ee\u9898\u3001\u6570\u72ec\u548c\u5176\u4ed6\u6210\u5343\u4e0a\u4e07\u7684\u95ee\u9898\uff09<\/span>\u5728\u7cbe\u786e\u610f\u4e49\u4e0a\u662f\u7b49\u4ef7\u7684\u3002\u201c\u4f60\u9762\u5bf9\u7684\u8fd9\u4e9b\u6240\u6709\u4e0d\u540c\u7684\u95ee\u9898\uff0c\u90fd\u795e\u5947\u5730\u53d8\u6210\u4e86\u540c\u4e00\u4e2a\u95ee\u9898\uff0c\u4f46\u6211\u4eec\u4ecd\u4e0d\u77e5\u9053\u5b83\u662f\u5426\u80fd\u88ab\u89e3\u51b3\u3002\u201dIlango\u8bf4\u3002<\/span><\/p>\n


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\u89e3\u51b3\u4efb\u4f55\u4e00\u4e2aNP\u5b8c\u5168\u95ee\u9898\u7684\u96be\u5ea6\u8db3\u4ee5\u5ab2\u7f8e\u89e3\u51b3 P \u548c NP \u95ee\u9898\u3002\u5982\u679cP \u2260 NP\uff0c\u5219\u6613\u4e8e\u89e3\u51b3\u548c\u96be\u4ee5\u89e3\u51b3\u7684\u95ee\u9898\u4e4b\u95f4\u7684\u5dee\u522b\u5c31\u662f\u9065\u4e0d\u53ef\u53ca\u7684\u5929\u5811\uff0c\u88ab\u4e0a\u5343\u4e2a\u67f1\u5b50\u7262\u7262\u652f\u6491\uff1b\u5982\u679cP = NP\uff0c\u90a3\u4e48\u6574\u4e2a\u7ed3\u6784\u5c31\u5728\u5d29\u6e83\u7684\u8fb9\u7f18\u6447\u6447\u6b32\u5760\uff0c\u53ea\u7b49\u4e00\u5757\u5de8\u77f3\u843d\u4e0b\u3002<\/span><\/p>\n


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

<\/p>\n

\u51e0\u4e4e\u6240\u6709\u770b\u4f3c\u56f0\u96be\u7684NP\u95ee\u9898\u90fd\u662fNP\u5b8c\u5168\u7684\uff1a\u5176\u4e2d\u4efb\u4f55\u4e00\u4e2a\u95ee\u9898\u7684\u96be\u5ea6\u7b49\u4ef7\u4e8eP \u548c NP \u95ee\u9898\u3002\uff5c\u6765\u6e90\uff1aSamuel Velasco\/<\/span><\/span>Quanta Magazine<\/span><\/em><\/section>\n


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Cook\u3001Levin \u548c Karp \u5c06\u8fd9\u4e9b\u770b\u4f3c\u4e0d\u76f8\u5173\u7684\u95ee\u9898\u7edf\u4e00\u4e86\u8d77\u6765\u3002\u73b0\u5728\uff0c\u6240\u6709\u590d\u6742\u6027\u7406\u8bba\u5bb6\u90fd\u53ea\u9700\u89e3\u51b3\u4e00\u4e2a\u95ee\u9898\uff1aP = NP\u5417\uff1f<\/span><\/p>\n


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\u4e94\u5341\u5e74\u540e\uff0c\u8fd9\u4e2a\u95ee\u9898\u4ecd\u7136\u6ca1\u6709\u7b54\u6848\u3002Kabanets \u628a\u5173\u4e8e\u8ba1\u7b97\u80fd\u529b\u6781\u9650\u7684\u63a8\u7406\u6bd4\u4f5c\u5728\u4e00\u4e2a\u5e7f\u9614\u65e0\u57a0\u7684\u9886\u57df\u4e2d\u8fdb\u884c\u52d8\u6d4b\uff0c\u53ea\u80fd\u770b\u5230\u4e00\u5c0f\u90e8\u5206\uff0c\u65e0\u6cd5\u9886\u7565\u5230\u5168\u5c40\u3002\u4e00\u4e2a\u62e5\u6709\u65e0\u9650\u8ba1\u7b97\u80fd\u529b\u7684\u201c\u795e\u201d\u5374\u53ef\u4ee5\u4ece\u5c71\u9876\u4fef\u77b0\uff0c\u4f46\u51e1\u4eba\u65e0\u6cd5\u6307\u671b\u83b7\u5f97\u8fd9\u79cd\u4f18\u52bf\u3002\u201c\u6211\u4eec\u8fd9\u4e9b\u8eab\u5904\u5c71\u811a\u4e0b\u7684\u4eba\u53ef\u4ee5\u8bd5\u7740\u8df3\u8d77\u6765\u83b7\u5f97\u66f4\u597d\u7684\u89c6\u91ce\uff0c\u201dKabanets \u8bf4\u3002<\/span><\/p>\n


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\u5047\u8bbe P = NP\u3002\u4e3a\u4e86\u8bc1\u660e\u8fd9\u4e00\u70b9\uff0c\u7814\u7a76\u8005\u4eec\u9700\u8981\u627e\u5230\u4e00\u4e2a\u5feb\u901f\u89e3\u51b3NP\u5b8c\u5168\u95ee\u9898\u7684\u7b97\u6cd5\uff0c\u8fd9\u4e2a\u65b9\u6cd5\u53ef\u80fd\u9690\u85cf\u5728\u5e7f\u9614\u56fe\u666f\u4e2d\u7684\u67d0\u4e2a\u9690\u79d8\u89d2\u843d\u3002\u6ca1\u6709\u4eba\u80fd\u4fdd\u8bc1\u5f88\u5feb\u53ef\u4ee5\u627e\u5230\u5b83\uff1a\u590d\u6742\u6027\u7406\u8bba\u5bb6\u4eec\u6216\u8bb8\u53ea\u9700\u8981\u7814\u7a76\u51e0\u5341\u5e74\uff0c\u5c31\u80fd\u5076\u7136\u53d1\u73b0\u4e00\u4e9b\u89e3\u51b3\u770b\u4f3c\u56f0\u96be<\/span>\uff08\u5c3d\u7ba1\u4e0d\u662fNP\u5b8c\u5168\uff09<\/span>\u95ee\u9898\u7684\u5de7\u5999\u7b97\u6cd5\u3002\u73b0\u5728\u6211\u4eec\u5047\u8bbeP \u2260 NP\u3002\u8981\u8bc1\u660e\u8fd9\u4e00\u70b9\u4f3c\u4e4e\u66f4\u52a0\u56f0\u96be\u3002\u590d\u6742\u6027\u7406\u8bba\u5b66\u5bb6\u5fc5\u987b\u786e\u5b9a\uff0c\u4e0d\u5b58\u5728\u5feb\u901f\u7b97\u6cd5\uff0c\u624d\u80fd\u6709\u6548\u5730\u62a2\u5148\u632b\u8d25\u672a\u6765\u6240\u6709\u7814\u7a76\u4eba\u5458\u7684\u52aa\u529b\u3002<\/span><\/p>\n


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\u6709\u4e00\u90e8\u5206\u95ee\u9898\u5728\u4e8e\u4e0d\u77e5\u4ece\u4f55\u5165\u624b\u3002\u4f46\u662f\uff0c\u8fd9\u5e76\u4e0d\u610f\u5473\u7740\u7814\u7a76\u8005\u4eec\u6ca1\u6709\u5c1d\u8bd5\u8fc7\u3002\u5728\u8fc7\u53bb\u51e0\u5341\u5e74\u91cc\uff0c\u4ed6\u4eec\u4ece\u8bb8\u591a\u89d2\u5ea6\u63a2\u8ba8\u4e86\u8fd9\u4e2a\u95ee\u9898\uff0c\u4f46\u5747\u4ee5\u5931\u8d25\u544a\u7ec8\u3002\u201c\u8fd9\u662f\u8ba1\u7b97\u673a\u7406\u8bba\u79d1\u5b66\u4e2d\u6700\u660e\u663e\u7684\u4e8b\u5b9e\u4e4b\u4e00\uff0c\u201d Carmosino \u8bf4\u3002\u201c\u5f53\u4e00\u79cd\u73b0\u8c61\u5982\u6b64\u6301\u4e45\u65f6\uff0c\u5c31\u9700\u8981\u4e00\u4e9b\u89e3\u91ca\u3002\u201d<\/span><\/p>\n


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2. \u969c\u788d<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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


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\u5230\u4e86 Carmosino \u8bfb\u5927\u5b66\u7684\u6700\u540e\u4e00\u5e74\uff0c\u597d\u5947\u5fc3\u5f15\u5bfc\u4ed6\u4ece\u54e5\u5fb7\u5c14\u8f6c\u5411\u4e86\u590d\u6742\u6027\u7406\u8bba\u7684\u7814\u7a76\u8bfe\u7a0b\u3002\u4ed6\u60ca\u8bb6\u5730\u53d1\u73b0\uff0c\u82b1\u5728\u5bb6\u5ead\u4f5c\u4e1a\u4e0a\u7684\u65f6\u95f4\u6bd4\u4ed6\u6700\u611f\u5174\u8da3\u7684\u9879\u76ee\u8fd8\u8981\u591a\uff0c\u8fd9\u4e2a\u9879\u76ee\u662f\u4e00\u4e2a\u8ba1\u7b97\u673a\u7a0b\u5e8f\uff0c\u53ef\u4ee5\u5b66\u4e60\u7ae5\u8bdd\u6545\u4e8b\u7684\u53d9\u8ff0\u7ed3\u6784\u5e76\u751f\u6210\u65b0\u7684\u7ae5\u8bdd\u6545\u4e8b\u3002\u201c\u6211\u60f3\uff0c\u6211\u5f97\u8ba4\u771f\u5bf9\u5f85\u8fd9\u4ef6\u4e8b\uff0c\u201d Carmosino \u56de\u5fc6\u8bf4\u3002\u4e0d\u4e45\u4e4b\u540e\uff0c\u56e0\u4e3a\u4ed6\u5bf9\u590d\u6742\u6027\u7406\u8bba\u7684\u7814\u7a76\u8fc7\u4e8e\u6295\u5165\uff0c\u4ee5\u81f3\u4e8e\u5bfc\u5e08\u6e29\u548c\u5730\u5efa\u8bae\u4ed6\u91cd\u65b0\u8003\u8651\u6bd5\u4e1a\u540e\u7684\u8ba1\u5212\u3002<\/span><\/p>\n


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\u201c\u4ed6\u8bf4\uff0c\u2018\u4f60\u77e5\u9053\uff0c\u5982\u679c\u4f60\u60f3\u7ee7\u7eed\u505a\u8fd9\u4e2a\uff0c\u5982\u679c\u4f60\u60f3\u7ee7\u7eed\u7814\u7a76\u8ba1\u7b97\u673a\u7406\u8bba\u548c\u590d\u6742\u6027\u7406\u8bba\uff0c\u4f60\u53ef\u4ee5\u53bb\u7814\u7a76\u751f\u9662\u3002\u2019\u201d Carmosino \u8bf4\u3002\u83b7\u5f97\u7855\u58eb\u5b66\u4f4d\u540e\uff0c\u4ed6\u57282012\u5e74\u642c\u5230\u5723\u5730\u4e9a\u54e5\uff0c\u5728 Impagliazzo \u7684\u6307\u5bfc\u4e0b\u653b\u8bfb\u535a\u58eb\u5b66\u4f4d\u3002<\/span><\/p>\n


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

<\/p>\n

Marco Carmosino \u5bf920\u4e16\u7eaa90\u5e74\u4ee3\u4e00\u9879\u91cd\u5927\u6210\u679c\u7684\u75f4\u8ff7\uff0c\u6fc0\u53d1\u4e8620\u5e74\u540e\u5728\u5143\u590d\u6742\u6027\u65b9\u9762\u7684\u7a81\u7834\u3002\uff5c\u6765\u6e90\uff1aKaitlin Abrahamson<\/span><\/section>\n


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\u8d77\u521d\uff0cCarmosino \u7684\u4e3b\u8981\u76ee\u6807\u662f\u66f4\u597d\u5730\u7406\u89e320\u5e74\u524d\u7684\u4e00\u7bc7\u5177\u6709\u91cc\u7a0b\u7891\u610f\u4e49\u7684\u8bba\u6587\uff0c\u8fd9\u7bc7\u8bba\u6587\u6fc0\u53d1\u4e86\u4ed6\u7684\u60f3\u8c61\u529b\u3002\u8be5\u8bba\u6587\u7531\u590d\u6742\u6027\u7406\u8bba\u5bb6 Alexander Razborov \u548c Steven Rudich \u64b0\u5199\uff0c\u8bc1\u660e P \u2260 NP \u7684\u201c\u81ea\u7136\u201d\u7b56\u7565\u80af\u5b9a\u4f1a\u5931\u8d25\uff0c\u56e0\u4e3a\u6210\u529f\u7684\u4ee3\u4ef7\u5c06\u662f\u52a0\u5bc6\u6280\u672f\u7684\u5f7b\u5e95\u5d29\u6e83\uff0c\u800c\u7814\u7a76\u4eba\u5458\u8ba4\u4e3a\u8fd9\u79cd\u60c5\u51b5\u975e\u5e38\u4e0d\u53ef\u80fd\u53d1\u751f\u3002\u7814\u7a76\u4eba\u5458\u5c06Razborov\u548cRudich\u7684\u7ed3\u679c\u89e3\u91ca\u4e3a\u8bc1\u660e P \u2260 NP \u7684\u6d41\u884c\u65b9\u6cd5\u7684\u969c\u788d\u3002<\/span><\/p>\n


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\u201c\u81ea\u7136\u8bc1\u660e\u969c\u788d<\/strong>\u201d<\/span>\uff08natural proofs barrier\uff09<\/span>\u53ea\u662f\u89e3\u51b3\u590d\u6742\u6027\u7406\u8bba\u4e2d\u5f00\u653e\u95ee\u9898\u5df2\u77e5\u7684\u8bb8\u591a\u969c\u788d\u4e4b\u4e00\u3002\u628a\u8fd9\u79cd\u969c\u788d\u6bd4\u4f5c\u8def\u969c\uff0c\u5c31\u50cf\u5728\u8b66\u544a\u6211\u4eec\u6240\u6709\u770b\u4f3c\u6709\u5e0c\u671b\u7684\u9053\u8def\u5b9e\u9645\u4e0a\u90fd\u662f\u4e00\u6761\u6b7b\u80e1\u540c\u3002\u603b\u4e4b\uff0c\u8fd9\u4e9b\u969c\u788d\u8868\u660e\uff0c\u4efb\u4f55\u89e3\u51b3P\u4e0eNP\u95ee\u9898\u7684\u8bc1\u660e\u90fd\u5fc5\u987b\u4e0e\u8fc7\u53bb\u7684\u8bc1\u660e\u65b9\u6cd5\u622a\u7136\u4e0d\u540c\uff1b\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u5927\u591a\u6570\u7814\u7a76\u8005\u8ba4\u4e3a\u89e3\u51b3\u65b9\u6848\u4ecd\u7136\u9065\u4e0d\u53ef\u53ca\u3002\u4f46\u81f3\u5c11\u8fd9\u4e9b\u969c\u788d\u53ef\u4ee5\u544a\u8bc9\u4ed6\u4eec\u54ea\u4e9b\u5730\u65b9\u4e0d\u5e94\u8be5\u53bb\u5c1d\u8bd5\u3002Ilango\u8868\u793a\uff1a\u201c\u590d\u6742\u6027\u7406\u8bba\u7684\u53d1\u5c55\u5b58\u5728\u8bb8\u591a\u969c\u788d\uff0c\u5907\u53d7\u8bc5\u5492\u4e0e\u795d\u798f\u3002\u201d<\/span><\/p>\n


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\u5f53 Carmosino \u9047\u5230\u81ea\u7136\u8bc1\u660e\u969c\u788d\u65f6\uff0c\u5b83\u5df2\u7ecf\u6709\u5c06\u8fd120\u5e74\u7684\u5386\u53f2\u4e86\u3002\u4f46\u4ed6\u6000\u7591\u5b83\u80fd\u7ed9\u7814\u7a76\u8005\u5e26\u6765\u66f4\u591a\u542f\u53d1\u3002\u8fd9\u4e00\u5929\u7ec8\u4f1a\u5230\u6765\uff0c\u4ed6\u548c\u4e09\u4e2a\u540c\u4e8b\u4ece\u5143\u590d\u6742\u6027\u7684\u89d2\u5ea6\u7814\u7a76\u81ea\u7136\u8bc1\u660e\u969c\u788d\uff0c\u5f97\u5230\u4e86\u4e00\u4e2a\u4ee4\u4eba\u60ca\u8bb6\u7684\u7ed3\u679c\u3002\u4ed6\u4eec\u7684\u8bc1\u660e\u5f15\u53d1\u4e86\u4eba\u4eec\u5bf9\u5143\u590d\u6742\u6027<\/span>\uff08meta-complexity\uff09<\/span>\u7684\u65b0\u5174\u8da3\uff0c\u5728\u4e4b\u540e\u51e0\u5e74\u91cc\u5f15\u53d1\u4e86\u4e00\u9635\u70ed\u6f6e\u3002<\/span><\/p>\n


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\u8981\u4ece\u81ea\u7136\u8bc1\u660e\u969c\u788d\u5230\u5143\u590d\u6742\u6027\uff0c\u6211\u4eec\u5fc5\u987b\u56de\u523020\u4e16\u7eaa70\u5e74\u4ee3\uff0c\u90a3\u65f6\u7684\u7814\u7a76\u8005\u4eec\u521a\u5f00\u59cb\u5904\u7406P\u4e0eNP\u95ee\u9898\u3002\u662f\u4ec0\u4e48\u8ba9\u8bc1\u660e\u95ee\u9898\u53d8\u5f97\u5982\u6b64\u56f0\u96be\uff1f<\/span><\/p>\n


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\u7535\u8def\u590d\u6742\u5ea6<\/span><\/strong><\/h3>\n


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\u6700\u521d\uff0c\u7814\u7a76\u4eba\u5458\u8bd5\u56fe\u8bc1\u660e P \u2260 NP \u2014\u2014 \u4e5f\u5c31\u662f\u8bf4\uff0c\u8bc1\u660e\u5b58\u5728\u4e00\u4e9b NP \u95ee\u9898 \uff0c\u5b83\u4eec\u4e0d\u80fd\u88ab\u4efb\u4f55\u53ef\u80fd\u7684\u591a\u9879\u5f0f\u7b97\u6cd5\u6240\u89e3\u51b3 \u2014\u2014 \u4f7f\u7528\u7684\u662f\u56fe\u7075\u7528\u6765\u8bc1\u660e\u4e00\u4e9b\u95ee\u9898\u6839\u672c\u65e0\u6cd5\u88ab\u4efb\u4f55\u7b97\u6cd5\u6240\u89e3\u51b3\u7684\u6280\u5de7\u7684\u53d8\u4f53\u3002\u4f46\u662f\u4ed6\u4eec\u5f88\u5feb\u53d1\u73b0\u4e86\u4e00\u4e2a\u8bc1\u660e\uff0c\u8868\u660e\u8fd9\u4e9b\u65b9\u6cd5\u662f\u884c\u4e0d\u901a\u7684 \u2014\u2014 \u8fd9\u662f\u89e3\u51b3 P \u548c NP \u95ee\u9898\u7684\u7b2c\u4e00\u4e2a\u4e3b\u8981\u969c\u788d\u3002\u4e8e\u662f\u4ed6\u4eec\u5f00\u59cb\u5bfb\u627e\u53e6\u4e00\u79cd\u65b9\u6cd5\uff0c\u5f88\u5feb\u5c31\u5728\u56fe\u7075\u7684\u540c\u65f6\u4ee3\u4eba\u9999\u519c<\/span>\uff08Claude Shannon\uff09<\/span>\u7684\u5de5\u4f5c\u4e2d\u627e\u5230\u4e86\u4e00\u4e2a\u3002<\/span><\/p>\n


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\u9999\u519c\u5728\u4ed6\u7684\u7855\u58eb\u8bba\u6587\u4e2d\u5f00\u53d1\u4e86\u4e00\u4e2a\u57fa\u4e8e\u7535\u8def\u7684\u8ba1\u7b97\u7406\u8bba\u6a21\u578b\u3002\uff5c\u6765\u6e90\uff1aCourtesy of MIT Museum<\/span><\/section>\n


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Shannon \u5728\u5317\u5bc6\u6b47\u6839\u5dde\u7684\u4e00\u4e2a\u5c0f\u9547\u957f\u5927\uff0c\u4f3c\u4e4e\u4e0d\u50cf\u662f\u80fd\u5f00\u521b\u4fe1\u606f\u65f6\u4ee3\u7684\u4eba\u7269\u3002\u7136\u800c\uff0c\u4ed6\u8bc1\u660e\u4e86\u8ba1\u7b97\u673a\u79d1\u5b66\u8fd9\u95e8\u65b0\u5174\u5b66\u79d1\u7684\u8de8\u5b66\u79d1\u6027\u8d28\u3002\u4ed6\u5bf9\u7535\u6c14\u5de5\u7a0b\u548c\u6570\u5b66\u903b\u8f91\u90fd\u5f88\u719f\u6089\u3002\u5728\u4ed6\u7684\u7855\u58eb\u8bba\u6587\u4e2d\uff0cShannon\u5c55\u793a\u4e86\u7531\u673a\u7535\u5f00\u5173\u7ec4\u6210\u7684\u7535\u8def\u5982\u4f55\u8868\u793a\u5305\u542b\u5e03\u5c14\u53d8\u91cf<\/span>\uff08\u53ea\u80fd\u53d6\u4e24\u4e2a\u503c\uff0c\u59820\u62161\uff0c\u771f\u6216\u5047\uff09<\/span>\u7684\u903b\u8f91\u8868\u8fbe\u5f0f\u3002<\/span><\/p>\n


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\u5728\u8fd9\u4e9b\u8868\u8fbe\u5f0f\u4e2d\uff0c\u5e03\u5c14\u53d8\u91cf\u901a\u8fc7\u201c\u903b\u8f91\u95e8\u63a7\u201d<\/span>\uff08logic gates\uff09<\/span>\u4e0e<\/span>\uff08AND\uff09<\/span>\u3001\u6216<\/span>\uff08OR\uff09<\/span>\u548c\u975e<\/span>\uff08NOT\uff09<\/span>\u8fde\u63a5\u5728\u4e00\u8d77\u3002\u4f8b\u5982\uff0c\u521d\u7b49\u8868\u8fbe\u5f0f\u201cA AND B\u201d\uff0c\u5f53A\u548cB\u90fd\u4e3a\u771f\u65f6\u4e3a\u771f\uff0c\u5426\u5219\u4e3a\u5047\uff1b\u53e6\u4e00\u65b9\u9762\uff0c\u5bf9\u4e8e\u201cA OR B\u201d\uff0c\u5982\u679cA\u548cB\u4e2d\u81f3\u5c11\u6709\u4e00\u4e2a\u4e3a\u771f\u5219\u4e3a\u771f\u3002NOT \u66f4\u7b80\u5355\uff1a\u5b83\u53ef\u4ee5\u53cd\u8f6c\u5355\u4e2a\u53d8\u91cf\u7684\u503c\u3002\u6709\u4e86\u8db3\u591f\u591a\u7684\u8fd9\u4e9b\u57fa\u672c\u6784\u4ef6\uff0c\u5c31\u53ef\u4ee5\u6267\u884c\u4efb\u4f55\u8ba1\u7b97\u3002<\/span><\/p>\n


<\/p>\n

\u9999\u519c\u7684\u5de5\u4f5c\u4e3a\u7406\u8bba\u5b66\u5bb6\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd\u601d\u8003\u8ba1\u7b97\u95ee\u9898\u96be\u5ea6\u7684\u65b0\u65b9\u6cd5\u2014\u2014\u201c\u7535\u8def\u590d\u6742\u5ea6<\/strong>\u201d<\/span>\uff08circuit complexity\uff09<\/span>\uff0c\u5c3d\u7ba1\u8fd9\u91cc\u8ba8\u8bba\u7684\u7535\u8def\u53ea\u662f\u6570\u5b66\u4e0a\u7684\u62bd\u8c61\u3002\u6709\u4e00\u6bb5\u65f6\u95f4\uff0c\u7814\u7a76\u4eba\u5458\u8ba4\u4e3a\u8fd9\u79cd\u65b9\u6cd5\u53ef\u4ee5\u89e3\u51b3P\u4e0eNP\u95ee\u9898\uff0c\u4f46\u8fd9\u6761\u8def\u6700\u7ec8\u8fd8\u662f\u9047\u5230\u4e86\u81ea\u7136\u8bc1\u660e\u969c\u788d\u3002<\/span><\/p>\n


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\u54c8\u4f5b\u9a6c\u514bI\u578b\u8ba1\u7b97\u673a\u7684\u57fa\u672c\u7ec4\u6210\u90e8\u5206\uff0c\u6444\u4e8e1944\u5e74\uff0c\u662f\u50cf\u9999\u519c\u8bba\u6587\u4e2d\u5206\u6790\u7684\u673a\u7535\u5f00\u5173\u3002\uff5c\u6765\u6e90\uff1aRBM Vintage Images\/Alamy Stock Photo<\/span><\/section>\n


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\u7535\u8def\u590d\u6742\u5ea6\u7684\u6846\u67b6\u8981\u6c42\u7814\u7a76\u8005\u4eec\u91cd\u65b0\u601d\u8003\u56fe\u7075\u8ba1\u7b97\u6a21\u578b\u4e2d\u6700\u57fa\u672c\u7684\u6982\u5ff5\u3002\u5728\u8fd9\u91cc\uff0c\u7814\u7a76\u4eba\u5458\u8003\u8651\u7684\u4e0d\u662f\u8ba1\u7b97\u95ee\u9898\u548c\u89e3\u51b3\u8fd9\u4e9b\u95ee\u9898\u7684\u7b97\u6cd5\uff0c\u800c\u662f\u5e03\u5c14\u51fd\u6570\u548c\u8ba1\u7b97\u5b83\u4eec\u7684\u7535\u8def\u3002\u5e03\u5c14\u51fd\u6570\u63a5\u53d7\u548c\u8f93\u51fa\u5e03\u5c14\u53d8\u91cf<\/span>\uff080\u62161\uff09<\/span>\u3002\u4e0e\u7b97\u6cd5\u4e00\u6837\uff0c\u7535\u8def\u63cf\u8ff0\u4e86\u5728\u7ed9\u5b9a\u8f93\u5165\u6761\u4ef6\u4e0b\u4ea7\u751f\u8f93\u51fa\u7684\u8fc7\u7a0b\u3002\u201c\u6211\u7684\u7406\u89e3\u662f\uff0c\u4eba\u4eec\u5f00\u59cb\u7814\u7a76\u7535\u8def\u590d\u6742\u5ea6\u662f\u56e0\u4e3a\u4ed6\u4eec\u8ba4\u4e3a\u56fe\u7075\u673a\u592a\u590d\u6742\u4e86\uff0c\u201d\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u7684\u590d\u6742\u6027\u7406\u8bba\u5bb6 Ryan Williams \u8bf4\u3002\u201c\u6211\u4eec\u53ef\u4ee5\u4e00\u4e2a\u95e8\u4e00\u4e2a\u95e8\u5730\u7814\u7a76\u7535\u8def\u3002\u201d<\/span><\/p>\n


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\u6240\u6709\u7684\u8ba1\u7b97\u95ee\u9898\u90fd\u53ef\u4ee5\u6709\u5f88\u591a\u79cd\u7b97\u6cd5\uff0c\u6709\u4e9b\u7b97\u6cd5\u66f4\u5feb\uff0c\u8bb8\u591a\u4e0d\u540c\u7684\u7535\u8def\u53ef\u4ee5\u8ba1\u7b97\u7ed9\u5b9a\u7684\u4efb\u610f\u5e03\u5c14\u51fd\u6570\uff0c\u6709\u4e9b\u7535\u8def\u7684\u95e8\u6570\u6bd4\u5176\u4ed6\u7535\u8def\u66f4\u5c11\u3002\u7814\u7a76\u4eba\u5458\u5c06\u7535\u8def\u590d\u6742\u5ea6\u5b9a\u4e49\u4e3a\u8ba1\u7b97\u8be5\u51fd\u6570\u7684\u6700\u5c0f\u7535\u8def\u7684\u603b\u95e8\u6570<\/strong>\u3002\u5bf9\u4e8e\u4e00\u4e2a\u8f93\u5165\u53d8\u91cf\u56fa\u5b9a\u7684\u51fd\u6570\uff0c\u7535\u8def\u590d\u6742\u5ea6\u4e5f\u662f\u56fa\u5b9a\u7684\u2014\u2014\u67d0\u4e9b\u51fd\u6570\u7684\u7535\u8def\u590d\u6742\u5ea6\u4f1a\u9ad8\u4e8e\u5176\u4ed6\u51fd\u6570\u3002<\/span><\/p>\n


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\u622a\u7136\u4e0d\u540c\u7684\u7535\u8def\u53ef\u4ee5\u4ea7\u751f\u540c\u6837\u7684\u771f\u503c\u8868\u3002\uff5c\u6765\u6e90\uff1aMerrill Sherman\/<\/span><\/span>Quanta Magazine<\/span><\/em><\/section>\n


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\u4f46\u5728\u5f88\u591a\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u589e\u52a0\u8f93\u5165\u7684\u53d8\u91cf\u6570\u6765\u8003\u8651\u76f8\u540c\u51fd\u6570\u66f4\u590d\u6742\u7684\u7248\u672c\uff0c\u5c31\u50cf\u66f4\u5927\u7684\u56fe\u5f62\u4f1a\u8ba9\u5bfb\u627e\u54c8\u5bc6\u987f\u8def\u5f84\u66f4\u96be\u4e00\u6837\u3002\u7814\u7a76\u8005\u4eec\u5728\u7814\u7a76\u7b97\u6cd5\u8fd0\u884c\u65f6\u95f4\u65f6\u53d1\u95ee\uff1a\u8ba1\u7b97\u5e03\u5c14\u51fd\u6570\u6240\u9700\u7684\u6700\u5c0f\u95e8\u6570\u662f\u5426\u968f\u7740\u8f93\u5165\u53d8\u91cf\u6570\u91cf\u7684\u589e\u52a0\u800c\u5448\u591a\u9879\u5f0f\u6216\u6307\u6570\u589e\u957f\uff1f\u7814\u7a76\u8005\u4eec\u4f9d\u636e\u8fd9\u4e2a\u5c06\u51fd\u6570\u5212\u5206\u6210\u201c\u6613\u4e8e\u8ba1\u7b97\u201d<\/span>\uff08\u591a\u9879\u5f0f\u589e\u957f\uff09<\/span>\u548c\u201c\u96be\u4ee5\u8ba1\u7b97\u201d<\/span>\uff08\u6307\u6570\u589e\u957f\uff09<\/span>\u4e24\u7c7b\u3002<\/span><\/p>\n


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\u6613\u4e8e\u8ba1\u7b97\u7684\u5e03\u5c14\u51fd\u6570\u7c7b\u4f3c\u4e8eP\u7c7b\u8ba1\u7b97\u95ee\u9898\uff0c\u5373\u53ef\u4ee5\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u89e3\u51b3\u7684\u95ee\u9898\u3002\u4f46\u662f\u4e5f\u5b58\u5728\u7c7b\u4f3c\u4e8eNP\u56f0\u96be<\/span>\uff08NP-hard\uff09<\/span>\u95ee\u9898\u7684\u51fd\u6570\uff0c\u7814\u7a76\u4eba\u5458\u53d1\u73b0\u8ba1\u7b97\u8fd9\u4e9b\u51fd\u6570\u7684\u6700\u4f73\u65b9\u6cd5\u968f\u7740\u95e8\u6570\u91cf\u5448\u6307\u6570\u589e\u957f\uff0c\u4f46\u7b54\u6848\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u9a8c\u8bc1\u3002\u5982\u679c\u590d\u6742\u6027\u7406\u8bba\u5bb6\u80fd\u591f\u8bc1\u660e\u786e\u5b9e\u6ca1\u6709\u66f4\u597d\u7684\u65b9\u6cd5\u80fd\u8ba1\u7b97\u8fd9\u6837\u7684\u51fd\u6570\uff0c\u90a3\u4e48\u8fd9\u5c31\u610f\u5473\u7740P \u2260 NP\u3002<\/span><\/p>\n


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\u8fd9\u662f\u572820\u4e16\u7eaa80\u5e74\u4ee3\u5927\u591a\u6570\u590d\u6742\u6027\u7406\u8bba\u5b66\u5bb6\u8ffd\u6c42\u7684\u7b56\u7565\uff0c\u800c\u4e14\u4ed6\u4eec\u5360\u7740\u4e0a\u98ce\u3002\u9999\u519c\u57281949\u5e74\u8bc1\u660e\u4e86\u51e0\u4e4e\u6240\u6709\u7684\u5e03\u5c14\u771f\u503c\u8868<\/span>\uff08\u4e00\u4e2a\u56fa\u5b9a\u5927\u5c0f\u7684\u5e03\u5c14\u51fd\u6570\u7684\u6240\u6709\u53ef\u80fd\u8f93\u5165\u548c\u8f93\u51fa\u7684\u957f\u5217\u8868\uff09<\/span>\u90fd\u5177\u6709\u5c3d\u53ef\u80fd\u9ad8\u7684\u7535\u8def\u590d\u6742\u5ea6\u3002\u4ed6\u7684\u8bba\u8bc1\u975e\u5e38\u7b80\u5355\uff1a\u7ec4\u5408\u5c11\u91cf\u95e8\u7684\u65b9\u6cd5\u8981\u6bd4\u7ec4\u5408\u8bb8\u591a\u95e8\u7684\u65b9\u6cd5\u5c11\u5f97\u591a\u3002\u201c\u6211\u4eec\u6ca1\u6709\u90a3\u4e48\u591a\u7684\u5c0f\u7535\u8def\uff0c\u201dAaronson\u8bf4\u3002<\/span><\/p>\n


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\u6240\u4ee5\u590d\u6742\u6027\u7406\u8bba\u5b66\u5bb6\u53d1\u73b0\u4ed6\u4eec\u81ea\u5df1\u9677\u5165\u4e86\u4e00\u4e2a\u5947\u602a\u7684\u56f0\u5883\u3002\u5982\u679c\u6240\u6709\u771f\u503c\u8868\u90fd\u6709\u5f88\u9ad8\u7684\u7535\u8def\u590d\u6742\u5ea6\uff0c\u90a3\u4e48\u51e0\u4e4e\u6bcf\u4e2a\u5e03\u5c14\u51fd\u6570\u90fd\u662f\u5f88\u96be\u8ba1\u7b97\u7684\u3002\u7814\u7a76\u4eba\u5458\u53ea\u9700\u8981\u627e\u5230\u4e00\u4e2a\u5df2\u77e5\u5c5e\u4e8eNP\u7c7b\u5e76\u4e14\u5177\u6709\u9ad8\u7535\u8def\u590d\u6742\u5ea6\u7684\u5e03\u5c14\u51fd\u6570\u3002\u8fd9\u80fd\u6709\u591a\u96be\uff1f<\/span><\/p>\n


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\u5bc6\u7801\u5b66\u4e0e\u590d\u6742\u6027<\/span><\/strong><\/span><\/h3>\n

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

\u8d77\u521d\uff0c\u8fdb\u5c55\u5f88\u5feb\u30021981\u5e74\uff0cSipser\u548c\u4e24\u4e2a\u5408\u4f5c\u8005\u8bc1\u660e\uff0c\u5982\u679c\u4ed6\u4eec\u4f7f\u7528\u7684\u7535\u8def\u5bf9\u95e8\u7684\u5e03\u7f6e\u6709\u4e00\u5b9a\u7684\u9650\u5236\uff0c\u90a3\u4e48\uff0c\u4e00\u4e2a\u7279\u5b9a\u7684\u5e03\u5c14\u51fd\u6570\u80af\u5b9a\u662f\u96be\u4ee5\u8ba1\u7b97\u7684\u3002Sipser\u8bf4\uff1a\u201c\u6211\u4eec\u5f53\u65f6\u5e7b\u60f3\uff0c\u53ef\u4ee5\u8bc1\u660e\u8fd9\u4e9b\u53d7\u9650\u6a21\u578b\u7684\u4e00\u4e9b\u6027\u8d28\uff0c\u7136\u540e\u57fa\u4e8e\u6240\u5b66\u77e5\u8bc6\u6765\u51cf\u5c11\u9650\u5236\u3002\u201d<\/span><\/p>\n


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<\/p>\n

1981\u5e74\uff0cMichael Sipser \u7528\u9650\u5236\u7535\u8def\u6a21\u578b\u8f85\u52a9\u8bc1\u660e\u4e86\u4e00\u4e2a\u5177\u6709\u91cc\u7a0b\u7891\u610f\u4e49\u7684\u7ed3\u679c\uff0c\u4f46\u6700\u7ec8\u9677\u5165\u505c\u6ede\u3002\uff5c\u6765\u6e90\uff1aBryce Vickmark<\/span><\/p>\n


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1985\u5e74\uff0cRazborov\u53c8\u8fc8\u51fa\u4e86\u4e00\u5927\u6b65\u3002\u5f53\u65f6\u4ed6\u521a\u5728\u83ab\u65af\u79d1\u5f00\u59cb\u8bfb\u7814\u7a76\u751f\uff0c\u5728\u89e3\u51b3\u4e00\u4e2a\u6570\u5b66\u5206\u652f\u7684\u95ee\u9898\u65f6\u5076\u7136\u52a0\u5165\u4e86\u8fd9\u9879\u5de5\u4f5c\uff0c\u7ed3\u679c\u53d1\u73b0\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u7684\u5148\u51b3\u6761\u4ef6\u662fP\u4e0eNP\u95ee\u9898\u3002\u201c\u6211\u5f88\u5e78\u8fd0\uff0c\u5f53\u65f6\u6211\u4e0d\u77e5\u9053\u8fd9\u4e2a\u95ee\u9898\u6709\u591a\u96be\uff0c\u201dRazborov\u8bf4\u3002\u201c\u5426\u5219\u4e5f\u8bb8\u6211\u6839\u672c\u90fd\u4e0d\u4f1a\u5f00\u59cb\u3002\u201d<\/span><\/p>\n


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Razborov \u5206\u6790\u4e86\u53ea\u5305\u542bAND\u548cOR\u95e8\u7684\u7535\u8def\uff0c\u5e76\u8bc1\u660e\u4e86\u65e0\u8bba\u95e8\u5982\u4f55\u6392\u5217\uff0c\u8fd9\u79cd\u7535\u8def\u90fd\u96be\u4ee5\u8ba1\u7b97\u7279\u5b9a\u7684NP\u5b8c\u5168\u7684\u51fd\u6570\u3002\u6240\u6709\u7814\u7a76\u4eba\u5458\u8981\u89e3\u51b3P\u4e0eNP\u95ee\u9898\uff0c\u5c31\u5fc5\u987b\u5c06 Razborov \u7684\u6280\u672f\u63a8\u5e7f\u5230\u5e26NOT\u95e8\u7684\u7535\u8def\u4e2d\u3002<\/span>Razborov\u8bf4:\u201c\u4eba\u4eec\u666e\u904d\u8ba4\u4e3a\uff0c\u518d\u591a\u8d70\u4e24\u6b65\uff0c\u6211\u4eec\u5c31\u4f1a\u6210\u529f\u3002\u201d\u4f46\u4e8b\u5b9e\u5e76\u975e\u5982\u6b64\u3002Razborov\u672c\u4eba\u5c31\u8bc1\u660e\u4e86\uff0c\u5982\u679c\u628aNOT\u95e8\u52a0\u5165\u8fdb\u6765\uff0c\u4ed6\u7684\u65b9\u6cd5\u5c31\u4f1a\u5931\u8d25\uff0c\u800c\u4e14\u6ca1\u6709\u4eba\u80fd\u627e\u5230\u5176\u4ed6\u7684\u65b9\u6cd5\u3002\u968f\u7740\u65f6\u95f4\u7684\u6d41\u901d\uff0c\u4ed6\u5f00\u59cb\u60f3\uff0c\u4e3a\u4ec0\u4e48\u8fd9\u6761\u8def\u7ebf\u4f1a\u5931\u6548\u3002<\/span><\/p>\n


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\u5728\u7f8e\u56fd\uff0cRuzick \u4e5f\u5728\u601d\u8003\u540c\u6837\u7684\u95ee\u9898\u3002\u4ed6\u548c Impagliazzo \u662f\u5927\u5b66\u540c\u5b66\uff0c\u53c8\u4e00\u8d77\u8bfb\u7814\u7a76\u751f\u3002\u4ed6\u4eec\u7684\u53cb\u8c0a\u6e90\u4e8e\u5bf9\u54e5\u5fb7\u5c14\u548c\u56fe\u7075\u81ea\u6307\u8bba\u8bc1\u7684\u5171\u540c\u7740\u8ff7\uff0c\u800c\u4e14\u4ed6\u4eec\u4fe9\u90fd\u5bf9\u6570\u5b66\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u57fa\u7840\u7684\u5f71\u54cd\u611f\u5174\u8da3\u3002\u201c\u6211\u4eec\u5f00\u73a9\u7b11\u8bf4\u6211\u4eec\u8981\u5f97\u5230\u4e00\u4e2a\u6807\u6709\u2018\u81ea\u6307\u2019\u7684\u6309\u94ae\uff0c\u201dImpagliazzo\u8bf4\u3002<\/span><\/p>\n


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1994\u5e74\uff0cAlexander Razborov (\u5de6)\u548c Steven Rudich \u53d1\u73b0\u4e86\u81ea\u7136\u8bc1\u660e\u969c\u788d\uff0c\u8fd9\u89e3\u91ca\u4e86\u4e4b\u524d\u8bc1\u660eP\u2260NP\u7684\u5c1d\u8bd5\u5931\u8d25\u7684\u539f\u56e0\u3002\uff5c\u6765\u6e90\uff1aJean Lachat (left); Courtesy of Carnegie Mellon University<\/span><\/section>\n


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\u4f5c\u4e3a\u7814\u7a76\u751f\uff0cRudich\u548cImpagliazzo\u90fd\u5728\u5bc6\u7801\u5b66\u7684\u590d\u6742\u6027\u7406\u8bba\u57fa\u7840\u4e0a\u5de5\u4f5c\uff0c\u8fd9\u4e00\u5b66\u79d1\u53ef\u80fd\u662f\u8bd5\u56fe\u8bc1\u660eP\u2260NP\u7684\u6700\u4f73\u5b9e\u8df5\u52a8\u673a\u3002\u5bc6\u7801\u5b66\u5bb6\u901a\u8fc7\u201c\u4f2a\u968f\u673a\u201d\u6765\u9690\u85cf\u79d8\u5bc6\u4fe1\u606f\u2014\u2014\u4ee5\u8fd9\u79cd\u65b9\u5f0f\u52a0\u5bc6\u7684\u4fe1\u606f\u5728\u4efb\u4f55\u7a83\u542c\u8005\u770b\u6765\u90fd\u50cf\u662f\u4e00\u5806\u968f\u673a\u7684\u6570\u5b57\uff0c\u4f46\u5b83\u4ecd\u7136\u53ef\u4ee5\u88ab\u9884\u671f\u7684\u63a5\u6536\u65b9\u89e3\u7801\u3002\u4f46\u662f\u4f60\u600e\u4e48\u80fd\u786e\u5b9a\u4e00\u4e2a\u60f3\u8981\u7a83\u542c\u7684\u4eba\u4f1a\u53d1\u73b0\u7834\u8bd1\u5bc6\u7801\u592a\u96be\u4e86\u5462?<\/span><\/p>\n


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\u8fd9\u662f\u590d\u6742\u6027\u7406\u8bba\u7684\u6218\u573a\u3002\u5982\u4eca\u6700\u5e7f\u6cdb\u7684\u52a0\u5bc6\u65b9\u6cd5\u90fd\u57fa\u4e8e\u770b\u4f3c\u56f0\u96be\u7684NP\u95ee\u9898\u3002\u82e5\u8981\u89e3\u5bc6\u6d88\u606f\uff0c\u653b\u51fb\u8005\u5c31\u9700\u8981\u5148\u53d1\u73b0\u80fd\u591f\u5feb\u901f\u89e3\u51b3NP\u95ee\u9898\u7684\u7b97\u6cd5\uff1b\u82e5\u8981\u8bc1\u660e\u52a0\u5bc6\u65b9\u6cd5\u7684\u5b89\u5168\uff0c\u6211\u4eec\u5c31\u5fc5\u987b\u5148\u8bc1\u660eP \u2260 NP\u3002\u201c\u5982\u679c\u4e0d\u80fd\u8bc1\u660e\uff0c\u90a3\u53ea\u80fd\u7948\u7977\u7a83\u5bc6\u8005\u6570\u5b66\u4e0d\u597d\u3002\u201dSipser\u8bf4\u3002<\/span><\/p>\n


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\u867d\u7136\u5bc6\u7801\u5b66\u672c\u8eab\u5f88\u8ff7\u4eba\uff0c\u4f46\u5b83\u4f3c\u4e4e\u4e0e\u81ea\u6307\u8bba\u8bc1\u76f8\u5dee\u751a\u8fdc\uff0c\u6b63\u662f\u81ea\u6307\u8bba\u8bc1\u5728\u6700\u521d\u5438\u5f15 Rudich \u548c Impagliazzo \u8fdb\u5165\u8be5\u9886\u57df\u3002\u4f46\u968f\u7740 Rudich \u52aa\u529b\u7406\u89e3\u4e3a\u4ec0\u4e48\u7535\u8def\u590d\u6742\u5ea6\u65b9\u6cd5\u9677\u5165\u505c\u6ede\uff0c\u4ed6\u5f00\u59cb\u610f\u8bc6\u5230\u8fd9\u4e24\u4e2a\u5b66\u79d1\u5b9e\u9645\u4e0a\u5e76\u6ca1\u6709\u90a3\u4e48\u9065\u8fdc\u3002\u7814\u7a76\u4eba\u5458\u5728\u5c1d\u8bd5\u8bc1\u660eP \u2260 NP\u65f6\u91c7\u53d6\u7684\u7b56\u7565\u5177\u6709\u81ea\u76f8\u77db\u76fe\u7684\u7279\u5f81\uff0c\u8ba9\u4eba\u60f3\u8d77\u4e86\u54e5\u5fb7\u5c14\u7684\u8457\u540d\u547d\u9898\u201c\u8fd9\u4e2a\u9648\u8ff0\u65e0\u6cd5\u8bc1\u660e\u201d\uff0c\u800c\u5bc6\u7801\u5b66\u53ef\u4ee5\u5e2e\u52a9\u89e3\u91ca\u539f\u56e0\u3002\u5728\u4fc4\u7f57\u65af\uff0cRazborov \u5728\u540c\u4e00\u65f6\u95f4\u53d1\u73b0\u4e86\u7c7b\u4f3c\u7684\u8054\u7cfb\u3002\u8fd9\u4e9b\u662f\u81ea\u7136\u8bc1\u660e\u969c\u788d\u7684\u79cd\u5b50\u3002<\/span><\/p>\n


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\u81ea\u7136\u8bc1\u660e\u969c\u788d\u7684\u6838\u5fc3\u95ee\u9898\u662f\uff0c\u533a\u5206\u9ad8\u590d\u6742\u5ea6\u51fd\u6570\u548c\u4f4e\u590d\u6742\u5ea6\u51fd\u6570\u7684\u4efb\u52a1\u7c7b\u4f3c\u4e8e\u533a\u5206\u7528\u4e8e\u52a0\u5bc6\u4fe1\u606f\u7684\u771f\u6b63\u968f\u673a\u6027\u548c\u4f2a\u968f\u673a\u6027<\/strong>\u3002\u6211\u4eec\u5e0c\u671b\u8bc1\u660e\u9ad8\u590d\u6742\u5ea6\u51fd\u6570\u4e0e\u4f4e\u590d\u6742\u5ea6\u51fd\u6570\u6709\u6839\u672c\u7684\u533a\u522b\uff0c\u4ee5\u8bc1\u660eP \u2260 NP\u3002\u4f46\u4e3a\u4e86\u5bc6\u7801\u5b66\u7684\u5b89\u5168\uff0c\u6211\u4eec\u4e5f\u5e0c\u671b\u4f2a\u968f\u673a\u4e0e\u771f\u968f\u673a\u96be\u4ee5\u533a\u5206\u3002\u4e5f\u8bb8\u6211\u4eec\u4e0d\u80fd\u4e24\u8005\u517c\u5f97\u3002<\/span><\/p>\n


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\u81ea\u7136\u8bc1\u660e\u969c\u788d<\/span><\/strong><\/span><\/h3>\n

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\u57281994\u5e74\uff0cRazborov \u548c Rudich \u610f\u8bc6\u5230\u4ed6\u4eec\u7684\u53d1\u73b0\u5982\u6b64\u76f8\u4f3c\uff01\u4e8e\u662f\u4ed6\u4eec\u5f00\u59cb\u5408\u4f5c\uff0c\u5c06\u6210\u679c\u7ed3\u5408\u8d77\u6765\u3002\u4ed6\u4eec\u9996\u5148\u53d1\u73b0\uff0c\u4e4b\u524d\u6240\u6709\u7528\u7535\u8def\u590d\u6742\u5ea6\u6765\u8bc1\u660e P\u2260NP \u7684\u5c1d\u8bd5\u90fd\u91c7\u7528\u4e86\u76f8\u540c\u7684\u7b56\u7565\uff1a\u8bc6\u522b\u4e00\u4e2aNP\u5b8c\u5168\u5e03\u5c14\u51fd\u6570\u7684\u7279\u6b8a\u6027\u8d28\uff0c\u7136\u540e\u8bc1\u660e\u4efb\u4f55\u4e00\u4e2a\u5bb9\u6613\u8ba1\u7b97\u7684\u51fd\u6570\u90fd\u6ca1\u6709\u8fd9\u79cd\u6027\u8d28\u3002\u8fd9\u8868\u660e\u9009\u62e9\u7684NP\u5b8c\u5168\u51fd\u6570\u786e\u5b9e\u5f88\u96be\u8ba1\u7b97\uff0c\u4ece\u800c\u8bc1\u660eP\u2260NP\u3002<\/span><\/p>\n


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Sipser\u3001Razborov\u7b49\u4eba\u7528\u540c\u6837\u7684\u7b56\u7565\u6210\u529f\u5730\u8bc1\u660e\u4e86\u4ed6\u4eec\u66f4\u6709\u9650\u7684\u7ed3\u679c\uff0c\u800c\u4e14\u5728\u6bcf\u4e2a\u6848\u4f8b\u4e2d\uff0c\u7814\u7a76\u4eba\u5458\u53d1\u73b0\u7684\u7279\u6b8a\u5c5e\u6027\u662f\u5927\u591a\u6570\u5e03\u5c14\u51fd\u6570\u6240\u5171\u6709\u7684\u3002\u56e0\u4e3a\u6ca1\u6709\u5df2\u77e5\u7684\u66ff\u4ee3\u65b9\u6cd5\uff0cRazborov \u548c Rudich \u751a\u81f3\u521b\u9020\u4e86\u201c\u81ea\u7136\u8bc1\u636e\u201d\u8fd9\u4e2a\u8bcd\u6765\u6307\u4ee3\u8fd9\u79cd\u6027\u8d28\u5171\u4eab\u7684\u60c5\u51b5\u3002\u5982\u679c\u201c\u975e\u81ea\u7136\u201d\u7684\u8bc1\u660e\u662f\u53ef\u80fd\u7684\uff0c\u90a3\u4e48\u5b83\u5fc5\u987b\u662f\u975e\u5e38\u53cd\u76f4\u89c9\u7684\uff0c\u800c\u4e14\u540d\u526f\u5176\u5b9e\u5730\u201c\u4e0d\u81ea\u7136\u201d\u3002<\/span><\/p>\n


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\u7136\u540e\uff0cRazborov \u548c Rudich \u8bc1\u660e\u4e86\u4ed6\u4eec\u7684\u4e3b\u8981\u7ed3\u8bba\uff1a\u8981\u60f3\u81ea\u7136\u5730\u8bc1\u660e P\u2260NP\uff0c\u6211\u4eec\u5c31\u9700\u8981\u5168\u9762\u5730\u8ba4\u8bc6\u6613\u4e8e\u8ba1\u7b97\u548c\u96be\u4ee5\u8ba1\u7b97\u51fd\u6570\u4e4b\u95f4\u7684\u533a\u522b\uff0c\u800c\u4e14\u8fd9\u4e9b\u77e5\u8bc6\u8fd8\u80fd\u591f\u63a8\u52a8\u5feb\u901f\u7b97\u6cd5\u7684\u53d1\u5c55\uff0c\u627e\u51fa\u201c\u9690\u85cf\u7684\u201d\u6613\u4e8e\u8ba1\u7b97\u7684\u51fd\u6570\u3002\u5982\u679c\u590d\u6742\u6027\u7406\u8bba\u5bb6\u80fd\u591f\u81ea\u7136\u5730\u8bc1\u660eP\u2260NP\uff0c\u4ed6\u4eec\u5c31\u4f1a\u53d1\u73b0\u4e00\u79cd\u51e0\u4e4e\u7edd\u5bf9\u6b63\u786e\u7684\u65b9\u6cd5\uff0c\u53ea\u8981\u770b\u4e00\u773c\u4efb\u610f\u771f\u503c\u8868\uff0c\u5c31\u80fd\u786e\u5b9a\u76f8\u5e94\u7684\u51fd\u6570\u7684\u7535\u8def\u590d\u6742\u5ea6\u662f\u9ad8\u8fd8\u662f\u4f4e\u2014\u2014\u8fd9\u662f\u4e00\u4e2a\u6bd4\u4ed6\u4eec\u7684\u76ee\u6807\u66f4\u5f3a\u3001\u66f4\u666e\u904d\u7684\u7ed3\u679c\u3002\u201c\u4f60\u51e0\u4e4e\u65e0\u6cd5\u963b\u6321\u610f\u5916\u4e4b\u559c\u3002\u201dCarmosino \u8fd9\u6837\u5f62\u5bb9\u3002<\/span><\/p>\n


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\u8fd9\u5c31\u597d\u50cf\u4f60\u8bd5\u56fe\u6838\u5b9e\u4e00\u4e2a\u5177\u4f53\u7684\u9648\u8ff0\uff0c\u4f46\u6bcf\u6b21\u5c1d\u8bd5\u90fd\u53d8\u6210\u4e86\u4e00\u4e2a\u901a\u7528\u68c0\u9a8c\u7684\u84dd\u56fe\u2014\u2014\u8fd9\u770b\u8d77\u6765\u592a\u597d\u4e86\uff0c\u4e0d\u50cf\u662f\u771f\u7684\u3002\u5bf9\u4e8e\u590d\u6742\u6027\u7406\u8bba\u5b66\u5bb6\u6765\u8bf4\uff0c\u81ea\u7136\u8bc1\u636e\u7684\u60ca\u4eba\u529b\u91cf\u540c\u6837\u4f7f\u6210\u529f\u7684\u53ef\u80fd\u6027\u964d\u4f4e\u3002\u4f46\u662f\uff0c\u5982\u679c\u8fd9\u6837\u7684\u8bc1\u660e\u6210\u529f\u4e86\uff0c\u7531\u4e8e\u7535\u8def\u590d\u6742\u6027\u548c\u4f2a\u968f\u673a\u6027\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u5bf9\u4e8e\u5bc6\u7801\u5b66\u6765\u8bf4\uff0c\u53ef\u80fd\u662f\u4e2a\u574f\u6d88\u606f\u3002<\/span><\/p>\n


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\u8981\u7406\u89e3\u8fd9\u79cd\u8054\u7cfb\uff0c\u8bf7\u60f3\u8c61\u4e00\u4e0b\uff0c\u67e5\u770b\u4e00\u4e2a\u5e03\u5c14\u51fd\u6570\u7684\u771f\u503c\u8868\u7684\u8f93\u51fa\u5217\uff0c\u5176\u4e2d\u5305\u542b\u8bb8\u591a\u8f93\u5165\u53d8\u91cf\uff0c\u5e76\u5c06\u6bcf\u4e2a\u201c\u771f\u201d\u66ff\u6362\u4e3a1\uff0c\u6bcf\u4e2a\u201c\u5047\u201d\u66ff\u6362\u4e3a0\uff1a<\/span><\/p>\n


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Merrill Sherman\/<\/span><\/span>Quanta Magazine<\/span><\/em><\/p>\n


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\u5982\u679c\u5e03\u5c14\u51fd\u6570\u5177\u6709\u8f83\u9ad8\u7684\u7535\u8def\u590d\u6742\u5ea6\uff0c\u90a3\u4e48\u8fd9\u4e00\u957f\u4e32\u8f93\u51fa\u5728\u539f\u5219\u4e0a\u4e0e\u75310\u548c1\u7ec4\u6210\u7684\u771f\u6b63\u968f\u673a\u5b57\u7b26\u4e32<\/span>\uff08\u6bd4\u5982\u901a\u8fc7\u53cd\u590d\u629b\u786c\u5e01\u83b7\u5f97\u7684\u5b57\u7b26\u4e32\uff09<\/span>\u662f\u65e0\u6cd5\u533a\u5206\u7684\u3002\u4f46\u5982\u679c\u51fd\u6570\u7684\u7535\u8def\u590d\u6742\u5ea6\u8f83\u4f4e\uff0c\u90a3\u4e48\u8c8c\u4f3c\u590d\u6742\u7684\u5b57\u7b26\u4e32\u4e5f\u5fc5\u987b\u5177\u6709\u7b80\u5355\u3001\u7b80\u6d01\u7684\u63cf\u8ff0\u3002\u8fd9\u4f7f\u5f97\u5b83\u975e\u5e38\u7c7b\u4f3c\u4e8e\u5bc6\u7801\u5b66\u4e2d\u4f7f\u7528\u7684\u4f2a\u968f\u673a\u5b57\u7b26\u4e32\uff0c\u5176\u7b80\u6d01\u7684\u63cf\u8ff0\u662f\u9690\u85cf\u5728\u660e\u663e\u7684\u968f\u673a\u6027\u4e2d\u7684\u79d8\u5bc6\u4fe1\u606f\u3002<\/span><\/p>\n


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\u5bc6\u7801\u5b66\u4e2d\u7684\u771f\u968f\u673a\u6027\u548c\u4f2a\u968f\u673a\u6027\u3002\uff5c\u6765\u6e90\uff1aMerrill Sherman\/<\/span><\/span>Quanta Magazine<\/span><\/em><\/p>\n


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\u56e0\u6b64\uff0cRazborov \u548c Rudich \u7684\u7ed3\u679c\u8868\u660e\uff0c\u4efb\u4f55 P\u2260NP \u7684\u81ea\u7136\u8bc1\u660e\u4ea7\u751f\u7684\u540c\u65f6\u4e5f\u4f1a\u8bde\u751f\u4e00\u79cd\u5feb\u901f\u7b97\u6cd5\uff0c\u53ef\u4ee5\u533a\u5206\u5305\u542b\u9690\u85cf\u4fe1\u606f\u7684\u4f2a\u968f\u673a\u5b57\u7b26\u4e32\u548c\u771f\u6b63\u7684\u968f\u673a\u5b57\u7b26\u4e32\u3002\u5b89\u5168\u5bc6\u7801\u5b66\u662f\u4e0d\u53ef\u80fd\u7684\u2014\u2014\u8fd9\u6b63\u597d\u4e0e\u7814\u7a76\u4eba\u5458\u5e0c\u671b\u901a\u8fc7\u8bc1\u660e P\u2260NP \u6765\u5efa\u7acb\u7684\u7ed3\u679c\u76f8\u53cd\u3002<\/span><\/p>\n


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\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u5b89\u5168\u5bc6\u7801\u5b66\u662f\u53ef\u80fd\u7684\uff0c\u90a3\u4e48\u81ea\u7136\u8bc1\u660e\u5c31\u4e0d\u80fd\u8bc1\u660eP\u2260NP\u2014\u2014\u8fd9\u662f\u5b89\u5168\u5bc6\u7801\u5b66\u7684\u5148\u51b3\u6761\u4ef6\u3002\u7b80\u5355\u5730\u8bf4\uff0c\u8fd9\u5c31\u662f\u81ea\u7136\u8bc1\u660e\u969c\u788d\u3002\u590d\u6742\u6027\u7406\u8bba\u4f3c\u4e4e\u9762\u4e34\u7740\u4e00\u4e2a\u6b8b\u9177\u7684\u7b11\u8bdd\u3002\u201c\u5982\u679c\u4f60\u76f8\u4fe1\u590d\u6742\u6027\uff0c\u90a3\u4e48\u4f60\u5c31\u5e94\u8be5\u76f8\u4fe1\u8bc1\u660e\u590d\u6742\u6027\u6709\u591a\u590d\u6742\uff0c\u201d Kabanets \u8bf4\u3002<\/span><\/p>\n


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\u5143\u590d\u6742\u6027<\/strong><\/span><\/h3>\n

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P\u2260NP \u731c\u60f3\u7684\u542b\u4e49\u548c\u8bc1\u660e\u5b83\u7684\u56f0\u96be\u4e4b\u95f4\u7684\u8054\u7cfb\u5f88\u6709\u8da3\uff0c\u4f46\u5f88\u96be\u786e\u5b9a\u3002\u4e00\u65b9\u9762\uff0c\u81ea\u7136\u8bc1\u660e\u969c\u788d\u53ea\u963b\u6b62\u4e86\u4e00\u79cd\u8bc1\u660eP\u2260NP\u7684\u65b9\u6cd5\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5b83\u4e0d\u628a\u8bc1\u660eP\u2260NP\u7684\u56f0\u96be\u4e0eP\u2260NP\u672c\u8eab\u8054\u7cfb\u8d77\u6765\uff0c\u800c\u662f\u4e0e\u5b89\u5168\u5bc6\u7801\u5b66\u8054\u7cfb\u8d77\u6765\u3002\u5b89\u5168\u5bc6\u7801\u5b66\u4e0e\u4e4b\u5bc6\u5207\u76f8\u5173\u4f46\u53c8\u4e0d\u5b8c\u5168\u7b49\u540c\u3002\u4e3a\u4e86\u771f\u6b63\u7406\u89e3\u8fd9\u79cd\u8054\u7cfb\uff0c\u7814\u7a76\u4eba\u5458\u5fc5\u987b\u719f\u6089\u5143\u590d\u6742\u6027<\/strong><\/span>\uff08meta-complexity\uff09<\/span>\u3002<\/span><\/p>\n


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Williams \u8bf4\uff1a\u201c\u6709\u4e00\u79cd\u76f4\u89c9\uff0c\u2018\u54e6\uff0c\u56e0\u4e3aP\u2260NP\uff0c\u6240\u4ee5\u5f88\u96be\u8bc1\u660eP\u2260NP\u2019\u3002\u4f46\u4e3a\u4e86\u8ba9\u8fd9\u79cd\u76f4\u89c9\u6709\u610f\u4e49\uff0c\u5fc5\u987b\u628a\u8bc1\u660e P\u2260NP \u4f5c\u4e3a\u4e00\u4e2a\u8ba1\u7b97\u95ee\u9898\u6765\u8003\u8651\u3002\u201d\u8fd9\u5c31\u662f Kabanets \u5728\u7814\u7a76\u751f\u65f6\u671f\u6240\u505a\u7684\u3002\u4ed6\u5728\u4e4c\u514b\u5170\u957f\u5927\uff0c\u5728\u82cf\u8054\u89e3\u4f53\u4e24\u5e74\u540e\u5b8c\u6210\u4e86\u8ba1\u7b97\u673a\u79d1\u5b66\u7684\u672c\u79d1\u5b66\u4e1a\u3002\u4f46\u5728\u968f\u540e\u7684\u6df7\u4e71\u4e2d\uff0c\u4ed6\u51e0\u4e4e\u6ca1\u6709\u673a\u4f1a\u7814\u7a76\u81ea\u5df1\u6700\u611f\u5174\u8da3\u7684\u7406\u8bba\u8bfe\u9898\u3002<\/span><\/p>\n


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Valentine Kabanets \u7814\u7a76\u751f\u65f6\u5199\u4e86\u4e00\u7bc7\u6709\u5f71\u54cd\u529b\u7684\u8bba\u6587\uff0c\u5173\u4e8e\u4e00\u4e2a\u5178\u578b\u7684\u5143\u590d\u6742\u6027\u95ee\u9898\uff0c\u4ed6\u79f0\u4e4b\u4e3a\u6700\u5c0f\u7535\u8def\u5c3a\u5bf8\u95ee\u9898\uff08minimum circuit size problem\uff0cMCSP\uff09\u3002\uff5c\u6765\u6e90\uff1aAntonina Kolokolova<\/span><\/section>\n


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\u201c\u6211\u60f3\u505a\u4e00\u4e9b\u66f4\u5b66\u672f\u7684\u4e8b\u60c5\uff0c\u201dKabanets\u56de\u5fc6\u9053\u3002\u201c\u6211\u4e5f\u597d\u5947\u5730\u60f3\u770b\u770b\u8fd9\u4e2a\u4e16\u754c\u3002\u201d\u4ed6\u642c\u5230\u52a0\u62ff\u5927\u653b\u8bfb\u7814\u7a76\u751f\u5b66\u4f4d\uff0c\u5728\u90a3\u91cc\u4ed6\u4e86\u89e3\u4e86\u81ea\u7136\u8bc1\u660e\u969c\u788d\u3002\u50cf Carmosino \u4e00\u6837\uff0cKabanets \u88ab\u7ed3\u679c\u6df1\u6df1\u5438\u5f15\uff1a\u201c\u8fd9\u79cd\u8054\u7cfb\u4f3c\u4e4e\u975e\u5e38\u6df1\u523b\u3002\u201d2000\u5e74\uff0c\u4ed6\u7814\u7a76\u751f\u5feb\u6bd5\u4e1a\u65f6\uff0c\u5728\u4e0e\u590d\u6742\u6027\u7406\u8bba\u5b66\u5bb6\u8521\u8fdb\u4e00<\/span>\uff08Jin-Yi Cai\uff09<\/span>\u7684\u8c08\u8bdd\u4e2d\uff0c\u53d1\u73b0\u81ea\u7136\u8bc1\u660e\u7684\u969c\u788d\u4e0d\u65ad\u51fa\u73b0\u3002\u8521\u8fdb\u4e00\u5f53\u65f6\u6b63\u5728\u591a\u4f26\u591a\u4f11\u5047\u3002\u4ed6\u4eec\u5f00\u59cb\u628a\u969c\u788d\u89c6\u4f5c\u9080\u8bf7\uff0c\u8fd9\u662f\u4e00\u4e2a\u7cbe\u786e\u7814\u7a76\u8bc1\u660e\u56f0\u96be\u95ee\u9898\u5230\u5e95\u6709\u591a\u96be\u7684\u673a\u4f1a\u3002\u4ed6\u4eec\u63d0\u51fa\u8fd9\u4e00\u65b0\u89c2\u70b9\u7684\u8bba\u6587\uff0c\u6210\u4e3a\u65b0\u5174\u7684\u5143\u590d\u6742\u6027\u9886\u57df\u4e2d\u6700\u5177\u5f71\u54cd\u529b\u7684\u65e9\u671f\u4f5c\u54c1\u4e4b\u4e00\u3002<\/span><\/p>\n


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\n

\u8bba\u6587\u9898\u76ee\uff1aCircuit minimization problem<\/span><\/p>\n

\u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/dl.acm.org\/doi\/10.1145\/335305.335314<\/span><\/p>\n<\/blockquote>\n


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Kabanets \u548c\u8521\u8fdb\u4e00\u7684\u8bba\u6587\u5f3a\u8c03\u4e86 Razborov \u548c Rudich \u7684\u81ea\u7136\u8bc1\u660e\u969c\u788d\u516c\u5f0f\u4e2d\u9690\u542b\u7684\u4e00\u4e2a\u8ba1\u7b97\u95ee\u9898\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u5e03\u5c14\u51fd\u6570\u7684\u771f\u503c\u8868\uff0c\u5224\u65ad\u5b83\u7684\u7535\u8def\u590d\u6742\u5ea6\u662f\u9ad8\u8fd8\u662f\u4f4e\u3002\u4ed6\u4eec\u79f0\u4e4b\u4e3a\u6700\u5c0f\u7535\u8def\u5c3a\u5bf8\u95ee\u9898<\/strong><\/span>\uff08minimum circuit size problem\uff09<\/span>\uff0c\u7b80\u79f0 MCSP\u3002\u6700\u5c0f\u7535\u8def\u5c3a\u5bf8\u95ee\u9898\u662f\u4e00\u4e2a\u5178\u578b\u7684\u5143\u590d\u6742\u6027\u95ee\u9898\uff1a\u5b83\u662f\u4e00\u4e2a\u8ba1\u7b97\u95ee\u9898\uff0c\u4f46\u5176\u4e3b\u9898\u4e0d\u662f\u56fe\u8bba\u6216\u5176\u4ed6\u5916\u90e8\u4e3b\u9898\uff0c\u800c\u662f\u590d\u6742\u6027\u7406\u8bba\u672c\u8eab\u3002\u5b9e\u9645\u4e0a\uff0c\u786e\u5b9e\uff0c\u8fd9\u5c31\u50cf\u662f\u9a71\u4f7f\u590d\u6742\u6027\u7406\u8bba\u5bb6\u4eec\u572820\u4e16\u7eaa80\u5e74\u4ee3\u4f7f\u7528\u7535\u8def\u590d\u6742\u6027\u65b9\u6cd5\u6765\u89e3\u51b3P\u4e0eNP\u95ee\u9898\u7684\u5b9a\u91cf\u7248\u672c\uff1a\u54ea\u4e9b\u5e03\u5c14\u51fd\u6570\u96be\u4ee5\u8ba1\u7b97\uff0c\u54ea\u4e9b\u5219\u5bb9\u6613\uff1fImpagliazzo \u8bf4\uff1a\u201c\u5982\u679c\u6211\u4eec\u80fd\u591f\u5f00\u53d1\u51fa\u4e00\u79cd\u89e3\u51b3\u6700\u5c0f\u7535\u8def\u5c3a\u5bf8\u95ee\u9898\u7684\u7b97\u6cd5\uff0c\u90a3\u5c31\u50cf\u662f\u5728\u81ea\u52a8\u5316\u6211\u4eec\u5728\u590d\u6742\u6027\u7406\u8bba\u4e2d\u6240\u505a\u7684\u5de5\u4f5c\u3002\u5b83\u81f3\u5c11\u5e94\u8be5\u8ba9\u6211\u4eec\u5bf9\u5982\u4f55\u628a\u5de5\u4f5c\u505a\u5f97\u66f4\u597d\u6709\u4e00\u4e2a\u6df1\u523b\u7684\u8ba4\u8bc6\u3002\u201d<\/span><\/p>\n


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\u590d\u6742\u6027\u7406\u8bba\u5bb6\u5e76\u4e0d\u62c5\u5fc3\u8fd9\u79cd\u795e\u5947\u7684\u7b97\u6cd5\u4f1a\u8ba9\u4ed6\u4eec\u5931\u53bb\u5de5\u4f5c\u2014\u2014\u56e0\u4e3a\u4ed6\u4eec\u8ba4\u4e3a\u5b83\u6839\u672c\u4e0d\u5b58\u5728\uff0c\u56e0\u4e3a Razborov \u548c Rudich \u8868\u660e\uff0c\u4efb\u4f55\u8fd9\u79cd\u80fd\u533a\u5206\u9ad8\u590d\u6742\u5ea6\u771f\u503c\u8868\u548c\u4f4e\u590d\u6742\u5ea6\u771f\u503c\u8868\u7684\u7b97\u6cd5\u90fd\u4f1a\u6bc1\u706d\u5bc6\u7801\u5b66\u3002\u8fd9\u610f\u5473\u7740MCSP\u53ef\u80fd\u662f\u4e00\u4e2a\u5f88\u96be\u8ba1\u7b97\u7684\u95ee\u9898\u3002\u4f46\u8fd9\u6709\u591a\u96be\u5462\uff1f\u5b83\u662fNP\u5b8c\u5168\u7684\u5417\uff0c\u5c31\u50cf\u54c8\u5bc6\u987f\u8def\u5f84\u95ee\u9898\u548c\u7814\u7a76\u4eba\u5458\u572820\u4e16\u7eaa60\u5e74\u4ee3\u52aa\u529b\u89e3\u51b3\u7684\u51e0\u4e4e\u6240\u6709\u5176\u4ed6\u95ee\u9898\u4e00\u6837\uff1f<\/span><\/p>\n


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\u5bf9\u4e8eNP\u95ee\u9898\uff0c\u201c\u5b83\u6709\u591a\u96be?\u201d\u8fd9\u4e2a\u95ee\u9898\u901a\u5e38\u5f88\u5bb9\u6613\u56de\u7b54\uff0c\u4f46\u6700\u5c0f\u7535\u8def\u5c3a\u5bf8\u95ee\u9898<\/span>\uff08MCSP\uff09<\/span>\u5f88\u5947\u602a\uff0c\u4f3c\u4e4e\u662f\u4f8b\u5916\u3002Kabanets \u8868\u793a\uff1a\u201c\u6211\u4eec\u5f88\u5c11\u9047\u5230\u4e0eNP\u5b8c\u5168\u95ee\u9898\u65e0\u5173\u7684\u2018\u771f\u7a7a\u2019\u95ee\u9898\uff0c\u5c3d\u7ba1\u5b83\u4eec\u4f3c\u4e4e\u5f88\u96be\u89e3\u51b3\u3002\u201d<\/span><\/p>\n


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Kabanets \u77e5\u9053\u4ed6\u548c\u8521\u8fdb\u4e00\u5e76\u4e0d\u662f\u7b2c\u4e00\u4e2a\u8003\u8651\u6700\u5c0f\u7535\u8def\u5c3a\u5bf8\u95ee\u9898\u7684\u4eba\u3002\u82cf\u8054\u7684\u6570\u5b66\u5bb6\u4eec\u65e9\u572820\u4e16\u7eaa50\u5e74\u4ee3\u5c31\u7814\u7a76\u8fc7\u4e00\u4e2a\u975e\u5e38\u7c7b\u4f3c\u7684\u95ee\u9898\uff0c\u4ed6\u4eec\u65e9\u671f\u8bd5\u56fe\u7406\u89e3\u4e0d\u540c\u8ba1\u7b97\u95ee\u9898\u7684\u5185\u5728\u96be\u5ea6\u300220\u4e16\u7eaa60\u5e74\u4ee3\u540e\u671f\uff0c\u5728\u53d1\u5c55NP\u5b8c\u5168\u7406\u8bba\u7684\u65f6\u5019\uff0cLeonid Levin \u66fe\u4e0e\u5b83\u6597\u4e89\u8fc7\uff0c\u4f46\u4ed6\u65e0\u6cd5\u8bc1\u660eMCSP\u662fNP\u5b8c\u5168\u7684\uff0c\u4e8e\u662f\u4ed6\u6ca1\u6709\u628aMCSP\u653e\u5728\u4ed6\u7684\u91cd\u8981\u8bba\u6587\u91cc\u3002<\/span><\/p>\n


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\u5728\u90a3\u4e4b\u540e\u768430\u5e74\u91cc\uff0c\u8fd9\u4e2a\u95ee\u9898\u51e0\u4e4e\u6ca1\u6709\u5f15\u8d77\u4eba\u4eec\u7684\u6ce8\u610f\uff0c\u76f4\u5230 Kabanets \u548c\u8521\u8fdb\u4e00\u6ce8\u610f\u5230\u5b83\u4e0e\u81ea\u7136\u8bc1\u660e\u969c\u788d\u7684\u8054\u7cfb\u3002Kabanets \u5e76\u6ca1\u6709\u60f3\u8981\u72ec\u81ea\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u2014\u2014\u76f8\u53cd\uff0c\u4ed6\u60f3\u77e5\u9053\u4e3a\u4ec0\u4e48\u8981\u8bc1\u660e\u201c\u8fd9\u4e2a\u770b\u4f3c\u56f0\u96be\u7684\u8ba1\u7b97\u56f0\u96be\u95ee\u9898\u5b9e\u9645\u4e0a\u662f\u56f0\u96be\u7684\u201d\u3002\u201c\u4ece\u67d0\u79cd\u610f\u4e49\u4e0a\u8bf4\uff0c\u8fd9\u662f\u5143\u5143\u590d\u6742\u6027<\/span>\uff08meta-meta-complexity\uff09<\/span>\uff0c\u201d\u725b\u6d25\u5927\u5b66\u7684\u590d\u6742\u6027\u7406\u8bba\u5bb6Rahul Santhanam\u8bf4\u3002<\/span><\/p>\n


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\u4f46\u662f\uff0c\u5b83\u662f\u4e00\u76f4\u90fd\u5f88\u56f0\u96be\u5417\uff1f\u8fd8\u662f\u81f3\u5c11\u6709\u4e00\u4e9b\u65b9\u6cd5\u53ef\u4ee5\u7406\u89e3\u4e3a\u4ec0\u4e48\u7814\u7a76\u4eba\u5458\u6ca1\u6709\u6210\u529f\u8bc1\u660e\u6700\u5c0f\u7535\u8def\u5c3a\u5bf8\u95ee\u9898<\/span>\uff08MCSP\uff09<\/span>\u662fNP\u5b8c\u5168\u7684\uff1fKabanets \u53d1\u73b0\uff0c\u662f\u7684\uff0c\u6709\u4e00\u4e2a\u539f\u56e0\uff1a\u7406\u89e3\u7535\u8def\u590d\u6742\u6027\u7684\u56f0\u96be\u5c31\u50cf\u4e00\u4e2a\u969c\u788d\uff0c\u963b\u788d\u4e86\u4efb\u4f55\u5df2\u77e5\u7684\u7b56\u7565\u6765\u8bc1\u660eMCSP\u7684NP\u5b8c\u5168\u6027\u2014\u2014\u8fd9\u4e2a\u95ee\u9898\u672c\u8eab\u662f\u7406\u89e3\u7535\u8def\u590d\u6742\u6027\u7684\u56f0\u96be\u3002\u81ea\u7136\u8bc1\u660e\u969c\u788d\u626d\u66f2\u7684\u201c\u81ea\u76f8\u77db\u76fe\u201d\u7684\u903b\u8f91\u4f3c\u4e4e\u662f\u4e0d\u53ef\u907f\u514d\u7684\u3002\u4e5f\u6709\u53ef\u80fd\u6700\u5c0f\u7535\u8def\u5c3a\u5bf8\u95ee\u9898<\/span>\uff08MCSP\uff09<\/span>\u4e0d\u662fNP\u5b8c\u5168\u7684\uff0c\u4f46\u4f3c\u4e4e\u4e5f\u4e0d\u592a\u53ef\u80fd\u2014\u2014\u56e0\u4e3a\u6211\u4eec\u5df2\u77e5\u67d0\u4e9b\u66f4\u7b80\u5355\u7684\u53d8\u4f53\u95ee\u9898\u662fNP\u5b8c\u5168\u7684\u3002<\/span><\/p>\n


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\u6700\u5c0f\u7535\u8def\u5c3a\u5bf8\u95ee\u9898\uff08MCSP\uff09\u662f\u5c11\u6570\u4e0d\u786e\u5b9a\u662fNP\u5b8c\u5168\u4e5f\u4e0d\u786e\u5b9a\u5c5e\u4e8eP\u7c7b\u7684\u95ee\u9898\u4e4b\u4e00\u3002\uff5c\u6765\u6e90\uff1aSamuel Velasco\/<\/span><\/span>Quanta Magazine<\/span><\/em><\/section>\n


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Impagliazzo \u8bf4\uff1a\u201c\u6211\u4eec\u53ea\u662f\u4e0d\u77e5\u9053\u600e\u4e48\u628a\u6211\u4eec\u7814\u7a76\u7684\u6240\u6709\u95ee\u9898\u8054\u7cfb\u8d77\u6765\u3002\u201d<\/span><\/p>\n


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Kabanets \u63ed\u793a\u4e86\u6700\u5c0f\u7535\u8def\u5c3a\u5bf8\u95ee\u9898<\/span>\uff08MCSP\uff09<\/span>\u7684\u5947\u602a\u884c\u4e3a\uff0c\u4f46\u4ed6\u4e0d\u77e5\u9053\u63a5\u4e0b\u6765\u8be5\u600e\u4e48\u529e\u3002\u5143\u590d\u6742\u6027\u7684\u7814\u7a76\u53d8\u5f97\u8d8a\u6765\u8d8a\u5c11\u300216\u5e74\u540e\uff0c\u5f53\u7814\u7a76\u4eba\u5458\u53d1\u73b0\u5143\u590d\u6742\u6027\u4e0e\u53e6\u4e00\u4e2a\u57fa\u672c\u95ee\u9898\u7684\u60ca\u4eba\u8054\u7cfb\u65f6\uff0c\u8fd9\u79cd\u60f3\u6cd5\u518d\u6b21\u84ec\u52c3\u5174\u76db\u3002\u8fd9\u4e2a\u95ee\u9898\u662f\uff1a\u5982\u679c\u4f60\u5927\u591a\u6570\u65f6\u5019\u53ea\u5173\u5fc3\u5f97\u5230\u6b63\u786e\u7684\u7b54\u6848\uff0c\u90a3\u4e48\u89e3\u51b3\u95ee\u9898\u6709\u591a\u96be?<\/span><\/p>\n


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\u590d\u6742\u6027\u7684\u4e16\u754c<\/span><\/strong><\/h3>\n

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\u5bf9\u4e8e\u65e5\u5e38\u95ee\u9898\uff0c\u6709\u901a\u5e38\u6709\u6548\u7684\u7b54\u6848\u5c31\u5f88\u597d\u4e86\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u4f1a\u6839\u636e\u65e5\u5e38\u7684\u4ea4\u901a\u72b6\u51b5\u89c4\u5212\u901a\u52e4\uff0c\u800c\u975e\u6700\u574f\u7684\u4ea4\u901a\u60c5\u51b5\u3002<\/span><\/p>\n


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\u4f46\u5927\u591a\u6570\u590d\u6742\u6027\u7406\u8bba\u5b66\u5bb6\u90fd\u96be\u4ee5\u6ee1\u8db3\uff1a\u53ea\u6709\u5f53\u4ed6\u4eec\u627e\u5230\u5bf9\u6240\u6709\u53ef\u80fd\u8f93\u5165\u90fd\u80fd\u5f97\u5230\u6b63\u786e\u7b54\u6848\u7684\u5feb\u901f\u7b97\u6cd5\u65f6\uff0c\u624d\u4f1a\u58f0\u79f0\u4e00\u4e2a\u95ee\u9898\u5f88\u5bb9\u6613\u3002\u8fd9\u79cd\u6807\u51c6\u65b9\u6cd5\u6839\u636e\u7814\u7a76\u4eba\u5458\u6240\u8bf4\u7684\u201c\u6700\u574f\u60c5\u51b5\u201d\u7684\u590d\u6742\u6027\u5bf9\u95ee\u9898\u8fdb\u884c\u5206\u7c7b\u3002\u4f46\u4e5f\u6709\u4e00\u79cd\u201c\u5e73\u5747\u60c5\u51b5\u201d<\/span>\uff08average-case\uff09<\/span>\u7684\u590d\u6742\u6027\u7406\u8bba\uff0c\u5728\u8fd9\u79cd\u7406\u8bba\u4e2d\uff0c\u5982\u679c\u6709\u4e00\u4e2a\u5feb\u901f\u7b97\u6cd5\u80fd\u5728\u5927\u591a\u6570\u60c5\u51b5\u4e0b\u5f97\u5230\u6b63\u786e\u7684\u7b54\u6848\uff0c\u90a3\u4e48\u8fd9\u4e2a\u95ee\u9898\u5c31\u662f\u7b80\u5355\u7684\u3002<\/span><\/p>\n


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\u5bf9\u4e8e\u5bc6\u7801\u5b66\u5bb6\u6765\u8bf4\uff0c\u8fd9\u79cd\u533a\u522b\u5f88\u91cd\u8981\u3002\u60f3\u8c61\u4e00\u4e2a\u8ba1\u7b97\u95ee\u9898\uff0c\u7b97\u6cd5\u80fd\u8f7b\u6613\u89e3\u51b3\u51e0\u4e4e\u6240\u6709\u7684\u60c5\u51b5\uff0c\u9664\u4e86\u4e2a\u522b\u60c5\u51b5\u3002\u6700\u574f\u60c5\u51b5\u7684\u590d\u6742\u6027\u7406\u8bba\u8ba4\u4e3a\u8fd9\u662f\u4e00\u4e2a\u56f0\u96be\u7684\u95ee\u9898\uff0c\u4f46\u5bf9\u4e8e\u5bc6\u7801\u5b66\u6765\u8bf4\u8fd9\u662f\u65e0\u7528\u7684\uff1a\u5982\u679c\u53ea\u6709\u5f88\u5c11\u7684\u6d88\u606f\u96be\u4ee5\u7834\u8bd1\uff0c\u90a3\u6709\u4ec0\u4e48\u610f\u4e49\u5462\uff1f<\/span><\/p>\n


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\u4e8b\u5b9e\u4e0a\uff0c\u5728 Levin \u5173\u4e8eNP\u5b8c\u5168\u7406\u8bba\u7684\u5f00\u521b\u6027\u5de5\u4f5c\u53d1\u8868\u5341\u5e74\u540e\uff0c\u4ed6\u624d\u5f00\u59cb\u5bf9\u5e73\u5747\u590d\u6742\u5ea6\u8fdb\u884c\u4e25\u683c\u7684\u7814\u7a76\u3002Levin 1978\u5e74\u79fb\u6c11\u5230\u7f8e\u56fd\uff0c\u572820\u4e16\u7eaa80\u5e74\u4ee3\u4e2d\u671f\uff0c\u4ed6\u5f00\u59cb\u5173\u6ce8\u5e73\u5747\u590d\u6742\u5ea6\u3002\u4ed6\u5f00\u59cb\u4e0e\u5176\u4ed6\u4eba\u5408\u4f5c\uff0c\u8fdb\u4e00\u6b65\u53d1\u5c55\u8fd9\u4e00\u7406\u8bba\uff0c\u5305\u62ec\u5f53\u65f6\u8fd8\u5728\u8bfb\u7814\u7684 Impagliazzo\u3002Impagliazzo \u53d1\u73b0\u867d\u7136\u7814\u7a76\u8005\u4eec\u5728\u52aa\u529b\u63a8\u8fdb\u5e73\u5747\u590d\u6742\u6027\u7406\u8bba\u7684\u53d1\u5c55\uff0c\u4f46\u4ed6\u4eec\u7ecf\u5e38\u504f\u79bb\u8ba8\u8bba\u7684\u4e3b\u9898\uff0c\u6ca1\u6709\u76f4\u63a5\u9488\u5bf9\u95ee\u9898\u8fdb\u884c\u8ba8\u8bba\u3002\u4ed6\u5e0c\u671b\u4ed6\u4eec\u90fd\u5bf9\u8fd9\u4e2a\u95ee\u9898\u6709\u76f8\u540c\u7684\u7406\u89e3\uff0c\u5c3d\u7ba1 Levin \u7684\u8bba\u6587\u4ee5\u7b80\u6d01\u8457\u79f0<\/span>\uff08\u5f00\u521b\u5e73\u5747\u590d\u6742\u6027\u9886\u57df\u7684\u90a3\u7bc7\u8bba\u6587\u4e0d\u5230\u4e24\u9875\u957f\uff09<\/span>\uff0c\u4f46\u8fd9\u4e5f\u65e0\u6d4e\u4e8e\u4e8b\u3002<\/span><\/p>\n


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\n

Leonid Levin \u5f00\u521b\u5e73\u5747\u590d\u6742\u6027\u9886\u57df\u7684\u8bba\u6587<\/span><\/p>\n

\u8bba\u6587\u9898\u76ee\uff1aAverage Case Complete Problems<\/span><\/p>\n

\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/epubs.siam.org\/doi\/10.1137\/0215020<\/span><\/p>\n<\/blockquote>\n


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Impagliazzo\u8bf4\uff1a\u201c\u6211\u672c\u6765\u6253\u7b97\u628a Levin \u7684\u5de5\u4f5c\u7ffb\u8bd1\u6210\u66f4\u6613\u61c2\u7684\u6587\u7ae0\u3002\u201d\u4ed6\u51b3\u5b9a\u9996\u5148\u5bf9\u5927\u7684\u56fe\u666f\u505a\u4e00\u4e2a\u7b80\u77ed\u3001\u6709\u8da3\u7684\u6982\u8ff0\uff0c\u7136\u540e\u518d\u6df1\u5165\u8ba8\u8bba\u6570\u5b66\u3002\u201c\u8fd9\u51e0\u4e4e\u5360\u6ee1\u4e86\u5f53\u65f6\u7684\u8bba\u6587\uff0c\u800c\u4e14\u4e5f\u662f\u4eba\u4eec\u552f\u4e00\u8bb0\u5f97\u7684\u90e8\u5206\u3002\u201d\u8be5\u8bba\u6587\u4e8e1995\u5e74\u53d1\u8868\uff0c\u7acb\u5373\u6210\u4e3a\u7ecf\u5178\u4e4b\u4f5c\u3002Impagliazzo \u6839\u636e\u4e0d\u540c\u7a0b\u5ea6\u7684\u8ba1\u7b97\u96be\u5ea6\u548c\u4e0d\u540c\u7684\u5bc6\u7801\u5b66\u80fd\u529b\uff0c\u5c06\u590d\u6742\u6027\u96be\u5ea6\u5206\u4e3a\u4e94\u7c7b\u4e16\u754c\uff0c\u5e76\u4e3a\u5b83\u4eec\u521b\u9020\u4e86\u795e\u5947\u7684\u540d\u5b57\u3002\u6211\u4eec\u751f\u6d3b\u5728\u5176\u4e2d\u4e00\u4e2a\u96be\u5ea6\u7684\u4e16\u754c\uff0c\u4f46\u4e0d\u77e5\u9053\u662f\u54ea\u4e00\u4e2a\u3002<\/span><\/p>\n


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\n

\u8bba\u6587\u9898\u76ee\uff1aA personal view of average-case complexity<\/span><\/p>\n

\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/ieeexplore.ieee.org\/document\/514853<\/span><\/p>\n<\/blockquote>\n


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<\/p>\n

Leonid Levin\uff08\u53f3\uff09\u572820\u4e16\u7eaa80\u5e74\u4ee3\u4e2d\u671f\u5f00\u59cb\u4e86\u5bf9\u5e73\u5747\u60c5\u51b5\u590d\u6742\u6027\u7684\u7814\u7a76\u3002Russell Impagliazzo \u540e\u6765\u5728\u4e00\u7bc7\u5173\u4e8e\u6211\u4eec\u53ef\u80fd\u751f\u6d3b\u7684\u4e94\u4e2a\u8ba1\u7b97\u4e16\u754c\u7684\u6807\u5fd7\u6027\u8bba\u6587\u4e2d\uff0c\u4f7f\u8fd9\u4e00\u4e3b\u9898\u53d8\u5f97\u66f4\u52a0\u5bb9\u6613\u7406\u89e3\u3002\uff5c\u6765\u6e90\uff1aCourtesy of Simons Foundation (left); Cydney Scott\/Boston University Photography<\/span><\/section>\n


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\u81ea\u4ece Impagliazzo \u7684\u8bba\u6587\u53d1\u8868\u4ee5\u6765\uff0c\u7814\u7a76\u4eba\u5458\u4e00\u76f4\u68a6\u60f3\u7740\u6d88\u9664\u4ed6\u7684\u5fae\u578b\u591a\u91cd\u5b87\u5b99\u7684\u4e00\u90e8\u5206 \u2014\u2014\u901a\u8fc7\u8bc1\u660e\u67d0\u4e9b\u4e16\u754c\u6839\u672c\u4e0d\u5b58\u5728\u6765\u7f29\u5c0f\u53ef\u80fd\u7684\u7a7a\u95f4\u3002\u6709\u4e24\u4e2a\u4e16\u754c\u7279\u522b\u5f15\u4eba\u6ce8\u76ee\uff0c\u5728\u5176\u4e2d\uff0c\u5373\u4f7f P \u2260 NP\uff0c\u5f53\u524d\u7684\u52a0\u5bc6\u7b97\u6cd5\u4e5f\u65e0\u6cd5\u5b9e\u73b0\u5b89\u5168\u7684\u52a0\u5bc6\u901a\u4fe1\u3002<\/span><\/p>\n


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\u5728\u5176\u4e2d\u4e00\u4e2a\u88ab\u79f0\u4e3a Heuristica \u7684\u4e16\u754c\u4e2d\uff0c\u6240\u6709NP\u5b8c\u5168\u95ee\u9898\u5728\u5927\u591a\u6570\u8f93\u5165\u4e0a\u90fd\u662f\u5bb9\u6613\u89e3\u51b3\u7684\uff0c\u4f46\u5feb\u901f\u7b97\u6cd5\u5076\u5c14\u4f1a\u51fa\u73b0\u9519\u8bef\uff0c\u56e0\u6b64\u6309\u7167\u6700\u574f\u60c5\u51b5\u590d\u6742\u6027\u7406\u8bba\u7684\u6807\u51c6\uff0c\u8fd9\u4e9b\u95ee\u9898\u4ecd\u7136\u88ab\u8ba4\u4e3a\u662f\u56f0\u96be\u7684\u3002\u56e0\u4e3a\u5728\u8fd9\u4e2a\u4e16\u754c\u4e2d\u51e0\u4e4e\u6240\u6709\u7684\u4ee3\u7801\u90fd\u5f88\u5bb9\u6613\u88ab\u7834\u89e3\uff0c\u56e0\u6b64\u52a0\u5bc6\u662f\u4e0d\u53ef\u80fd\u7684\u3002\u5728\u53e6\u4e00\u4e2a\u540d\u4e3a Pessiland \u7684\u4e16\u754c\u4e2d\uff0c\u52a0\u5bc6\u4e4b\u6240\u4ee5\u4e0d\u53ef\u80fd\u662f\u53e6\u4e00\u4e2a\u539f\u56e0\uff1a\u6bcf\u4e2a\u95ee\u9898\u5728\u5e73\u5747\u60c5\u51b5\u4e0b\u90fd\u662f\u56f0\u96be\u7684\uff0c\u4f46\u52a0\u5bc6\u4e00\u6761\u6d88\u606f\u4f1a\u8ba9\u5b83\u7684\u76ee\u6807\u63a5\u6536\u8005\u4e5f\u65e0\u6cd5\u7406\u89e3\u3002<\/span><\/p>\n


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\u8fd9\u4e24\u4e2a\u4e16\u754c\u4e0e\u5143\u590d\u6742\u6027\u95ee\u9898\u5bc6\u5207\u76f8\u5173\u2014\u2014\u7279\u522b\u662f Heuristica \u7684\u547d\u8fd0\u4e0e\u6700\u5c0f\u7535\u8def\u5c3a\u5bf8\u95ee\u9898<\/span>\uff08MCSP\uff09<\/span>\u662f\u5426\u662fNP\u5b8c\u5168\u7684\u95ee\u9898\u6709\u5173\u3002Kabanets \u548c Levin \u591a\u5e74\u524d\u6240\u7740\u8ff7\u7684\u95ee\u9898\u4e0d\u4ec5\u4ec5\u662f\u51fa\u4e8e\u597d\u5947\uff1a\u6709\u4e00\u4e2a\u5b8c\u6574\u7684\u4e16\u754c\u5c8c\u5c8c\u53ef\u5371\u3002\u4e3a\u4e86\u6392\u9664\u6389 Heuristica\uff0c\u7814\u7a76\u8005\u4eec\u5fc5\u987b\u6d88\u9664\u6700\u574f\u60c5\u51b5\u548c\u5e73\u5747\u60c5\u51b5\u4e4b\u95f4\u7684\u533a\u522b\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u4ed6\u4eec\u5fc5\u987b\u8bc1\u660e\u4efb\u4f55\u5047\u8bbe\u7684\u7b97\u6cd5\u90fd\u53ef\u4ee5\u5728\u5927\u591a\u6570\u60c5\u51b5\u4e0b\u6b63\u786e\u89e3\u51b3NP\u5b8c\u5168\u95ee\u9898\uff0c\u5e76\u4e14\u53ef\u4ee5\u5728\u6240\u6709\u60c5\u51b5\u4e0b\u5b9e\u9645\u89e3\u51b3\u95ee\u9898\u3002\u8fd9\u79cd\u8054\u7cfb\u79f0\u4e3a\u6700\u574f\u60c5\u51b5\u5230\u5e73\u5747\u60c5\u51b5\u7684\u7ea6\u7b80<\/span>\uff08worst-case to average-case reduction\uff09<\/span>\uff0c\u867d\u7136\u5df2\u7ecf\u8bc1\u660e\u5bf9\u4e8e\u67d0\u4e9b\u95ee\u9898\uff0c\u8fd9\u79cd\u7ea6\u7b80\u662f\u5b58\u5728\u7684\uff0c\u4f46\u8fd9\u4e9b\u95ee\u9898\u90fd\u4e0d\u662fNP\u5b8c\u5168\u7684\uff0c\u56e0\u6b64\u8fd9\u4e9b\u7ed3\u679c\u5e76\u4e0d\u4f1a\u7ed9\u51fa\u66f4\u591a\u7684\u4fe1\u606f\u3002\u5982\u679c\u80fd\u591f\u8bc1\u660e Heuristica \u4e0d\u5b58\u5728\uff0c\u90a3\u4e48\u5728 P \u2260 NP \u7684\u60c5\u51b5\u4e0b\u5b9e\u73b0\u5b89\u5168\u7684\u52a0\u5bc6\u901a\u4fe1\u5c31\u66f4\u5bb9\u6613\u4e86\u3002<\/span><\/p>\n


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\u4f46\u8981\u6392\u9664\u6389 Heuristica \u5e76\u4e0d\u5bb9\u6613\u30022003\u5e74\uff0c\u4e24\u4f4d\u590d\u6742\u6027\u7406\u8bba\u5bb6\u8868\u660e\uff0c\u8bc1\u660e\u5df2\u77e5NP\u5b8c\u5168\u95ee\u9898\u7684\u6700\u574f\u60c5\u51b5\u5230\u5e73\u5747\u60c5\u51b5\u7684\u7ea6\u7b80\u7684\u73b0\u6709\u65b9\u6cd5\u5c06\u5bfc\u81f4\u8352\u8c2c\u7684\u540e\u679c\uff0c\u8fd9\u8868\u660e\u8fd9\u6837\u7684\u8bc1\u660e\u53ef\u80fd\u884c\u4e0d\u901a\u3002\u7814\u7a76\u4eba\u5458\u5fc5\u987b\u627e\u5230\u53e6\u4e00\u79cd\u65b9\u6cd5\uff0c\u73b0\u5728\u4ed6\u4eec\u8ba4\u4e3a\u6700\u5c0f\u7535\u8def\u5c3a\u5bf8\u95ee\u9898<\/span>\uff08MCSP\uff09<\/span>\u53ef\u80fd\u6b63\u662f\u4ed6\u4eec\u9700\u8981\u7684\u95ee\u9898\u3002\u4f46\u8fd9\u5728\u5341\u591a\u5e74\u540e\u624d\u53d8\u5f97\u6e05\u6670\u8d77\u6765\u3002Carmosino \u5bf9\u81ea\u7136\u8bc1\u660e\u969c\u788d\u7684\u6267\u7740\u8ffd\u6c42\uff0c\u8ba9\u6211\u4eec\u7b2c\u4e00\u6b21\u770b\u5230\u4e86\u8fd9\u79cd\u8054\u7cfb\u3002<\/span><\/p>\n


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

\n

\u8bba\u6587\u9898\u76ee\uff1aOn worst-case to average-case reductions for NP problems<\/span><\/p>\n

\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/ieeexplore.ieee.org\/document\/1238205<\/span><\/p>\n<\/blockquote>\n


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3. \u673a\u9047<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u901a\u8fc7 Kabanets \u548c\u5176\u4ed6\u56db\u540d\u7814\u7a76\u4eba\u5458\u4e8e2013\u5e74\u53d1\u8868\u7684\u4e00\u7bc7\u8bba\u6587\uff0cCarmosino \u5728\u7814\u7a76\u751f\u671f\u95f4\u9996\u6b21\u63a5\u89e6\u5230\u5143\u590d\u6742\u6027\u7814\u7a76\uff0c\u8be5\u8bba\u6587\u8fdb\u4e00\u6b65\u53d1\u5c55\u4e86 Kabanets \u5341\u591a\u5e74\u524d\u5f00\u521b\u7684\u81ea\u7136\u8bc1\u660e\u969c\u788d\u7684\u65b9\u6cd5\u3002\u8fd9\u8ba9\u4ed6\u66f4\u52a0\u76f8\u4fe1\uff0c\u6211\u4eec\u4ecd\u7136\u53ef\u4ee5\u4ece Razborov \u548c Rudich \u7684\u7ecf\u5178\u8bba\u6587\u4e2d\u5b66\u5230\u5f88\u591a\u4e1c\u897f\u3002<\/span><\/p>\n


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

\n

\u8bba\u6587\u9898\u76ee\uff1aMining Circuit Lower Bound Proofs for Meta-Algorithms<\/span><\/p>\n

\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/eccc.weizmann.ac.il\/report\/2013\/057\/<\/span><\/p>\n<\/blockquote>\n


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\u201c\u5f53\u65f6\u6211\u6c89\u8ff7\u4e8e\u90a3\u7bc7\u8bba\u6587\uff0c\u201dCarmosino \u8bf4\u3002\u201c\u4e00\u5207\u90fd\u6ca1\u6709\u6539\u53d8\u3002\u201d\u5728\u8bbf\u95ee\u52a0\u5dde\u5927\u5b66\u4f2f\u514b\u5229\u5206\u6821\u957f\u8fbe\u4e00\u5b66\u671f\u7684\u7814\u8ba8\u4f1a\u65f6\uff0c\u4ed6\u7684\u75f4\u8ff7\u7ec8\u4e8e\u7ed3\u51fa\u679c\u5b9e\u3002\u5728\u90a3\u91cc\uff0c\u4ed6\u82b1\u4e86\u5f88\u591a\u65f6\u95f4\u4e0e Impagliazzo\u3001Kabanets \u548c Antonina Kolokolova \u4ea4\u8c08\uff0cAntonina Kolokolova \u662f\u7ebd\u82ac\u5170\u7eaa\u5ff5\u5927\u5b66\u7684\u590d\u6742\u6027\u7406\u8bba\u5bb6\uff0c\u66fe\u4e0e Kabanets \u5408\u4f5c\u64b0\u51992013\u5e74\u7684\u8bba\u6587\u3002Carmosino \u4e4b\u524d\u66fe\u4e0e\u4ed6\u4eec\u4e09\u4eba\u5408\u4f5c\u8fc7\uff0c\u8fd9\u79cd\u6210\u529f\u7684\u5408\u4f5c\u7ed9\u4e86\u4ed6\u4fe1\u5fc3\uff0c\u4ed6\u80fd\u591f\u5411\u8fd9\u4e09\u4e2a\u4eba\u63d0\u51fa\u5173\u4e8e\u8fd9\u4e2a\u4e3b\u9898\u7684\u6700\u8ff7\u4eba\u95ee\u9898\u3002<\/span><\/p>\n


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\u201c\u4ed6\u4ee5\u4e00\u79cd\u597d\u7684\u65b9\u5f0f\u56f0\u6270\u7740\u4eba\u4eec\uff0c\u201dKabanets \u56de\u5fc6\u9053\u3002\u8d77\u521d\uff0cCarmosino \u4e3a\u8bc1\u660e Razborov \u548c Rudich \u8bba\u6587\u4e2d\u81ea\u7136\u8bc1\u660e\u969c\u788d\u7684\u6700\u5c0f\u7535\u8def\u5c3a\u5bf8\u95ee\u9898<\/span>\uff08MCSP\uff09<\/span>\u7248\u672c\u5177\u6709NP\u5b8c\u5168\u6027\u63d0\u51fa\u4e86\u65b0\u7684\u60f3\u6cd5\uff0c\u4f46\u8fd9\u4e9b\u60f3\u6cd5\u5e76\u6ca1\u6709\u594f\u6548\u3002\u76f8\u53cd\uff0cImpagliazzo \u4e0d\u7ecf\u610f\u95f4\u7684\u8bc4\u8bba\u4f7f\u8fd9\u56db\u540d\u7814\u7a76\u4eba\u5458\u610f\u8bc6\u5230\uff0c\u81ea\u7136\u8bc1\u660e\u969c\u788d\u53ef\u4ee5\u4ea7\u751f\u6bd4\u4efb\u4f55\u4eba\u60f3\u8c61\u7684\u66f4\u5f3a\u5927\u7684\u7b97\u6cd5\u2014\u2014\u5728\u81ea\u7136\u8bc1\u660e\u969c\u788d\u4e2d\u5b58\u5728\u4e00\u4e2a\u79d8\u5bc6\u5730\u56fe\u3002<\/span><\/p>\n


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2016\u5e74\uff0cAntonina Kolokolova \u4e0e Carmosino\u3001Impagliazzo \u548c Kabanets\u5408\u4f5c\uff0c\u8bc1\u660e\u4e86MCSP\u548c\u201c\u5b66\u4e60\u201d\u4e4b\u95f4\u4ee4\u4eba\u60ca\u8bb6\u7684\u8054\u7cfb\uff0c\u8fd9\u5f15\u8d77\u4e86\u5bf9\u5143\u590d\u6742\u6027\u7684\u65b0\u5173\u6ce8\u3002\uff5c\u6765\u6e90\uff1aColette Philips<\/span><\/section>\n


<\/p>\n

\u57282016\u5e74\u7684\u4e00\u7bc7\u6587\u7ae0\u4e2d\uff0c\u8fd9\u56db\u540d\u7814\u7a76\u4eba\u5458\u8bc1\u660e\uff0c\u67d0\u79cd\u5e73\u5747\u60c5\u51b5\u4e0b\u7684MCSP\u7b97\u6cd5\u53ef\u4ee5\u7528\u6765\u6784\u5efa\u4e00\u79cd\u6700\u574f\u60c5\u51b5\u4e0b\u7684\u7b97\u6cd5\uff0c\u7528\u4e8e\u8bc6\u522b\u9690\u85cf\u5728\u968f\u673a\u6570\u5b57\u4e32\u4e2d\u7684\u6a21\u5f0f\u2014\u2014\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u5c06\u6b64\u4efb\u52a1\u79f0\u4e3a\u201c\u5b66\u4e60<\/strong>\u201d\u3002\u8fd9\u662f\u4e00\u4e2a\u60ca\u4eba\u7684\u7ed3\u679c\uff0c\u56e0\u4e3a\u4ece\u76f4\u89c2\u4e0a\u770b\uff0c\u5b66\u4e60\u4f3c\u4e4e\u6bd4MCSP\u7b97\u6cd5\u6267\u884c\u7684\u4e8c\u5143\u5206\u7c7b\u4efb\u52a1<\/span>\uff08\u590d\u6742\u6027\u9ad8\u8fd8\u662f\u4f4e\uff09<\/span>\u66f4\u96be\u3002\u800c\u4e14\u4ee4\u4eba\u60ca\u8bb6\u7684\u662f\uff0c\u5b83\u5c06\u4e00\u4e2a\u4efb\u52a1\u7684\u6700\u574f\u60c5\u51b5\u590d\u6742\u6027\u4e0e\u53e6\u4e00\u4e2a\u4efb\u52a1\u7684\u5e73\u5747\u60c5\u51b5\u590d\u6742\u6027\u8054\u7cfb\u8d77\u6765\u3002<\/span><\/p>\n


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

\n

\u8bba\u6587\u9898\u76ee\uff1aLearning algorithms from natural proofs<\/span><\/p>\n

\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/dl.acm.org\/doi\/10.5555\/2982445.2982455<\/span><\/p>\n<\/blockquote>\n


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\u201c\u8fd9\u79cd\u8054\u7cfb\u662f\u5426\u5b58\u5728\u5e76\u4e0d\u660e\u663e\uff0c\u201dImpagliazzo\u8bf4\u3002\u5bf9\u4e8e\u4e00\u822c\u7684\u5e03\u5c14\u7535\u8def\uff0cMCSP\u7684\u5feb\u901f\u7b97\u6cd5\u7eaf\u5c5e\u5047\u8bbe\uff1a\u9664\u975e\u6211\u4eec\u80fd\u8bc1\u660eMCSP\u662f\u4e00\u4e2a\u5bb9\u6613\u8ba1\u7b97\u7684\u95ee\u9898\uff0c\u5426\u5219\u8fd9\u79cd\u5feb\u901f\u7b97\u6cd5\u6839\u672c\u4e0d\u53ef\u80fd\u5b58\u5728\uff0c\u800c\u8fd9\u610f\u5473\u7740\u8fd9\u56db\u540d\u7814\u7a76\u4eba\u5458\u8bba\u6587\u4e2d\u6697\u793a\u7684\u5b66\u4e60\u7b97\u6cd5\u4e5f\u662f\u540c\u6837\u5047\u8bbe\u7684\u3002<\/span><\/p>\n


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\u4f46\u662f\u5bf9\u4e8e\u4e00\u4e9b\u66f4\u7b80\u5355\u7684MCSP\u7248\u672c\u2014\u2014\u5f53\u7535\u8def\u5177\u6709\u7279\u5b9a\u9650\u5236\u65f6\uff0c\u533a\u5206\u590d\u6742\u5ea6\u9ad8\u548c\u4f4e\u7684\u771f\u503c\u8868\uff0c\u65e9\u5728\u5f88\u591a\u5e74\u524d\u5c31\u5df2\u7ecf\u6709\u4e86\u5feb\u901f\u7b97\u6cd5\u3002Carmosino\u3001Impagliazzo\u3001Kabanets \u548c Kolokolova\u7684\u8bba\u6587\u8868\u660e\uff0c\u8fd9\u4e9b\u7b97\u6cd5\u53ef\u4ee5\u8f6c\u5316\u4e3a\u540c\u6837\u53d7\u5230\u9650\u5236\u7684\u201c\u5b66\u4e60\u201d\u7b97\u6cd5\u3002\u5c3d\u7ba1\u8fd9\u4e9b\u7b97\u6cd5\u53d7\u5230\u9650\u5236\uff0c\u4f46\u5b83\u4eec\u4ecd\u7136\u6bd4\u7814\u7a76\u4eba\u5458\u6b64\u524d\u5728\u4e25\u683c\u7406\u8bba\u6c34\u5e73\u4e0a\u6240\u7406\u89e3\u7684\u4efb\u4f55\u7b97\u6cd5\u90fd\u8981\u5f3a\u5927\u3002\u201c\u4e0d\u77e5\u4e3a\u4f55\uff0c\u4ed6\u4eec\u7684\u2018\u81ea\u6307\u2019\u80fd\u8ba9\u4f60\u505a\u4e00\u4e9b\u4f3c\u4e4e\u5728\u66f4\u6807\u51c6\u7684\u95ee\u9898\u4e0a\u505a\u4e0d\u5230\u7684\u4e8b\u60c5\u3002\u201dIlango\u8bf4\u3002\u8fd9\u4e00\u7ed3\u679c\u5f15\u8d77\u4e86\u5176\u4ed6\u4e3b\u9898\u7684\u590d\u6742\u6027\u7406\u8bba\u5bb6\u7684\u5173\u6ce8\u3002\u8fd9\u4e5f\u662f\u5728\u4e4b\u540e\u51e0\u5e74\uff0c\u5143\u590d\u6742\u6027\u548c\u5e73\u5747\u60c5\u51b5\u590d\u6742\u6027\u4e4b\u95f4\u51fa\u73b0\u8fdb\u4e00\u6b65\u8054\u7cfb\u7684\u9884\u5146\u3002\u6700\u91cd\u8981\u7684\u662f\uff0c\u8fd9\u8bc1\u660e\u4e86\u7814\u7a76\u4eba\u5458\u53ef\u4ee5\u901a\u8fc7\u95ee\u4e00\u4e9b\u7b80\u5355\u7684\u95ee\u9898\u6765\u53d6\u5f97\u5927\u7684\u8fdb\u6b65\uff0c\u867d\u7136\u8fd9\u4e9b\u95ee\u9898\u4e00\u5f00\u59cb\u4f3c\u4e4e\u53ea\u4f1a\u963b\u788d\u4ed6\u4eec\u7684\u8fdb\u6b65\u3002Impagliazzo \u8bf4\uff1a\u201c\u8fd9\u79cd\u5bf9\u5076\u6027<\/span>\uff08duality\uff09<\/span>\u8d2f\u7a7f\u4e86\u8fc7\u53bb\u81f3\u5c1130\u621640\u5e74\u7684\u590d\u6742\u6027\u7814\u7a76\u3002\u673a\u9047\u4e0e\u6311\u6218\u5f80\u5f80\u5e76\u5b58\u3002\u201d<\/span><\/p>\n


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\u90e8\u5206\u95ee\u9898\u7684\u8bc1\u660e<\/span><\/strong><\/span><\/h3>\n

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\u81ea\u4ece Carmosino \u548c\u4ed6\u7684\u540c\u4e8b\u53d1\u8868\u4e86\u8bba\u6587\u4e4b\u540e\uff0c\u8fdb\u5c55\u624d\u5f97\u4ee5\u52a0\u901f\u3002Kolokolova \u8bf4\uff1a\u201c\u590d\u6742\u6027\u7814\u7a76\u7684\u8fdb\u5c55\u65e5\u65b0\u6708\u5f02\uff0c\u73b0\u5728\u6709\u5f88\u591a\u975e\u5e38\u975e\u5e38\u806a\u660e\u7684\u5e74\u8f7b\u4eba\u52a0\u5165\u3002\u201d<\/span><\/p>\n


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Ilango \u5c31\u662f\u8fd9\u7fa4\u5e74\u8f7b\u4eba\u4e4b\u4e00\uff0c\u5728\u8bfb\u7814\u7684\u524d\u4e09\u5e74\u5185\uff0c\u4ed6\u91c7\u7528\u53cc\u7ba1\u9f50\u4e0b\u7684\u7b56\u7565\uff0c\u8bc1\u660e\u4e86\u201cMCSP\u95ee\u9898\u662fNP\u5b8c\u5168\u7684\u201d\u8fd9\u6837\u8270\u5de8\u7684\u5f00\u653e\u95ee\u9898\uff1a\u6b63\u5982\u7535\u8def\u590d\u6742\u6027\u7814\u7a76\u8005\u5728\u4e0a\u4e16\u7eaa80\u5e74\u4ee3\u6311\u6218 P \u548c NP \u95ee\u9898\u65f6\u90a3\u6837\uff0c\u5728\u8bc1\u660eMCSP\u66f4\u7b80\u5355\u7248\u672cNP\u5b8c\u5168\u7684\u540c\u65f6\uff0c\u4e5f\u8bc1\u660e\u4e86 MCSP \u66f4\u590d\u6742\u7248\u672c\u7684 NP \u5b8c\u5168\u6027\u3002\u8bc1\u660e\u590d\u6742\u7248\u672c\u7684 MCSP \u7684NP\u5b8c\u5168\u6027\u5728\u76f4\u89c9\u4e0a\u4f3c\u4e4e\u66f4\u96be\uff0c\u56e0\u6b64\u8981\u8bc1\u660e\u5b83\u66f4\u56f0\u96be\u5c31\u66f4\u5bb9\u6613\u3002Ilango \u5c06\u4ed6\u5bf9\u5143\u590d\u6742\u6027\u7684\u5174\u8da3\u5f52\u529f\u4e8e Eric Allender\uff0c\u4ed6\u662f\u7f57\u683c\u65af\u5927\u5b66\u7684\u590d\u6742\u6027\u7406\u8bba\u5bb6\uff0c\u662f\u5c11\u6570\u57282000\u5e74\u4ee3\u548c2010\u5e74\u4ee3\u521d\u7ee7\u7eed\u7814\u7a76\u5143\u590d\u6742\u6027\u7684\u7814\u7a76\u4eba\u5458\u4e4b\u4e00\u3002\u201c\u4ed6\u7684\u70ed\u60c5\u5f88\u6709\u611f\u67d3\u529b\uff0c\u201d Ilango\u8bf4\u3002<\/span><\/p>\n


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\u53e6\u4e00\u4f4d\u53d7 Allender \u542f\u53d1\u7684\u5e74\u8f7b\u7814\u7a76\u5458\u662f Shuichi Hirahara\uff0c\u76ee\u524d\u662f\u4e1c\u4eac\u56fd\u5bb6\u4fe1\u606f\u7814\u7a76\u6240<\/span>\uff08National Institute of Informatics\uff09<\/span>\u7684\u6559\u6388\u30022018\u5e74\uff0c\u5f53Hirahara\u8fd8\u662f\u4e00\u540d\u7814\u7a76\u751f\u65f6\uff0c\u4ed6\u63ed\u793a\u4e86 Carmosino \u548c\u4ed6\u7684\u5408\u4f5c\u8005\u53d1\u73b0\u7684\u5143\u590d\u6742\u6027\u4e0e\u5e73\u5747\u590d\u6742\u6027\u4e4b\u95f4\u7684\u672c\u8d28\u5173\u7cfb\u3002\u8fd9\u56db\u540d\u7814\u7a76\u4eba\u5458\u53d1\u73b0\u4e86\u4e00\u4e2a\u95ee\u9898\uff1aMCSP\u7684\u5e73\u5747\u590d\u6742\u6027\u4e0e\u5e03\u5c14\u5b66\u4e60<\/strong>\u95ee\u9898<\/strong>\u7684\u6700\u574f\u60c5\u51b5\u590d\u6742\u6027\u4e4b\u95f4\u7684\u8054\u7cfb<\/strong>\u3002Hirahara \u8fdb\u4e00\u6b65\u53d1\u5c55\u4e86\u4ed6\u4eec\u7684\u6280\u672f\uff0c\u63a8\u5bfc\u51faMCSP\u7684\u6700\u574f\u60c5\u51b5\u5230\u5e73\u5747\u60c5\u51b5\u7684\u7ea6\u7b80\u3002\u4ed6\u7684\u7ed3\u679c\u8868\u660e\uff0c\u50cf Carmosino \u548c\u4ed6\u7684\u540c\u4e8b\u8003\u8651\u7684\u90a3\u79cd\u5047\u8bbe\u7684\u5e73\u5747\u60c5\u51b5 MCSP \u7b97\u6cd5\u5b9e\u9645\u4e0a\u8db3\u591f\u5f3a\u5927\uff0c\u5373\u4f7f MCSP \u95ee\u9898\u7a0d\u6709\u4e0d\u540c\uff0c\u8be5\u7b97\u6cd5\u4ecd\u7136\u80fd\u591f\u6210\u529f\u5730\u89e3\u51b3\u95ee\u9898\uff0c\u800c\u4e14\u4e0d\u4f1a\u72af\u9519\u3002<\/span><\/p>\n


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Rahul Ilango\uff08\u5de6\uff09\u548c Shuichi Hirahara \u6700\u8fd1\u5f00\u53d1\u4e86\u65b0\u7684\u5bc6\u7801\u6280\u672f\u6765\u8bc1\u660eMCSP\u7684\u53d8\u4f53\u662fNP\u5b8c\u5168\u7684\u3002\uff5c\u6765\u6e90\uff1aJennifer Krupa (left); Takuma Imamura<\/span><\/section>\n


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Hirahara\u7684\u7ed3\u679c\u4ee4\u4eba\u5174\u594b\uff0c\u56e0\u4e3a\u8bb8\u591a\u7814\u7a76\u4eba\u5458\u6000\u7591MCSP\u662fNP\u5b8c\u5168\u7684\uff0c\u4e0e\u5176\u4ed6\u6240\u6709\u5df2\u77e5\u6700\u574f\u60c5\u51b5\u5230\u5e73\u5747\u60c5\u51b5\u7684\u7ea6\u7b80\u95ee\u9898\u4e0d\u540c\u3002\u5982\u679c\u4ed6\u4eec\u80fd\u591f\u5c06 Hirahara \u7684\u7ed3\u679c\u6269\u5c55\u5230\u6240\u6709\u5e73\u5747\u60c5\u51b5\u7b97\u6cd5\uff0c\u5e76\u8bc1\u660eMCSP\u662fNP\u5b8c\u5168\u7684\uff0c\u90a3\u4e48\u8fd9\u5c06\u8bc1\u660e\u524d\u9762\u8c08\u8bba\u7684 Heuristica \u4e16\u754c\u5c06\u574d\u584c\u3002\u201c\u90a3\u771f\u7684\u4f1a\u662f\u4e00\u4e2a\u9707\u64bc\u4eba\u5fc3\u7684\u7ed3\u679c\uff0c\u201dSanthanam \u8bf4\u3002\u8bc1\u660eMCSP\u662fNP\u5b8c\u5168\u7684\u53ef\u80fd\u662f\u4e00\u4e2a\u8270\u5de8\u7684\u4efb\u52a1\u3002\u6bd5\u7adf\uff0c\u8fd9\u4e2a\u95ee\u9898\u5df2\u7ecf\u516c\u5f00\u4e8650\u591a\u5e74\u3002\u4f46\u662f\u5728\u53bb\u5e74 Hirahara \u53d6\u5f97\u4e86\u7a81\u7834\u4e4b\u540e\uff0c\u7814\u7a76\u4eba\u5458\u73b0\u5728\u79bb\u76ee\u6807\u66f4\u8fd1\u4e86\uff0c\u6bd4\u51e0\u5e74\u524d\u4efb\u4f55\u4eba\u7684\u9884\u671f\u90fd\u8981\u8fd1\u3002<\/span><\/p>\n


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Hirahara \u8bc1\u660e\u4e86\u90e8\u5206MCSP\u95ee\u9898<\/span>\uff08MCSP\u95ee\u9898\u7684\u4e00\u4e2a\u53d8\u4f53\uff09<\/span>\u7684NP\u5b8c\u5168\u6027\uff0c\u8fd9\u4e2a\u95ee\u9898\u5ffd\u7565\u4e86\u6bcf\u4e2a\u771f\u503c\u8868\u4e2d\u7684\u67d0\u4e9b\u9879\u3002\u4ed6\u7684\u8bc1\u660e\u5efa\u7acb\u5728 Ilango \u5f00\u53d1\u7684\u65b9\u6cd5\u4e0a\uff0c\u8be5\u65b9\u6cd5\u8868\u660e\u90e8\u5206MCSP<\/span>\uff08partial MCSP\uff09<\/span>\u95ee\u9898\u7b49\u4ef7\u4e8e\u4e00\u4e2a\u770b\u4f3c\u65e0\u5173\u7684\u95ee\u9898\u3002\u8fd9\u4e2a\u95ee\u9898\u6d89\u53ca\u4e00\u79cd\u540d\u4e3a\u79d8\u5bc6\u5171\u4eab\u7684\u52a0\u5bc6\u6280\u672f\uff0c\u8fd9\u662f\u4e00\u79cd\u5c06\u52a0\u5bc6\u4fe1\u606f\u5206\u914d\u7ed9\u8bb8\u591a\u4eba\u7684\u65b9\u6cd5\uff0c\u53ea\u6709\u5728\u4ed6\u4eec\u4e2d\u7684\u67d0\u4e9b\u4eba\u5408\u4f5c\u65f6\uff0c\u4fe1\u606f\u624d\u80fd\u88ab\u89e3\u7801\u3002<\/span><\/p>\n


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\u5bf9\u4e8e\u4efb\u4f55\u5b9e\u9645\u7684\u5bc6\u7801\u5b66\u5e94\u7528\uff0c\u4f60\u90fd\u5e0c\u671b\u4e8b\u5148\u77e5\u9053\u9700\u8981\u591a\u5c11\u4eba\u8fdb\u884c\u5408\u4f5c\uff0c\u4f46\u662f\u5728\u989d\u5916\u7684\u5bc6\u7801\u5b66\u6280\u5de7\u7684\u5e2e\u52a9\u4e0b\uff0c\u53ef\u4ee5\u6784\u9020\u4e00\u4e2a\u4ee4\u4eba\u6cae\u4e27\u7684\u573a\u666f\uff0c\u5728\u5176\u4e2d\u6211\u4eec\u751a\u81f3\u5f88\u96be\u77e5\u9053\u9700\u8981\u591a\u5c11\u4eba\u5408\u4f5c\u3002Hirahara \u627e\u5230\u4e86\u4e00\u79cd\u65b9\u6cd5\u6765\u8bc1\u660e\u5982\u6b64\u8bbe\u8ba1\u7684\u5bc6\u7801\u95ee\u9898\u662fNP\u5b8c\u5168\u7684\uff0c\u5e76\u4e14\u8868\u660e\u8be5\u8bc1\u660e\u6697\u793a\u4e86\u90e8\u5206MCSP\u7684NP\u5b8c\u5168\u6027\u3002<\/span><\/p>\n


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\u90e8\u5206 MCSP \u7684NP\u5b8c\u5168\u6027\u5f97\u5230\u8bc1\u660e\uff0c\u800c\u8bc1\u660e\u5b8c\u6574\u7684 MCSP \u7684 NP \u5b8c\u5168\u6027\u4ecd\u7136\u9762\u4e34\u969c\u788d\u3002\uff5cSamuel Velasco\/<\/span><\/span>Quanta Magazine<\/span><\/em><\/section>\n


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\u8fd9\u4e2a\u7ed3\u679c\u7ed9\u5143\u590d\u6742\u6027\u7814\u7a76\u4eba\u5458\u5e26\u6765\u7684\u9f13\u52b1\u751a\u81f3\u8d85\u8fc7\u4e86 Hirahara \u65e9\u671f\u7684\u5de5\u4f5c\uff0c\u5176\u4ed6\u7814\u7a76\u4eba\u5458\u4e5f\u6ce8\u610f\u5230\u4e86\u8fd9\u4e00\u70b9\u2014\u2014\u590d\u6742\u6027\u7406\u8bba\u5bb6 Lance Fortnow \u79f0\u5176\u4e3a\u5e74\u5ea6\u6210\u679c\u3002\u8fd9\u662f\u56e0\u4e3a\u5904\u7406\u8fd9\u6837\u7684\u201c\u90e8\u5206\u51fd\u6570\u201d\u7248\u672c\u7684\u8ba1\u7b97\u95ee\u9898\u4e00\u76f4\u662f\u5176\u4ed6NP\u5b8c\u5168\u8bc1\u660e\u7684\u5173\u952e\u4e2d\u95f4\u6b65\u9aa4\u3002\u201c\u8fd9\u662f\u4e00\u9879\u4e86\u4e0d\u8d77\u7684\u5de5\u4f5c\uff0c\u201dWilliams \u8bf4\u3002\u201c\u6bcf\u4e2a\u4eba\u90fd\u8ba4\u4e3a\uff0c\u8fd9\u79cd\u201c\u90e8\u5206\u95ee\u9898\u201d\u4e0e\u5b8c\u6574\u95ee\u9898\u7684\u96be\u5ea6\u5927\u81f4\u76f8\u540c\u3002\u201d<\/span><\/p>\n


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\u8bc1\u660e\u5b8c\u6574\u7684 MCSP \u7684NP\u5b8c\u5168\u95ee\u9898\u4ecd\u7136\u9762\u4e34\u969c\u788d\u3002\u4f46\u8fd9\u4e9b\u969c\u788d\u5e76\u4e0d\u9700\u8981\u6211\u4eec\u627e\u5230\u65b0\u7684\u5de5\u5177\u5305\uff0c\u53ef\u80fd\u901a\u8fc7\u5df2\u77e5\u6280\u672f\u7684\u6b63\u786e\u6574\u5408\u5c31\u80fd\u89e3\u51b3\u8fd9\u4e2a\u969c\u788d\u3002\u8fd9\u4e00\u8bc1\u660e\u5c06\u6700\u7ec8\u89e3\u51b3\u81ea\u590d\u6742\u6027\u7406\u8bba\u5b58\u5728\u4ee5\u6765\u963b\u788d\u5206\u7c7b\u7684\u5c11\u6570\u51e0\u4e2a\u95ee\u9898\u4e4b\u4e00\u3002Levin \u5728\u90ae\u4ef6\u4e2d\u8c26\u865a\u5730\u5199\u9053\uff1a\u201c\u6211\u6ca1\u80fd\u770b\u5230\u5b83\uff0c\u6211\u5b9e\u5728\u662f\u592a\u7b28\u4e86:-)\u3002\u201d<\/span><\/p>\n


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\u7f3a\u5931\u7684\u788e\u7247<\/span><\/strong><\/span><\/h3>\n


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MCSP\u751a\u81f3\u4e0d\u662f\u552f\u4e00\u5f15\u53d1\u91cd\u5927\u7a81\u7834\u7684\u5143\u590d\u6742\u6027\u95ee\u9898\u30022020\u5e74\uff0c\u5eb7\u5948\u5c14\u79d1\u6280\u6821\u533a\u7684\u5bc6\u7801\u5b66\u5bb6 Rafael Pass \u548c\u4ed6\u7684\u7814\u7a76\u751f Yanyi Liu \u53d1\u73b0\u4e86\u4e00\u4e2a\u4e0d\u540c\u7684\u5143\u590d\u6742\u6027\u95ee\u9898\uff0c\u800c\u4e14\u4ed6\u4eec\u8fd8\u5b9a\u4e49\u4e86 Heuristica \u548c Pessiland \u4e4b\u95f4\u8fb9\u754c\u7684\u57fa\u672c\u5bc6\u7801\u5b66\u534f\u8bae\u4e4b\u95f4\u7684\u8054\u7cfb\u3002Pessiland \u662f Impagliazzo \u63d0\u51fa\u7684\u4e94\u4e2a\u4e16\u754c\u4e2d\u6700\u7cdf\u7cd5\u7684\u4e00\u4e2a<\/span>\uff08NP \u5b8c\u5168\u95ee\u9898\u5728\u5e73\u5747\u60c5\u51b5\u4e0b\u96be\u4ee5\u89e3\u51b3\uff0c\u4f46\u5bc6\u7801\u5b66\u4ecd\u7136\u4e0d\u5b89\u5168\uff09<\/span>\u3002\u4ed6\u4eec\u7814\u7a76\u7684\u95ee\u9898\u662f\u6d88\u706d Pessiland \u7684\u4e3b\u529b\u519b\uff0c\u4ed6\u4eec\u6700\u8fd1\u7684\u5de5\u4f5c\u8868\u660e\uff0c\u5b83\u4e5f\u53ef\u4ee5\u6d88\u706d Heuristica\u3002<\/span><\/p>\n


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

Pass \u8bf4\uff1a\u201c\u62fc\u56fe\u6709\u4e0d\u540c\u788e\u7247\u7f3a\u5931\u4e86\uff0c\u4f46\u5bf9\u6211\u6765\u8bf4\uff0c\u8fd9\u4e9b\u9886\u57df\u7684\u8054\u7cfb\u5982\u6b64\u7d27\u5bc6\u5b9e\u5728\u662f\u592a\u795e\u5947\u4e86\uff01\u201dHirahara \u8b66\u544a\u8bf4\uff0c\u5bf9\u4e8e\u90a3\u4e9b\u8bd5\u56fe\u6d88\u706d Impagliazzo \u572830\u5e74\u524d\u6784\u60f3\u7684\u90e8\u5206\u4e16\u754c\u7684\u7814\u7a76\u8005\u4eec\u6765\u8bf4\uff0c\u524d\u65b9\u4ecd\u6709\u6311\u6218\u3002\u201c\u4f46\u6211\u60f3\u8bf4\u7684\u662f\uff0c\u67d0\u5929\u6211\u4eec\u4e00\u5b9a\u80fd\u591f\u6392\u9664\u6389 Heuristica \u548c Pessiland\uff0c\u53ea\u662f\u6211\u4e0d\u77e5\u9053\u8fd9\u4e00\u5929\u4ec0\u4e48\u65f6\u5019\u5230\u6765\u3002\u201d<\/span><\/p>\n


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

\u8bb8\u591a\u7814\u7a76\u4eba\u5458\u9884\u8ba1\uff0c\u6700\u5927\u7684\u56f0\u96be\u5c06\u662f\u5f25\u5408\u4e24\u79cd\u4e0d\u540c\u5e73\u5747\u590d\u6742\u6027\u6a21\u578b\u4e4b\u95f4\u770b\u4f3c\u65e0\u5bb3\u7684\u5dee\u8ddd\u3002\u5bc6\u7801\u5b66\u5bb6\u901a\u5e38\u7814\u7a76\u5728\u4e24\u4e2a\u65b9\u5411\u4e0a\u90fd\u4f1a\u72af\u9519\u8bef\u7684\u5e73\u5747\u60c5\u51b5\u7b97\u6cd5\uff0c\u5076\u5c14\u4f1a\u5c06\u968f\u673a\u5b57\u7b26\u4e32\u9519\u8bef\u5730\u6807\u8bb0\u4e3a\u4f2a\u968f\u673a\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002\u4e0e\u6b64\u540c\u65f6\uff0cHirahara \u4ece\u6700\u574f\u60c5\u51b5\u5230\u5e73\u5747\u60c5\u51b5\u7684\u7ea6\u7b80\u9002\u7528\u4e8e\u53ea\u72af\u7b2c\u4e00\u79cd\u7c7b\u578b\u9519\u8bef\u7684\u5e73\u5747\u60c5\u51b5\u7b97\u6cd5\u3002\u50cf\u8fd9\u6837\u7684\u5fae\u5999\u533a\u522b\u53ef\u80fd\u4f1a\u5728\u590d\u6742\u6027\u7406\u8bba\u4e2d\u4ea7\u751f\u91cd\u5927\u5f71\u54cd\u3002\u4f46\u662f\uff0c\u5c3d\u7ba1\u5b58\u5728\u8fd9\u4e2a\u969c\u788d\u548c\u5176\u4ed6\u8bb8\u591a\u95ee\u9898\uff0cAllender \u4ecd\u4e0d\u7981\u8868\u73b0\u51fa\u8c28\u614e\u7684\u4e50\u89c2\u60c5\u7eea\u3002Allender \u8bf4\uff1a\u201c\u6211\u5c3d\u91cf\u4e0d\u8ba9\u81ea\u5df1\u62a5\u6709\u8fc7\u9ad8\u7684\u671f\u671b\uff0c\u56e0\u4e3a\u4ee5\u5f80\u7684\u8bb0\u5f55\u8868\u660e\uff0c\u5f88\u591a\u8fdb\u5c55\u662f\u65e0\u7528\u7684\u3002\u4f46\u6211\u4eec\u770b\u5230\u4e86\u5f88\u591a\u4ee4\u4eba\u5174\u594b\u7684\u8fdb\u5c55\u2014\u2014\u514b\u670d\u770b\u4f3c\u969c\u788d\u7684\u65b9\u6cd5\u3002\u201d<\/span><\/p>\n


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

\u5982\u679c\u8981\u95ee\u7814\u7a76\u8005\u4eec\u5728\u4e0e\u201cP\u4e0eNP\u201d\u95ee\u9898<\/span>\uff08the P versus NP question\uff09<\/span>\u7684\u6597\u4e89\u4e2d\u5b66\u5230\u4e86\u4ec0\u4e48\uff1f\u6216\u8005\u8bf4\u4ece\u4e2d\u7406\u89e3\u4e86\u4ec0\u4e48\uff0c\u90a3\u4e00\u5b9a\u662f\u590d\u6742\u6027\u7406\u8bba\u672c\u8eab\u662f\u590d\u6742\u7684\u3002\u4f46\u4e5f\u6b63\u662f\u8fd9\u4e2a\u6311\u6218\u8ba9\u63a2\u7d22\u53d8\u5f97\u5982\u6b64\u6709\u610f\u4e49\u3002Carmosino \u8bf4\uff1a\u201c\u8fd9\u4e2a\u95ee\u9898\u771f\u7684\u5f88\u96be\uff0c\u8fd9\u4e00\u70b9\u5b9e\u5728\u662f\u592a\u68d2\u4e86\uff0c\u6211\u5c06\u6c38\u4e0d\u538c\u5026\uff01\u201d<\/span><\/p>\n


<\/p>\n


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

AI By Complexity\u8bfb\u4e66\u4f1a\u62db\u52df\u4e2d<\/strong>
<\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


<\/section>\n

\u5927\u6a21\u578b\u3001\u591a\u6a21\u6001\u3001\u591a\u667a\u80fd\u4f53\u5c42\u51fa\u4e0d\u7a77\uff0c\u5404\u79cd\u5404\u6837\u7684\u795e\u7ecf\u7f51\u7edc\u53d8\u4f53\u5728AI\u5927\u821e\u53f0\u5404\u663e\u8eab\u624b\u3002\u590d\u6742\u7cfb\u7edf\u9886\u57df\u5bf9\u4e8e\u6d8c\u73b0\u3001\u5c42\u7ea7\u3001\u9c81\u68d2\u6027\u3001\u975e\u7ebf\u6027\u3001\u6f14\u5316\u7b49\u95ee\u9898\u7684\u63a2\u7d22\u4e5f\u5728\u6301\u7eed\u63a8\u8fdb\u3002\u800c\u4f18\u79c0\u7684AI\u7cfb\u7edf\u3001\u521b\u65b0\u6027\u7684\u795e\u7ecf\u7f51\u7edc\uff0c\u5f80\u5f80\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u5177\u5907\u4f18\u79c0\u590d\u6742\u7cfb\u7edf\u7684\u7279\u5f81\u3002\u56e0\u6b64\uff0c\u53d1\u5c55\u4e2d\u7684\u590d\u6742\u7cfb\u7edf\u7406\u8bba\u65b9\u6cd5\u5982\u4f55\u6307\u5bfc\u672a\u6765AI\u7684\u8bbe\u8ba1\uff0c\u6b63\u5728\u6210\u4e3a\u5907\u53d7\u5173\u6ce8\u7684\u95ee\u9898\u3002<\/span><\/p>\n


<\/p>\n

\u96c6\u667a\u4ff1\u4e50\u90e8\u8054\u5408\u52a0\u5229\u798f\u5c3c\u4e9a\u5927\u5b66\u5723\u8fed\u6208\u5206\u6821\u52a9\u7406\u6559\u6388\u5c24\u4ea6\u5e84\u3001\u5317\u4eac\u5e08\u8303\u5927\u5b66\u526f\u6559\u6388\u5218\u5b87\u3001\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7cfb\u7edf\u79d1\u5b66\u5b66\u9662\u5728\u8bfb\u535a\u58eb\u5f20\u7ae0\u3001\u725f\u7267\u4e91\u548c\u5728\u8bfb\u7855\u58eb\u6768\u660e\u54f2\u3001\u6e05\u534e\u5927\u5b66\u5728\u8bfb\u535a\u58eb\u7530\u6d0b\u5171\u540c\u53d1\u8d77\u300cAI By Complexity\u300d\u8bfb\u4e66\u4f1a<\/a>\uff0c\u63a2\u7a76\u5982\u4f55\u5ea6\u91cf\u590d\u6742\u7cfb\u7edf\u7684\u201c\u597d\u574f\u201d\uff1f\u5982\u4f55\u7406\u89e3\u590d\u6742\u7cfb\u7edf\u7684\u673a\u5236\uff1f\u8fd9\u4e9b\u7406\u89e3\u662f\u5426\u53ef\u4ee5\u542f\u53d1\u6211\u4eec\u8bbe\u8ba1\u66f4\u597d\u7684AI\u6a21\u578b\uff1f\u5728\u672c\u8d28\u4e0a\u5e2e\u52a9\u6211\u4eec\u8bbe\u8ba1\u66f4\u597d\u7684AI\u7cfb\u7edf\u3002\u8bfb\u4e66\u4f1a\u4e8e6\u670810\u65e5\u5f00\u59cb\uff0c\u6bcf\u5468\u4e00\u665a\u4e0a20:00-22:00\u4e3e\u529e\u3002\u6b22\u8fce\u4ece\u4e8b\u76f8\u5173\u9886\u57df\u7814\u7a76\u3001\u5bf9AI+Complexity\u611f\u5174\u8da3\u7684\u670b\u53cb\u4eec\u62a5\u540d\u8bfb\u4e66\u4f1a\u4ea4\u6d41\uff01<\/span><\/p>\n


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

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


<\/section>\n

<\/section>\n
\u8be6\u60c5\u8bf7\u89c1\uff1a<\/span><\/section>\n
AI by Complexity \u8bfb\u4e66\u4f1a\u542f\u52a8\uff1a\u590d\u6742\u6027\u600e\u6837\u91cf\u5316\u548c\u9a71\u52a8\u4e0b\u4e00\u4ee3AI\u7cfb\u7edf<\/span><\/a><\/section>\n


<\/p>\n


<\/p>\n

\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/strong><\/section>\n
1. <\/strong>P\uff0cNP\uff0cPSPACE\u90fd\u662f\u4ec0\u4e48\u9b3c\uff1f\u4e00\u6587\u8bb2\u6e05\u8ba1\u7b97\u590d\u6742\u6027\u5206\u7c7b<\/a><\/strong><\/span><\/section>\n
2. <\/strong>\u56fe\u7075\u548c\u51af\u00b7\u8bfa\u4f9d\u66fc\u7684\u9057\u4ea7\uff1a\u751f\u547d\u8ba1\u7b97\u673a\u7684\u67b6\u6784<\/a><\/strong><\/span><\/section>\n
3.<\/strong> \u56fe\u7075\u5b8c\u5907\u4e0e\u76ee\u6807\u5b8c\u5907\uff1a\u4ece\u901a\u7528\u8ba1\u7b97\u673a\u5230\u901a\u7528\u4eba\u5de5\u667a\u80fd\u7684\u9884\u8a00<\/a><\/strong><\/span><\/section>\n
<\/strong><\/strong><\/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><\/strong>5.<\/strong> \u9f99\u5e74\u5927\u8fd0\u8d77\uff0c\u5b66\u4e60\u6b63\u5f53\u65f6\uff01\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><\/section>\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

<\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u5bfc\u8bed \u8bc1\u660e\u4e00\u4e2a\u95ee\u9898\u96be\u4ee5\u89e3\u51b3\u8fd9\u4ef6\u4e8b\u7a76\u7adf\u6709\u591a\u96be\uff1f\u8fd9\u662f\u5143\u590d\u6742\u6027\u7406\u8bba\u5b66\u5bb6\u4e00\u76f4\u8ffd\u95ee\u7684\u95ee\u9898\u3002\u7ecf\u8fc7\u6570\u5341\u5e74\uff0c\u63a2\u7d22\u7684\u8def\u5f84\u4eceP\u4e0eNP\u95ee\u9898\u8f6c\u53d8\u5230\u5143\u590d\u6742\u6027\u95ee\u9898\uff0c\u4ed6\u4eec\u8bd5\u56fe\u901a\u8fc7\u590d\u6742\u6027\u7406\u8bba\u7684\u89c6\u89d2\u89c2\u5bdf\u590d\u6742\u6027\u7406\u8bba\u672c\u8eab\u3002 \u7814\u7a76\u9886\u57df\uff1a\u8ba1\u7b97\u590d\u6742\u6027\uff0c\u7406\u8bba\u8ba1\u7b97\u673a\u79d1\u5b66\uff0cP\u4e0eNP\u95ee\u9898\uff0c\u4fe1\u606f\u8bba\uff0c\u5143\u590d\u6742\u6027\uff0c\u81ea\u6307 \u00c1ngel Go\u00f1i-Moreno&n…<\/p>\n","protected":false},"author":0,"featured_media":50844,"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\/50869"}],"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"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=50869"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/50869\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/50844"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=50869"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=50869"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=50869"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=50869"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}