{"id":51026,"date":"2024-06-25T15:48:55","date_gmt":"2024-06-25T07:48:55","guid":{"rendered":"https:\/\/swarma.org\/?p=51026"},"modified":"2024-06-25T15:48:55","modified_gmt":"2024-06-25T07:48:55","slug":"p-np%e9%97%ae%e9%a2%9850%e5%b9%b4%ef%bc%9a%e5%9f%ba%e7%a1%80%e7%90%86%e8%ae%ba%e4%b8%be%e6%ad%a5%e7%bb%b4%e8%89%b0%ef%bc%8c%e4%bd%86ai%e6%ad%a3%e5%9c%a8%e4%b8%8d%e5%8f%af%e8%83%bd%e4%b8%ad%e5%af%bb","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=51026","title":{"rendered":"P\/NP\u95ee\u989850\u5e74\uff1a\u57fa\u7840\u7406\u8bba\u4e3e\u6b65\u7ef4\u8270\uff0c\u4f46AI\u6b63\u5728\u4e0d\u53ef\u80fd\u4e2d\u5bfb\u627e\u53ef\u80fd"},"content":{"rendered":"
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\u662f\u5426\u5b58\u5728300\u4e2aFacebook\u7528\u6237\u5f7c\u6b64\u4e4b\u95f4\u90fd\u662f\u597d\u53cb\u7684\u5173\u7cfb\uff1f\u4f60\u5c06\u5982\u4f55\u4e3a\u8fd9\u4e2a\u95ee\u9898\u63d0\u4f9b\u4e00\u4e2a\u89e3\u7b54\uff1f\u5047\u8bbe\u4f60\u5728Facebook\u516c\u53f8\u5de5\u4f5c\uff0c\u53ef\u4ee5\u8bbf\u95ee\u516c\u53f8\u6240\u6709\u6570\u636e\uff0c\u4e86\u89e3\u54ea\u4e9b\u7528\u6237\u662f\u597d\u53cb\u5173\u7cfb\u3002\u4f60\u73b0\u5728\u9700\u8981\u8bbe\u8ba1\u4e00\u4e2a\u7b97\u6cd5\u6765\u5bfb\u627e\u5f7c\u6b64\u90fd\u662f\u597d\u53cb\u5e76\u4e14\u4eba\u6570\u8db3\u591f\u591a\u7684\u670b\u53cb\u7fa4\u4f53<\/span>\uff08Clique\uff09<\/span>\u3002\u4f60\u53ef\u4ee5\u5148\u5c1d\u8bd5\u641c\u7d22\u6240\u6709\u6ee1\u8db3\u6761\u4ef6\u7684300\u4eba\u670b\u53cb\u7fa4\u4f53\uff0c\u4f46\u7531\u4e8e\u5b9e\u9645\u4eba\u6570\u8fc7\u591a\uff0c\u65e0\u6cd5\u5168\u90e8\u641c\u7d22\u3002\u4f60\u4e5f\u53ef\u4ee5\u9009\u62e9\u4e00\u4e9b\u66f4\u660e\u667a\u7684\u65b9\u6cd5\uff0c\u6bd4\u5982\u5148\u5c1d\u8bd5\u641c\u7d22\u4e00\u4e9b\u5c0f\u578b\u670b\u53cb\u7fa4\u4f53\uff0c\u4e4b\u540e\u518d\u5c0f\u7684\u7fa4\u4f53\u5408\u5e76\u4e3a\u66f4\u5927\u7684\u7fa4\u4f53\uff0c\u4f46\u4f60\u4f1a\u53d1\u73b0\u4f60\u6240\u505a\u7684\u4f3c\u4e4e\u90fd\u4e0d\u8d77\u4f5c\u7528\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6ca1\u6709\u4eba\u77e5\u9053\u6bd4\u904d\u5386\u6240\u6709\u670b\u53cb\u7fa4\u4f53\u660e\u663e\u66f4\u5feb\u7684\u641c\u7d22\u65b9\u6cd5\uff0c\u540c\u65f6\u6211\u4eec\u4e5f\u4e0d\u77e5\u9053\u66f4\u5feb\u7684\u65b9\u6cd5\u662f\u5426\u4e0d\u5b58\u5728<\/strong>\u3002<\/span><\/span><\/section>\n

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\u8fd9\u57fa\u672c\u4e0a\u5c31\u662fP\/NP\u95ee\u9898\u3002NP\u4ee3\u8868\u6211\u4eec\u53ef\u4ee5\u9ad8\u6548\u68c0\u9a8c\u5176\u89e3\u7b54\u7684\u95ee\u9898<\/strong>\u3002\u5982\u679c\u6211\u544a\u77e5\u4f60\u6709300\u4eba\u53ef\u80fd\u5f62\u6210\u4e86\u4e00\u4e2a\u6ee1\u8db3\u6761\u4ef6\u7684\u56e2\u4f53\uff0c\u4f60\u53ef\u4ee5\u76f8\u5bf9\u8f83\u5feb\u5730\u68c0\u9a8c\u4ed6\u4eec\u5f7c\u6b64\u4e4b\u95f4\u5f62\u6210\u768444850\u5bf9\u7528\u6237\u662f\u5426\u90fd\u662f\u597d\u53cb\u5173\u7cfb\u3002\u4e0a\u6587\u7684\u5206\u56e2\u95ee\u9898<\/span>\uff08Clique problem\uff09<\/span>\u4fbf\u662f\u4e00\u4e2aNP\u95ee\u9898\u3002\u800cP\u5219\u8868\u793a\u6211\u4eec\u53ef\u4ee5\u9ad8\u6548\u5730\u627e\u5230\u89e3\u7684\u95ee\u9898\u3002\u5bf9\u4e8e\u5206\u56e2\u95ee\u9898\uff0c\u6211\u4eec\u4e0d\u77e5\u9053\u5b83\u662f\u5426\u5728P\u95ee\u9898\u8fd9\u4e2a\u96c6\u5408\u4e2d\u3002\u6216\u8bb8\u4f1a\u4ee4\u4f60\u60ca\u8bb6\u7684\u662f\uff0c\u5206\u56e2\u95ee\u9898\u6709\u4e00\u4e2a\u88ab\u79f0\u4e3aNP\u5b8c\u5907<\/span>\uff08NP-complete\uff09<\/span>\u7684\u6027\u8d28\u2014\u2014\u5373\u5f53\u4e14\u4ec5\u5f53P=NP\u65f6\uff0c\u6211\u4eec\u624d\u53ef\u4ee5\u9ad8\u6548\u5730\u89e3\u51b3\u5206\u56e2\u95ee\u9898\u3002\u8bb8\u591a\u5176\u4ed6\u95ee\u9898\u4e5f\u6709\u8fd9\u4e00\u6027\u8d28\uff0c\u6bd4\u5982\u4e09\u7740\u8272\u95ee\u9898<\/span>\uff08\u4e00\u526f\u5730\u56fe\u80fd\u5426\u53ef\u4ee5\u4ec5\u88ab\u4e09\u79cd\u989c\u8272\u7740\u8272\u4f7f\u5f97\u4efb\u610f\u76f8\u90bb\u7684\u4e24\u4e2a\u56fd\u5bb6\u62e5\u6709\u4e0d\u540c\u7684\u989c\u8272\uff1f\uff09<\/span>\uff0c\u65c5\u884c\u5546\u95ee\u9898<\/span>\uff08\u5728\u4f17\u591a\u7684\u57ce\u5e02\u4e2d\u627e\u5230\u4e00\u4e2a\u6700\u77ed\u8def\u7ebf\uff0c\u4f7f\u5f97\u5546\u4eba\u8bbf\u95ee\u6bcf\u5ea7\u57ce\u5e02\u4e00\u6b21\u5e76\u56de\u5230\u521d\u59cb\u7684\u4f4d\u7f6e\uff09<\/span>\uff0c\u4ee5\u53ca\u5176\u4ed6\u6210\u5343\u4e0a\u4e07\u7684\u95ee\u9898\u3002<\/span><\/span><\/section>\n

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\u4e25\u683c\u5730\u6765\u8bf4\uff0cP\u8868\u793a\u201c\u591a\u9879\u5f0f\u65f6\u95f4\u201d<\/strong><\/span>\uff08polynomial time\uff09<\/span>\uff0c\u5bf9\u5e94\u4e00\u7c7b\u6c42\u89e3\u65f6\u95f4\u662f\u4ee5\u8f93\u5165\u957f\u5ea6\u4e3a\u81ea\u53d8\u91cf\u7684\u56fa\u5b9a\u591a\u9879\u5f0f\u7684\u95ee\u9898\u3002\u800cNP\u8868\u793a\u201c\u975e\u786e\u5b9a\u6027\u591a\u9879\u5f0f\u65f6\u95f4\u201d<\/strong><\/span>\uff08nondeterministic polynomial time\uff09<\/span>\uff0c\u5bf9\u5e94\u4e00\u7c7b\u975e\u786e\u5b9a\u6027\u56fe\u7075\u673a\u53ef\u4ee5\u4e0d\u53ef\u601d\u8bae\u5730\u9009\u62e9\u51fa\u6700\u4f73\u7b54\u6848\u7684\u95ee\u9898\u3002\u5728\u672c\u6587\u4e2d\uff0c\u8bfb\u8005\u53ef\u4ee5\u628aP\u548cNP\u7b80\u5355\u5730\u770b\u4f5c\u53ef\u9ad8\u6548\u6c42\u89e3\u7684\u95ee\u9898\u4ee5\u53ca\u53ef\u9ad8\u6548\u9a8c\u8bc1\u7684\u95ee\u9898\u3002<\/span><\/span><\/section>\n

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\u5982\u679c\u8bfb\u8005\u5e0c\u671b\u5bf9\u4e8eP\/NP\u95ee\u9898\u7684\u91cd\u8981\u6027\u6709\u66f4\u6df1\u5165\u7684\u975e\u4e13\u4e1a\u8ba8\u8bba\uff0c\u53ef\u4ee5\u9605\u8bfb\u62112009\u5e74\u7684\u7efc\u8ff0<\/span>\u6587\u7ae0[13]\u6216\u8005<\/span>\u6211\u57282013\u5e74\u57fa\u4e8e\u8fd9\u7bc7\u7efc\u8ff0\u6587\u7ae0\u5199\u4f5c\u7684\u79d1<\/span>\u666e\u4e66\u7c4d[14]\u3002<\/span>\u5bf9\u4e8e\u66f4\u4e13\u4e1a\u7684\u4ecb\u7ecd\uff0c\u7531\u8fc8\u514b\u5c14\u00b7\u52a0\u91cc<\/span>\uff08Michael Garey\uff09<\/span>\u548c\u5927\u536b\u00b7\u7ea6\u7ff0\u900a<\/span>\uff08David Johnson\uff09<\/span><\/span>[16]<\/span>\u57281979\u5e74\u521b\u4f5c\u7684\u4e13\u8457\u5bf9\u4e8e\u9700\u8981\u7406\u89e3\u54ea\u4e9b\u95ee\u9898\u662fNP\u5b8c\u5907\u95ee\u9898\u7684\u8bfb\u8005\u975e\u5e38\u5408\u9002\u3002\u8fd9\u672c\u4e13\u8457\u81f3\u4eca\u4ecd\u7136\u662f\u8fd9\u65b9\u9762\u7684\u5b9d\u8d35\u53c2\u8003\u8d44\u6599\u3002<\/span><\/section>\n

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\u4e3a\u4ec0\u4e48\u6211\u4eec\u73b0\u5728\u8c08\u8bbaP\/NP\u95ee\u9898\uff1f<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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1971\u5e74\u4e00\u4e2a\u5468\u4e8c\u7684\u4e0b\u5348\uff0c\u5728\u7f8e\u56fd\u4fc4\u4ea5\u4fc4\u5dde\u8c22\u514b\u6d77\u8328\u5e02\u7684\u65af\u6258\u5f17\u8428\u9ed8\u585e\u7279\u9152\u5e97\uff0c\u53f2\u8482\u82ac\u00b7\u5e93\u514b<\/span>\uff08Stephen Cook\uff09<\/span>\u5728ACM\u8ba1\u7b97\u7406\u8bba\u4e13\u9898\u7814\u8ba8\u4f1a\u4e0a\u5411\u4e0e\u4f1a\u8005\u5c55\u793a\u4e86\u4ed6\u7684\u8bba\u6587\uff0c\u4ed6\u8bc1\u660e\u4e86\u5e03\u5c14\u8868\u8fbe\u5f0f\u53ef\u6ee1\u8db3\u6027\u95ee\u9898<\/span>\uff08Boolean Satisfiability Problem\uff09<\/span>\u662fNP\u5b8c\u5907\u7684\uff0c\u5e76\u4e14\u8bc1\u660e\u4e86\u91cd\u8a00\u5f0f\u95ee\u9898<\/span>\uff08Tautology\uff09<\/span>\u662fNP\u56f0\u96be<\/span>\uff08NP-hard\uff09<\/span>\u7684<\/span><\/span>[10]\u3002<\/span>\u8fd9\u4e9b\u5b9a\u7406\u4e5f\u8868\u660e\uff0c\u91cd\u8a00\u5f0f\u95ee\u9898\u662f\u4e00\u4e2a\u4e0d\u5728P\u96c6\u5408\u4e2d\u4e0d\u9519\u7684\u5019\u9009\uff0c\u5e76\u4e14\u6211\u8ba4\u4e3a\u82b1\u8d39\u76f8\u5f53\u5927\u7684\u7cbe\u529b\u6765\u5c1d\u8bd5\u8bc1\u660e\u8fd9\u4e2a\u731c\u60f3\u662f\u503c\u5f97\u7684\u3002\u8fd9\u6837\u7684\u8bc1\u660e\u5c06\u4f1a\u662f\u590d\u6742\u6027\u7406\u8bba\u7684\u91cd\u5927\u7a81\u7834\u3002<\/span><\/section>\n

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\u4e0e\u4e00\u4e2a\u6570\u5b66\u6982\u5ff5\u201c\u7ea6\u4f1a\u201d\u51e0\u4e4e\u603b\u662f\u4e00\u4e2a\u6311\u6218\uff0c\u5386\u53f2\u4e0a\u4e5f\u8bb8\u8fd8\u6709\u5f88\u591aP\/NP\u95ee\u9898\u53ef\u80fd\u7684\u8bde\u751f\u65f6\u95f4\u3002\u7b97\u6cd5\u548c\u8bc1\u660e\u7684\u57fa\u672c\u6982\u5ff5\u53ef\u4ee5\u88ab\u8ffd\u6eaf\u5230\u53e4\u5e0c\u814a\u65f6\u671f\uff0c\u4f46\u636e\u6211\u4eec\u6240\u77e5\uff0cP\/NP\u8fd9\u6837\u4e00\u822c\u6027\u7684\u95ee\u9898\u4ed6\u4eec\u4ece\u672a\u8003\u8651\u8fc7\u3002\u9ad8\u6548\u8ba1\u7b97\u4e0e\u975e\u786e\u5b9a\u6027\u7684\u7406\u8bba\u57fa\u7840\u662f\u572820\u4e16\u7eaa60\u5e74\u4ee3\u53d1\u5c55\u8d77\u6765\u7684\uff0c\u800cP\/NP\u95ee\u9898\u5728\u6b64\u4e4b\u524d\u5c31\u5f62\u6210\u4e86\uff0c\u53ea\u662f\u6211\u4eec\u4e0d\u77e5\u9053\u5177\u4f53\u65f6\u95f4\u800c\u5df2\u3002<\/span><\/section>\n

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\u57281956\u5e74\u5e93\u5c14\u7279\u00b7\u54e5\u5fb7\u5c14<\/span>\uff08Kurt G\u00f6del\uff09<\/span>\u5199\u7ed9\u7ea6\u7ff0\u00b7\u51af\u00b7\u8bfa\u4f0a\u66fc<\/span>\uff08John von Neumann\uff09<\/span>\u7684\u4e00\u5c01\u4fe1\u4e2d\uff0c\u54e5\u5fb7\u5c14\u672c\u8d28\u6027\u5730\u63cf\u8ff0\u4e86P\/NP\u95ee\u9898\u3002\u76ee\u524d\u6211\u4eec\u5c1a\u4e0d\u6e05\u695a\uff0c\u5f53\u65f6\u8eab\u53d7\u764c\u75c7\u4fb5\u88ad\u7684\u51af\u00b7\u8bfa\u4f0a\u66fc\u662f\u5426\u9605\u8bfb\u4e86\u8fd9\u5c01\u4fe1\u3002\u76f4\u52301988\u5e74\uff0c\u8fd9\u5c01\u4fe1\u624d\u88ab\u4eba\u4eec\u53d1\u73b0\uff0c\u5e76\u5e7f\u4e3a\u4f20\u64ad\u3002\u800cP\/NP\u95ee\u9898\u662f\u76f4\u5230\u7406\u67e5\u5fb7\u00b7\u5361\u5c14\u666e<\/span>\uff08Richard Karp\uff09<\/span>1972\u5e74\u53d1\u8868\u8bba<\/span><\/span>\u6587[23]\u6307<\/span>\u51fa\u5927\u91cf\u8457\u540d\u7ec4\u5408\u95ee\u9898<\/span>\uff08\u5305\u62ec\u5206\u56e2\u95ee\u9898\u3001\u4e09\u7740\u8272\u95ee\u9898\u3001\u4ee5\u53ca\u65c5\u884c\u5546\u95ee\u9898\uff09<\/span>\u662fNP\u5b8c\u5907\u7684\u4e4b\u540e\u624d\u771f\u6b63\u6210\u4e3a\u4e00\u79cd\u73b0\u8c61\u30021973\u5e74\uff0c\u5f53\u65f6\u5728\u82cf\u8054\u7684\u5217\u6602\u5c3c\u5fb7\u00b7\u83b1\u6587<\/span>\uff08Leonid Levin\uff09<\/span>\u5728\u51761971\u5e74\u72ec\u7acb\u7814\u7a76\u7684\u57fa\u7840\u4e0a\u53d1\u8868\u4e86\u4e00\u7bc7\u8bba\u6587\uff0c\u5176\u4e2d\u5b9a\u4e49\u4e86P\/NP\u95ee<\/span><\/span>\u9898[27]\u3002\u800c\u5f53<\/span>\u83b1\u6587\u7684\u8bba\u6587\u4f20\u5230\u897f\u65b9\u7684\u65f6\u5019\uff0cP\/NP\u95ee\u9898\u5df2\u7ecf\u6210\u4e3a\u8ba1\u7b97\u9886\u57df\u6700\u91cd\u8981\u7684\u95ee\u9898\u4e86\u3002<\/span><\/span><\/section>\n

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\u4e50\u89c2\u4e4b\u5730\uff08Optiland\uff09<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u57281995\u5e74\u7684\u4e00\u7bc7\u7ecf\u5178\u8bba<\/span>\u6587\u4e2d[20]\uff0c\u62c9<\/span>\u585e\u5c14\u00b7\u56e0\u5e15\u5229\u4e9a\u4f50<\/span>\uff08Russell Impagliazzo\uff09<\/span>\u63cf\u8ff0\u4e86\u5bf9\u4e8eP\/NP\u95ee\u9898\u62e5\u6709\u4e0d\u540c\u7a0b\u5ea6\u53ef\u80fd\u6027\u7684\u4e94\u4e2a\u4e16\u754c\uff1a<\/span><\/span><\/p>\n

1. \u7b97\u6cd5\u4e16\u754c<\/span>\uff08Algorithmica\uff09<\/span>\uff1aP=NP\u6216\u8005\u67d0\u79cd\u7406\u8bba\u4e0a\u7684\u7b49\u4ef7\uff0c\u6bd4\u5982NP\u95ee\u9898\u7684\u5feb\u901f\u968f\u673a\u7b97\u6cd5\u3002<\/span><\/span><\/p>\n

2. \u542f\u53d1\u4e16\u754c<\/span>\uff08Heuristica\uff09<\/span>: \u5728\u6700\u574f\u7684\u60c5\u51b5\u4e0bNP\u95ee\u9898\u5f88\u96be\u6c42\u89e3\uff0c\u4f46\u662f\u901a\u5e38\u60c5\u51b5\u4e0b\u6c42\u89e3\u662f\u5bb9\u6613\u7684\u3002<\/span><\/span><\/p>\n

3. \u60b2\u89c2\u4e16\u754c<\/span>\uff08Pessiland\uff1b\u8bd1\u8005\u6ce8\uff1a\u5f15\u7533\u81ea\u62c9\u4e01\u8bed\u60b2\u89c2\u4e3b\u4e49pessimus\uff09<\/span>\uff1a\u6211\u4eec\u53ef\u4ee5\u8f7b\u6613\u5730\u6784\u5efa\u96be\u4ee5\u6c42\u89e3\u7684NP\u95ee\u9898\uff0c\u4f46\u662f\u5f88\u96be\u6784\u5efa\u6211\u4eec\u77e5\u9053\u89e3\u7b54\u7684NP\u95ee\u9898\u3002\u8fd9\u662f\u6240\u6709\u53ef\u80fd\u6027\u4e2d\u6700\u574f\u7684\uff0c\u56e0\u4e3a\u5728\u8fd9\u4e2a\u4e16\u754c\u4e2d\uff0c\u6211\u4eec\u65e2\u4e0d\u80fd\u5728\u901a\u5e38\u60c5\u51b5\u4e0b\u89e3\u51b3\u56f0\u96be\u7684\u95ee\u9898\uff0c\u4e5f\u4e0d\u80fd\u7531\u8fd9\u4e9b\u95ee\u9898\u7684\u96be\u5ea6\u83b7\u5f97\u4efb\u4f55\u660e\u663e\u7684\u52a0\u5bc6\u4f18\u52bf\u3002<\/span><\/span><\/p>\n

4. \u5355\u5411\u52a0\u5bc6\u4e16\u754c<\/span>\uff08Minicrypt\uff09<\/span>\uff1a\u5355\u5411\u52a0\u5bc6\u51fd\u6570\u5b58\u5728\uff0c\u4f46\u662f\u6211\u4eec\u6ca1\u6709\u516c\u5f00\u5bc6\u94a5\u52a0\u5bc6\u7b97\u6cd5\u3002<\/span><\/span><\/p>\n

5. \u52a0\u5bc6\u72c2\u6b22\u4e16\u754c<\/span>\uff08Cryptomania\uff09<\/span>: \u516c\u5f00\u5bc6\u94a5\u52a0\u5bc6\u662f\u53ef\u80fd\u7684\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u53cc\u65b9\u53ef\u4ee5\u901a\u8fc7\u516c\u5f00\u7684\u4fe1\u9053\u4ea4\u6362\u52a0\u5bc6\u4fe1\u606f\u3002<\/span><\/span><\/section>\n

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\u8fd9\u4e9b\u5bf9\u5e94\u4e0d\u540c\u60c5\u51b5\u7684\u4e0d\u540c\u4e16\u754c\u7279\u610f\u6ca1\u6709\u88ab\u6b63\u5f0f\u5b9a\u4e49\u3002\u6839\u636e\u6211\u4eec\u5bf9\u4e8eP\/NP\u95ee\u9898\u7684\u4e86\u89e3\uff0c\u5b83\u4eec\u8868\u660e\u4e86\u672a\u77e5\u7684\u5404\u79cd\u53ef\u80fd\u6027\u3002\u4eba\u4eec\u901a\u5e38\u8ba4\u4e3a<\/span>\uff08\u4e0d\u662f\u5168\u4f53\u7edf\u4e00\u5730\uff09<\/span>\uff0c\u6211\u4eec\u751f\u6d3b\u5728\u53ef\u4ee5\u201c\u52a0\u5bc6\u72c2\u6b22\u201d\u7684\u4e16\u754c\u91cc\u3002<\/span><\/span><\/section>\n

<\/section>\n
\u56e0\u5e15\u5229\u4e9a\u4f50\u4eceP\/NP\u7684\u7406\u8bba\u4e2d\u603b\u7ed3\u51fa\uff1a\u201c\u9c7c\u4e0e\u718a\u638c\u4e0d\u53ef\u517c\u5f97<\/span>\uff08You can’t have it all\uff09<\/span>\u201d\u3002\u6211\u4eec\u53ef\u4ee5\u6c42\u89e3\u56f0\u96be\u7684NP\u95ee\u9898\uff0c\u6216\u8005\u53ef\u4ee5\u62e5\u6709\u5bc6\u7801\u5b66\uff0c\u4e24\u8005\u5fc5\u6709\u5176\u4e00\uff0c\u4f46\u4e0d\u4f1a\u5171\u5b58\u3002\u4e0d\u8fc7\uff0c\u6216\u8bb8\u6211\u4eec\u6b63\u5728\u524d\u5f80\u4e00\u4e2a\u73b0\u5b9e\u4e2d\u7684\u201c\u4e50\u89c2\u4e4b\u5730\u201d<\/span>\uff08Optiland\uff1b\u8bd1\u8005\u6ce8\uff1a\u4e0epessiland\u5bf9\u5e94\uff0c\u5f15\u7533\u81eaOptimum\uff09<\/span>\u3002\u673a\u5668\u5b66\u4e60\u548c\u8f6f\u4ef6\u4e0e\u786c\u4ef6\u4f18\u5316\u7684\u8fdb\u5c55\uff0c\u4f7f\u6211\u4eec\u80fd\u591f\u5bf9\u4e8e\u6b64\u524d\u957f\u671f\u88ab\u8ba4\u4e3a\u662f\u56f0\u96be\u6216\u4e0d\u53ef\u80fd\u7684\u95ee\u9898\u53d6\u5f97\u8fdb\u5c55\uff0c\u6bd4\u5982\u8bed\u97f3\u8bc6\u522b\u4e0e\u86cb\u767d\u8d28\u6298\u53e0\u7b49\u95ee\u9898\uff0c\u5e76\u4e14\u5728\u5927\u591a\u6570\u60c5\u51b5\u4e0b\u6211\u4eec\u7684\u52a0\u5bc6\u534f\u8bae\u4ecd\u7136\u662f\u5b89\u5168\u7684\u3002<\/span><\/span><\/section>\n

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\u5728\u62112009\u5e74\u7684\u7efc\u8ff0<\/span>\u6587\u7ae0[13] \u201c\u5982\u679c<\/span>P=NP\u4f1a\u600e\u4e48\u6837\uff1f\u201d\u7ae0\u8282\u91cc\uff0c\u6211\u5f53\u65f6\u5199\u9053\uff0c\u201c\u901a\u8fc7\u4f7f\u7528\u5965\u5361\u59c6\u5243\u5200\u539f\u5219<\/span>\uff08Occam\u2019s razor\uff09<\/span>\uff0c\u5b66\u4e60\u53d8\u5f97\u5bb9\u6613\u4e86\u2014\u2014\u6211\u4eec\u53ea\u9700\u5bfb\u627e\u4e0e\u6570\u636e\u4e00\u81f4\u7684\u6700\u7b80\u5355\u7684\u65b9\u6cd5\u201d\u3002\u8fd1\u4e4e\u5b8c\u7f8e\u7684\u89c6\u89c9\u8bc6\u522b\u3001\u8bed\u8a00\u7406\u89e3\u3001\u7ffb\u8bd1\uff0c\u4ee5\u53ca\u6240\u6709\u5176\u4ed6\u7684\u5b66\u4e60\u4efb\u52a1\u90fd\u53d8\u5f97\u5bb9\u6613\u89e3\u51b3\u3002\u6211\u4eec\u4e5f\u5c06\u66f4\u597d\u5730\u9884\u6d4b\u5929\u6c14\u3001\u5730\u9707\u4ee5\u53ca\u5176\u4ed6\u81ea\u7136\u73b0\u8c61\u3002<\/span><\/span><\/section>\n

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\u5982\u4eca\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u9762\u90e8\u626b\u63cf\u6765\u89e3\u9501\u667a\u80fd\u624b\u673a\uff0c\u901a\u8fc7\u8be2\u95ee\u624b\u673a\u95ee\u9898\u5f97\u5230\u901a\u5e38\u8f83\u4e3a\u7406\u60f3\u7684\u56de\u590d\uff0c\u4e5f\u53ef\u4ee5\u5c06\u6211\u4eec\u7684\u95ee\u9898\u7ffb\u8bd1\u4e3a\u53e6\u4e00\u79cd\u8bed\u8a00\u3002\u667a\u80fd\u624b\u673a\u4f1a\u63a5\u6536\u5173\u4e8e\u5929\u6c14\u548c\u6781\u7aef\u6c14\u5019\u7684\u8b66\u62a5\uff0c\u800c\u5176\u9884\u6d4b\u80fd\u529b\u6bd4\u6211\u4eec\u5341\u51e0\u5e74\u524d\u60f3\u8c61\u7684\u8981\u597d\u5f97\u591a\u3002\u540c\u65f6\uff0c\u9664\u4e86\u5c0f\u957f\u5ea6\u5bc6\u94a5\u52a0\u5bc6\u4f1a\u53d7\u5230\u7c7b\u4f3c\u66b4\u529b\u7834\u89e3\u7684\u653b\u51fb\u4e4b\u5916\uff0c\u5bc6\u7801\u5b66\u7406\u8bba\u57fa\u672c\u6ca1\u6709\u88ab\u64bc\u52a8\u3002\u63a5\u4e0b\u6765\uff0c\u8ba9\u6211\u4eec\u6765\u770b\u4e00\u770b\u8ba1\u7b97\u3001\u4f18\u5316\u4ee5\u53ca\u5b66\u4e60\u9886\u57df\u6700\u8fd1\u7684\u8fdb\u5c55\u662f\u5982\u4f55\u5c06\u6211\u4eec\u9886\u5165\u201c\u4e50\u89c2\u4e4b\u5730\u201d\u7684\u3002<\/span><\/section>\n

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2016\u5e74\uff0c\u6bd4\u5c14\u00b7\u5e93\u514b<\/span>\uff08Bill Cook, \u4e0e\u524d\u6587\u4e2d\u7684\u53f2\u8482\u592b\u00b7\u5e93\u514b\u6ca1\u6709\u5173\u7cfb\uff09<\/span>\u548c\u4ed6\u7684\u540c\u4e8b\u4eec\u51b3\u5b9a\u8fce\u63a5\u8fd9\u9879<\/span><\/span>\u6311\u6218[9]\uff1a\u5982<\/span>\u4f55\u4f7f\u7528\u6700\u77ed\u7684\u8def\u7a0b\u5230\u8bbf\u82f1\u56fd\u7684\u6bcf\u4e00\u5bb6\u9152\u5427\uff1f\u4ed6\u4eec\u5217\u51fa\u4e8624727\u5bb6\u9152\u5427\u7684\u540d\u5355\uff0c\u5e76\u786e\u5b9a\u4e86\u6700\u540e\u7684\u9152\u5427\u65c5\u884c\u8def\u7ebf\u2014\u2014\u4e00\u6b21\u603b\u957f\u5ea645495239\u7c73\u7684\u5f92\u6b65\u65c5\u884c\u3002\u8fd9\u4e00\u8ddd\u79bb\u6bd4\u7ed5\u5730\u7403\u4e00\u5708\u8fd8\u8981\u957f\u4e00\u4e9b\u3002<\/span><\/section>\n

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\u5b9e\u9645\u4e0a\uff0c\u5e93\u514b\u5bf9\u8be5\u95ee\u9898\u505a\u4e86\u4e00\u4e9b\u7b80\u5316\uff1a\u4ed6\u5ffd\u7565\u4e86\u4e00\u4e9b\u9152\u5427\u4f7f\u5f97\u8be5\u95ee\u9898\u6709\u4e00\u4e2a\u5408\u9002\u7684\u89c4\u6a21\u3002\u5728\u4e00\u4e9b\u82f1\u56fd\u5a92\u4f53\u8fdb\u884c\u62a5<\/span><\/span>\u9053[7]\u4e4b\u540e<\/span>\uff0c\u8bb8\u591a\u4eba\u62b1\u6028\u540d\u5355\u4e2d\u6ca1\u6709\u4ed6\u4eec\u6700\u7231\u7684\u9152\u5427\u3002\u56e0\u6b64\u5e93\u514b\u56e2\u961f\u91cd\u65b0\u6574\u7406\u4e86\u4e00\u4efd\u5305\u542b49687\u5bb6\u9152\u5427\u7684\u540d\u5355\uff0c\u800c\u65b0\u7684\u884c\u7a0b\u957f\u5ea6\u662f63739687\u7c73<\/span>\uff08\u89c1\u4e0b\u56fe\uff09<\/span>\u3002\u4e0e\u4e4b\u524d\u7684\u8def\u5f84\u76f8\u6bd4\uff0c\u4eba\u4eec\u53ea\u9700\u8981\u591a\u8d7040%\u7684\u8def\u7a0b\uff0c\u4fbf\u80fd\u5230\u8bbf\u6570\u91cf\u662f\u4e4b\u524d\u4e24\u500d\u591a\u7684\u9152\u5427\u3002\u8fd9\u4e2a\u9152\u5427\u65c5\u884c\u7684\u95ee\u9898\u4e0e\u65c5\u884c\u5546\u95ee\u9898<\/span>\uff08\u6700\u8457\u540d\u7684NP\u5b8c\u5907\u95ee\u9898\u4e4b\u4e00\uff09<\/span>\u662f\u7b49\u4ef7\u7684\u3002\u5230\u8bbf49687\u5bb6\u9152\u5427\u6240\u6709\u53ef\u80fd\u8def\u7ebf\u7684\u6570\u91cf\u5927\u7ea6\u662f\u201c3\u540e\u9762\u8ddf\u7740211761\u4e2a0\u201d\u3002\u5f53\u7136\u5e93\u514b\u7684\u7535\u8111\u4e0d\u4f1a\u904d\u5386\u6240\u6709\u8def\u7ebf\uff0c\u4ed6\u4eec\u4f7f\u7528\u4e86\u5404\u79cd\u4f18\u5316\u6280\u672f\u3002\u66f4\u4ee4\u4eba\u5370\u8c61\u6df1\u523b\u7684\u662f\uff0c\u8fd9\u4efd\u8def\u7ebf\u8fd8\u9644\u5e26\u4e00\u4efd\u57fa\u4e8e\u7ebf\u6027\u89c4\u5212\u5bf9\u5076\u6027\u7684\u6700\u4f18\u6027\u8bc1\u660e\u3002<\/span><\/span><\/section>\n

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\u7a7f\u8fc749687\u5bb6\u82f1\u56fd\u9152\u5427\u7684\u6700\u77ed\u8def\u7ebf\u4e28\u56fe\u7247\u6765\u6e90\uff1amath.uwaterloo.ca\/tsp\/uk<\/span><\/section>\n

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\u5e93\u514b\u56e2\u961f\u4e5f\u627f\u62c5\u4e86\u4e00\u4e2a\u66f4\u5927\u7684\u4efb\u52a1\u2014\u2014\u5bfb\u627e\u4e00\u6761\u7a7f\u8d8a200\u591a\u4e07\u6052\u661f\u7684\u6700\u77ed\u8def\u5f84\uff0c\u5176\u4e2d\u6052\u661f\u4e4b\u95f4\u7684\u8ddd\u79bb\u53ef\u4ee5\u88ab\u8ba1\u7b97\u3002\u4ed6\u4eec\u83b7\u5f97\u7684\u8def\u7ebf\u603b\u957f\u5ea6\u4e3a28884456\u79d2\u5dee\u8ddd<\/span>\uff08\u8bd1\u8005\u6ce8\uff1a1\u79d2\u5dee\u8ddd\u7ea6\u4e3a3.26\u5149\u5e74\uff09<\/span>\uff0c\u548c\u7406\u8bba\u6700\u4f73\u503c\u76f8\u6bd4\u53ea\u6709683\u79d2\u5dee\u8ddd\u7684\u5dee\u522b\u3002<\/span><\/span><\/section>\n

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\u9664\u4e86\u65c5\u884c\u5546\u95ee\u9898\uff0c\u6211\u4eec\u5728\u6c42\u89e3\u5e03\u5c14\u53ef\u6ee1\u8db3\u6027\u95ee\u9898\u548c\u6df7\u5408\u6574\u6570\u89c4\u5212\u95ee\u9898<\/span>\uff08Mixed-integer programming question\uff09<\/span>\u9886\u57df\u4e5f\u53d6\u5f97\u4e86\u91cd\u5927\u8fdb\u5c55\u2014\u2014\u4e00\u79cd\u7ebf\u6027\u89c4\u5212\u65b9\u6cd5\u7684\u53d8\u4f53\uff0c\u5176\u4e2d\u4e00\u4e9b\u53d8\u91cf<\/span>\uff08\u4e0d\u4e00\u5b9a\u662f\u5168\u90e8\uff09<\/span>\u5fc5\u987b\u662f\u6574\u6570\u3002\u901a\u8fc7\u4f7f\u7528\u9ad8\u5ea6\u7cbe\u70bc\u7684\u542f\u53d1\u5f0f\u65b9\u6cd5\u3001\u9ad8\u901f\u5904\u7406\u5668\u3001\u4e13\u4e1a\u786c\u4ef6\u4ee5\u53ca\u5206\u5e03\u5f0f\u4e91\u8ba1\u7b97\uff0c\u4eba\u4eec\u57fa\u672c\u5df2\u7ecf\u53ef\u4ee5\u89e3\u51b3\u5b9e\u8df5\u4e2d\u51fa\u73b0\u7684\u5177\u6709\u6570\u4ee5\u4e07\u8ba1\u7684\u53d8\u91cf\u548c\u6570\u5341\u4e07\u751a\u81f3\u4e0a\u767e\u4e07\u7684\u7ea6\u675f\u7684\u95ee\u9898\u3002<\/span><\/span><\/section>\n

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\u9762\u5bf9\u9700\u8981\u6c42\u89e3\u7684NP\u95ee\u9898\uff0c\u4eba\u4eec\u901a\u5e38\u4f1a\u5c06\u95ee\u9898\u8f6c\u8ff0\u4e3a\u5e03\u5c14\u53ef\u6ee1\u8db3\u6027\u95ee\u9898\u6216\u6df7\u5408\u6574\u6570\u89c4\u5212\u95ee\u9898\uff0c\u8fdb\u800c\u4f7f\u7528\u6700\u597d\u7684\u6c42\u89e3\u5668\u6c42\u89e3\u3002\u8fd9\u4e9b\u5de5\u5177\u5df2\u7ecf\u88ab\u6210\u529f\u5730\u5e94\u7528\u5728\u7535\u8def\u4e0e\u7f16\u7801\u7684\u9a8c\u8bc1\u4e0e\u81ea\u52a8\u5316\u6d4b\u8bd5\u3001\u8ba1\u7b97\u751f\u7269\u5b66\u3001\u7cfb\u7edf\u5b89\u5168\u3001\u4ea7\u54c1\u4e0e\u5305\u88c5\u8bbe\u8ba1\u3001\u91d1\u878d\u4ea4\u6613\u4e2d\uff0c\u751a\u81f3\u7528\u4e8e\u6c42\u89e3\u56f0\u96be\u7684\u6570\u5b66\u95ee\u9898\u3002<\/span><\/section>\n

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\u5982\u4eca\uff0c\u4efb\u4f55\u300aACM\u901a\u8baf\u6742\u5fd7\u300b\u7684\u8bfb\u8005\u548c\u5176\u4ed6\u5927\u591a\u6570\u4eba\u90fd\u4e0d\u4f1a\u5ffd\u89c6\u673a\u5668\u5b66\u4e60\u5e26\u6765\u7684\u53d8\u9769\u6027\u5f71\u54cd\uff0c\u5c24\u5176\u662f\u901a\u8fc7\u795e\u7ecf\u7f51\u7edc\u5b9e\u73b0\u7684\u673a\u5668\u5b66\u4e60\u3002\u4f7f\u7528\u4eba\u5de5\u795e\u7ecf\u5143<\/span>\uff08\u7b3c\u7edf\u5730\u8bb2\uff0c\u8ba1\u7b97\u52a0\u6743\u9608\u503c\u51fd\u6570\uff09<\/span>\u5b9e\u73b0\u5efa\u6a21\u8ba1\u7b97\u7684\u6982\u5ff5\u53ef\u4ee5\u8ffd\u6eaf\u523020\u4e16\u7eaa40\u5e74\u4ee3\u6c83\u4f26\u00b7\u9ea6\u5361\u6d1b\u514b<\/span>\uff08Warren McCulloch\uff09<\/span>\u548c\u6c83\u5c14\u7279\u00b7\u76ae\u8328<\/span>\uff08Walter Pitts\uff09<\/span><\/span>[28]\u7684<\/span>\u7814\u7a76\u3002\u572820\u4e16\u7eaa90\u5e74\u4ee3\uff0c\u7ea6\u4e66\u4e9a\u00b7\u672c\u5e0c\u5965<\/span>\uff08Yoshua Bengio\uff09<\/span>\u3001\u6770\u5f17\u91cc\u00b7\u8f9b\u987f<\/span>\uff08Geoffrey Hinton\uff09<\/span>\u548c\u6768\u7acb\u6606<\/span>\uff08Yann LeCun\uff09<\/span><\/span>[26]\u63d0<\/span>\u51fa\u4e86\u53cd\u5411\u4f20\u64ad\u7b49\u7b97\u6cd5\uff0c\u4e3a\u591a\u5c42\u795e\u7ecf\u7f51\u7edc\u5b66\u4e60\u8bad\u7ec3\u7684\u53d1\u5c55\u5960\u5b9a\u4e86\u57fa\u7840\u3002\u66f4\u5feb\u3001\u66f4\u5e7f\u6cdb\u7684\u5206\u5e03\u5f0f\u8ba1\u7b97\u3001\u4e13\u4e1a\u786c\u4ef6\u548c\u6d77\u91cf\u6570\u636e\u4e5f\u5e2e\u52a9\u5e76\u63a8\u52a8\u4e86\u673a\u5668\u5b66\u4e60\u7684\u53d1\u5c55\uff0c\u4f7f\u5f97\u5b83\u53ef\u4ee5\u975e\u5e38\u51fa\u8272\u5730\u5b8c\u6210\u4f17\u591a\u539f\u672c\u9700\u8981\u4eba\u7c7b\u5b8c\u6210\u7684\u4efb\u52a1\u3002\u8ba1\u7b97\u673a\u534f\u4f1a<\/span>\uff08the Association for Computing Machinery\uff0cACM\uff09<\/span>\u4e5f\u4e3a\u672c\u5e0c\u5965\u3001\u8f9b\u987f\u548c\u7acb\u6606\u6388\u4e88\u4e862018\u5e74\u7684\u56fe\u7075\u5956\uff0c\u4ee5\u8868\u5f70\u4ed6\u4eec\u7684\u5de5\u4f5c\u5bf9\u4eba\u7c7b\u793e\u4f1a\u4ea7\u751f\u7684\u6df1\u8fdc\u5f71\u54cd\u3002<\/span><\/span><\/section>\n

<\/section>\n
\u90a3\u4e48\uff0c\u673a\u5668\u5b66\u4e60\u4e0eP\/NP\u95ee\u9898\u6709\u4ec0\u4e48\u8054\u7cfb\uff1f<\/span>\uff08\u5728\u672c\u8282\u4e2d\uff0c\u5f53\u6211\u4eec\u63d0\u53caP=NP\uff0c\u5b83\u8868\u793a\u6240\u6709\u7684NP\u95ee\u9898\u5728\u5b9e\u8df5\u4e2d\u90fd\u6709\u76f8\u5173\u7684\u9ad8\u6548\u7b97\u6cd5\u3002\uff09<\/span>\u5965\u5361\u59c6\u5243\u5200\u539f\u5219\u6307\u51fa\uff0c\u201c\u5982\u65e0\u5fc5\u8981\uff0c\u52ff\u589e\u5b9e\u4f53\u201d\uff0c\u6216\u8005\u8bf4\uff0c\u6700\u7b80\u5355\u7684\u89e3\u91ca\u53ef\u80fd\u624d\u662f\u6b63\u786e\u7684\u3002\u5982\u679cP=NP\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u8fd9\u4e00\u601d\u60f3\u6765\u5efa\u7acb\u4e00\u4e2a\u5f3a\u5927\u7684\u5b66\u4e60\u7b97\u6cd5\uff1a\u627e\u5230\u4e00\u4e2a\u4e0e\u6570\u636e\u4e00\u81f4\u7684\u6700\u5c0f\u7684\u56de\u8def\u3002\u4f46\u5373\u4fbf\u53ef\u80fd\u6ca1\u6709P=NP\u8fd9\u4e2a\u7ed3\u8bba\uff0c\u673a\u5668\u5b66\u4e60\u4e5f\u53ef\u4ee5\u8fd1\u4f3c\u5730\u5b9e\u73b0\u8fd9\u79cd\u65b9\u6cd5\uff0c\u4ece\u800c\u8d4b\u4e88\u4e86\u795e\u7ecf\u7f51\u7edc\u60ca\u4eba\u7684\u80fd\u529b\u3002\u7136\u800c\uff0c\u795e\u7ecf\u7f51\u7edc\u4e0d\u592a\u53ef\u80fd\u662f\u90a3\u4e2a\u201c\u6700\u5c0f\u7684\u201d\u56de\u8def\u3002\u5982\u4eca\u4f7f\u7528\u6df1\u5ea6\u5b66\u4e60\u6280\u672f\u8bad\u7ec3\u7684\u795e\u7ecf\u7f51\u7edc\u5f80\u5f80\u7ed3\u6784\u662f\u56fa\u5b9a\u7684\uff0c\u5176\u53c2\u6570\u4e0e\u7f51\u7edc\u4e2d\u7684\u6743\u91cd\u6709\u5173\u3002\u4e3a\u4e86\u62e5\u6709\u8db3\u591f\u7684\u8868\u8fbe\u80fd\u529b\uff0c\u4eba\u4eec\u901a\u5e38\u9700\u8981\u8bbe\u7f6e\u6570\u767e\u4e07\u751a\u81f3\u66f4\u591a\u7684\u6743\u91cd\u53c2\u6570\u3002\u800c\u6570\u91cf\u4f17\u591a\u7684\u53c2\u6570\u9650\u5236\u4e86\u795e\u7ecf\u7f51\u7edc\u7684\u80fd\u529b\uff1a\u5b83\u4eec\u53ef\u4ee5\u5f88\u597d\u5730\u8fdb\u884c\u9762\u90e8\u8bc6\u522b\uff0c\u4f46\u662f\u5374\u65e0\u6cd5\u6839\u636e\u793a\u4f8b\u6765\u5b66\u4e60\u5982\u4f55\u8fdb\u884c\u4e58\u6cd5\u8fd0\u7b97\u3002<\/span><\/span><\/section>\n

<\/section>\n
\u901a\u7528\u5206\u5e03\uff08Universal distribution\uff09\u548cGPT-3 <\/strong>\u8ba9\u6211\u4eec\u8003\u8651\u4efb\u610f\u957f\u5ea6\u4e8c\u8fdb\u5236\u5b57\u7b26\u4e32\u7684\u5206\u5e03\u3002\u5c3d\u7ba1\u5747\u5300\u5206\u5e03\u662f\u660e\u663e\u4e0d\u5408\u7406\u7684\uff0c\u4f46\u662f\u6211\u4eec\u662f\u5426\u53ef\u4ee5\u6784\u5efa\u5206\u5e03\u4f7f\u5f97\u4efb\u610f\u76f8\u540c\u957f\u5ea6\u7684\u5b57\u7b26\u4e32\u62e5\u6709\u76f8\u540c\u7684\u6982\u7387\uff1f\u5b9e\u9645\u4e0a\uff0c\u6709\u4e9b\u5b57\u7b26\u4e32\u786e\u5b9e\u4f1a\u6bd4\u5176\u4ed6\u7684\u66f4\u91cd\u8981\u3002\u6bd4\u5982\uff0c\u03c0<\/span>\u7684\u524d100\u4e07\u4f4d\u6570\u5b57\u6bd4\u968f\u673a\u751f\u6210\u4e00\u4e2a100\u4e07\u4f4d\u6570\u5b57\u66f4\u6709\u610f\u4e49\u3002\u56e0\u6b64\u6216\u8bb8\u4f60\u4f1a\u5e0c\u671b\u7ed9\u66f4\u6709\u610f\u4e49\u7684\u5b57\u7b26\u4e32\u8bbe\u7f6e\u66f4\u9ad8\u7684\u6982\u7387\u3002\u5b9e\u73b0\u8fd9\u4e00\u76ee\u6807\u7684\u65b9\u6cd5\u5f88\u591a\uff0c\u800c\u5b9e\u9645\u4e0a\u5b58\u5728\u4e00\u4e2a\u63a5\u8fd1\u4e8e\u4efb\u4f55\u5176\u4ed6\u53ef\u8ba1\u7b97\u5206\u5e03\u7684\u901a\u7528\u5206\u5e03<\/span>\uff08\u8bfb\u8005\u53ef\u4ee5\u53c2\u8003\u79d1\u5c14\u4ec0\u8d6b\u7b49\u4eba\u7684\u6587\u7ae0<\/span><\/span>[25]\uff09<\/span><\/span>\u3002\u901a\u7528\u5206\u5e03\u4e0e\u5b66\u4e60\u8bad\u7ec3\u6709\u5f88\u5927\u7684\u8054\u7cfb\uff0c\u4f8b\u5982\uff0c\u4efb\u610f\u4ee5\u5c0f\u8bef\u5dee\u7387\u5b66\u4e60\u8fd9\u79cd\u5206\u5e03\u7684\u7b97\u6cd5\u5c06\u53ef\u4ee5\u5b66\u4e60\u6240\u6709\u53ef\u4ee5\u8ba1\u7b97\u7684\u5206\u5e03\u3002\u53ef\u60dc\u7684\u662f\uff0c\u5373\u4fbfP=NP\uff0c\u901a\u7528\u5206\u5e03\u4e5f\u662f\u4e0d\u53ef\u8ba1\u7b97\u7684\u3002\u4e0d\u8fc7\uff0c\u5982\u679cP=NP\uff0c\u6211\u4eec\u4ecd\u7136\u53ef\u4ee5\u5f97\u5230\u4e00\u4e9b\u6709\u7528\u7684\u4e1c\u897f\u2014\u2014\u6211\u4eec\u53ef\u4ee5\u521b\u5efa\u4e00\u4e2a\u53ef\u9ad8\u6548\u8ba1\u7b97\u7684\u5206\u5e03\uff0c\u4f7f\u5f97\u5b83\u5bf9\u4e8e\u5176\u4ed6\u53ef\u9ad8\u6548\u8ba1\u7b97\u7684\u5206\u5e03\u662f\u901a\u7528\u7684\u3002<\/span><\/section>\n

<\/section>\n
\u6211\u4eec\u80fd\u4ece\u673a\u5668\u5b66\u4e60\u4e2d\u83b7\u5f97\u4ec0\u4e48\uff1f\u4ee5GPT<\/span>\uff08Generative Pre-trained Transformer\uff0c\u751f\u6210\u5f0f\u9884\u8bad\u7ec3\u8f6c\u6362\u5668\uff09<\/span>\u4e3a\u4f8b\uff0c\u7279\u522b\u662f2020\u5e74\u53d1\u5e03\u7684GP<\/span><\/span>T-3[5]\u3002GPT<\/span>-3\u4ece\u5c3d\u53ef\u80fd\u591a\u7684\u4e66\u9762\u8bed\u6599\u5e93\u4e2d\u63d0\u53d6\u4e864100\u4ebf\u4e2a\u6807\u8bb0\uff0c\u8fdb\u800c\u8bad\u7ec3\u4e861750\u4ebf\u4e2a\u53c2\u6570\u3002\u5b83\u53ef\u4ee5\u56de\u7b54\u95ee\u9898\uff0c\u53ef\u4ee5\u6839\u636e\u63d0\u793a\u4e66\u5199\u6587\u7ae0\uff0c\u751a\u81f3\u53ef\u4ee5\u751f\u6210\u4ee3\u7801\u3002\u5c3d\u7ba1\u5b83\u8fd8\u6709\u6f2b\u957f\u7684\u4f18\u5316\u4e4b\u8def\u8981\u8d70\uff0c\u4f46\u662f\u5b83\u5df2\u7ecf\u53ef\u4ee5\u50cf\u4eba\u7c7b\u4e00\u6837\u521b\u9020\u5185\u5bb9\uff0c\u5e76\u56e0\u6b64\u53d7\u5230\u597d\u8bc4\u3002\u6211\u4eec\u53ef\u4ee5\u628aGPT-3\u770b\u4f5c\u662f\u4e00\u79cd\u5206\u5e03\uff0c\u5e76\u8003\u8651\u7b97\u6cd5\u8f93\u51fa\u5bf9\u5e94\u7684\u6982\u7387\u2014\u2014\u5373\u4e00\u4e2a\u5f31\u7248\u672c\u7684\u901a\u7528\u5206\u5e03\u3002\u5982\u679c\u6211\u4eec\u4ee5\u4e00\u4e2a\u7ed9\u5b9a\u7684\u524d\u7f00\u9650\u5236\u901a\u7528\u5206\u5e03\uff0c\u90a3\u4e48\u5b83\u5c31\u63d0\u4f9b\u4e00\u4e2a\u7531\u8be5\u524d\u7f00\u63d0\u793a\u7684\u968f\u673a\u6837\u672c\u3002GPT-3\u4e5f\u53ef\u4ee5\u57fa\u4e8e\u8fd9\u6837\u7684\u63d0\u793a\uff0c\u65e0\u9700\u8fdb\u4e00\u6b65\u8bad\u7ec3\u5c31\u80fd\u5904\u7406\u6781\u5927\u8303\u56f4\u7684\u76f8\u5173\u9886\u57df\u77e5\u8bc6\u3002\u968f\u7740\u8fd9\u65b9\u9762\u7814\u7a76\u7684\u8fdb\u5c55\uff0c\u6211\u4eec\u4e5f\u5c06\u8d8a\u6765\u8d8a\u63a5\u8fd1\u4e00\u4e2a\u901a\u7528\u5ea6\u91cf\u6807\u51c6\u5e76\u4ece\u4e2d\u5b9e\u73b0\u5185\u7f6e\u5f0f\u5b66\u4e60\uff1a\u57fa\u4e8e\u7ed9\u5b9a\u4e0a\u4e0b\u6587\u751f\u6210\u4e00\u4e2a\u968f\u673a\u7684\u4f8b\u5b50\u3002<\/span><\/span><\/section>\n

<\/section>\n
\u79d1\u5b66\u4e0e\u533b\u836f <\/strong>\u5728\u79d1\u5b66\u4e16\u754c\uff0c\u6211\u4eec\u5df2\u7ecf\u901a\u8fc7\u5927\u89c4\u6a21\u6a21\u62df\u53d6\u5f97\u4e86\u4f17\u591a\u8fdb\u5c55\uff0c\u6bd4\u5982\u63a2\u7d22\u6838\u805a\u53d8\u53cd\u5e94\u3002\u7814\u7a76\u8005\u4eec\u4f7f\u7528\u4e00\u79cd\u79d1\u5b66\u65b9\u6cd5\u7684\u8303\u5f0f\uff1a\u9996\u5148\u5bf9\u4e8e\u7269\u7406\u7cfb\u7edf\u5efa\u7acb\u5047\u8bbe\uff1b\u7136\u540e\u4f7f\u7528\u6a21\u578b\u8fdb\u884c\u9884\u6d4b\uff1b\u518d\u7528\u5b9e\u9a8c\u6a21\u62df\u68c0\u9a8c\u8be5\u9884\u6d4b\uff0c\u800c\u4e0d\u662f\u76f4\u63a5\u5b9e\u73b0\u6838\u805a\u53d8\u53cd\u5e94\u3002\u5982\u679c\u6d4b\u8bd5\u7ed3\u679c\u4e0e\u9884\u671f\u4e0d\u540c\uff0c\u518d\u4fee\u6539\u6216\u63a8\u7ffb\u8fd9\u4e2a\u6a21\u578b\u5e76\u91cd\u590d\u4ee5\u4e0a\u7684\u8fc7\u7a0b\u3002<\/span><\/section>\n

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\u5728\u6211\u4eec\u62e5\u6709\u4e00\u4e2a\u6709\u8bf4\u670d\u529b\u7684\u6a21\u578b\u4e4b\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u5728\u73b0\u5b9e\u53cd\u5e94\u5806\u4e2d\u8fdb\u884c\u4e00\u4e9b\u6602\u8d35\u7684\u5b9e\u9a8c\u6d4b\u8bd5\u3002\u5982\u679cP=NP\uff0c\u50cf\u4e0a\u6587\u63d0\u53ca\u7684\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u5965\u5361\u59c6\u5243\u5200\u7406\u8bba\u6765\u5efa\u7acb\u5047\u8bf4\u2014\u2014\u627e\u5230\u4e00\u4e2a\u4e0e\u6570\u636e\u4e00\u81f4\u7684\u6700\u5c0f\u56de\u8def\u3002\u673a\u5668\u5b66\u4e60\u7684\u6280\u5de7\u53ef\u4ee5\u7d27\u63a5\u7740\u6cbf\u7740\u8fd9\u4e2a\u601d\u8def\u81ea\u52a8\u5730\u521b\u5efa\u5047\u8bbe\u3002\u4e0d\u7ba1\u6570\u636e\u662f\u6765\u81ea\u4e8e\u6a21\u62df\u3001\u5b9e\u9a8c\u8fd8\u662f\u4f20\u611f\u5668\uff0c\u673a\u5668\u5b66\u4e60\u90fd\u53ef\u4ee5\u521b\u5efa\u51fa\u5339\u914d\u6570\u636e\u7684\u6a21\u578b\u3002\u7136\u540e\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u8fd9\u4e9b\u6a21\u578b\u6765\u8fdb\u884c\u9884\u6d4b\uff0c\u5e76\u50cf\u524d\u6587\u63d0\u5230\u8fc7\u7684\u90a3\u6837\u68c0\u9a8c\u505a\u51fa\u7684\u9884\u6d4b\u3002<\/span><\/section>\n

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\u5c3d\u7ba1\u673a\u5668\u5b66\u4e60\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u627e\u5230\u672a\u53d1\u73b0\u7684\u5047\u8bbe\u548c\u6a21\u578b\uff0c\u4f46\u6240\u83b7\u5f97\u7684\u7ed3\u679c\u672a\u5fc5\u662f\u6b63\u786e\u7684\u3002\u6211\u4eec\u901a\u5e38\u53ef\u4ee5\u63a5\u53d7\u670995%\u7f6e\u4fe1\u6c34\u5e73\u7684\u5047\u8bbe<\/span>\uff08\u8fd9\u610f\u5473\u572820\u4e2a\u4e0d\u5408\u683c\u7684\u5047\u8bbe\u4e2d\uff0c\u6709\u4e00\u4e2a\u53ef\u80fd\u4f1a\u88ab\u63a5\u53d7\uff09<\/span>\u3002\u673a\u5668\u5b66\u4e60\u4e0e\u6570\u636e\u79d1\u5b66\u7684\u5de5\u5177\u4e3a\u6211\u4eec\u751f\u6210\u5047\u8bbe\u7684\u540c\u65f6\uff0c\u4e5f\u5e26\u6765\u4e86\u7ed3\u679c\u4e0d\u7b26\u5408\u4e8b\u5b9e\u7684\u98ce\u9669\u3002\u533b\u5b66\u7814\u7a76\u4eba\u5458\uff0c\u7279\u522b\u662f\u8bd5\u56fe\u89e3\u51b3\u764c\u75c7\u7b49\u75be\u75c5\u7684\u7814\u7a76\u4eba\u5458\uff0c\u5e38\u5e38\u9047\u5230\u7b97\u6cd5\u4e0a\u7684\u963b\u788d\uff0c\u56e0\u4e3a\u751f\u7269\u7cfb\u7edf\u6781\u5176\u590d\u6742\u3002\u6211\u4eec\u77e5\u9053DNA\u6784\u6210\u4e00\u79cd\u7f16\u7801\uff0c\u5b83\u63cf\u8ff0\u4e86\u6211\u4eec\u7684\u8eab\u4f53\u5982\u4f55\u5f62\u6210\u4ee5\u53ca\u8eab\u4f53\u4e0d\u540c\u90e8\u5206\u7684\u529f\u80fd\uff0c\u4f46\u6211\u4eec\u5bf9\u5176\u8fd0\u4f5c\u539f\u7406\u77e5\u4e4b\u751a\u5c11\u3002<\/span><\/span><\/section>\n

<\/section>\n
2020\u5e7411\u670830\u65e5\uff0c\u8c37\u6b4c\u7684DeepMind\u516c\u53f8\u53d1\u5e03\u4e86AlphaFold\u2014\u2014\u4e00\u79cd\u57fa\u4e8e\u6c28\u57fa\u9178\u5e8f\u5217\u9884\u6d4b\u86cb\u767d\u8d28\u7ed3\u6784\u7684\u65b0<\/span>\u7b97\u6cd5[22]\u3002AlphaF<\/span>old\u7684\u9884\u6d4b\u51c6\u786e\u5ea6\u51e0\u4e4e\u8fbe\u5230\u4e86\u4eba\u5de5\u5b9e\u9a8c\u7684\u6c34\u5e73\uff0c\u5373\u901a\u8fc7\u5b9e\u9a8c\u6784\u5efa\u6c28\u57fa\u9178\u5e8f\u5217\u5e76\u6d4b\u8bd5\u5176\u751f\u6210\u7684\u86cb\u767d\u8d28\u7ed3\u6784\u3002\u867d\u7136\u5173\u4e8eDeepMind\u662f\u5426\u771f\u7684\u201c\u89e3\u51b3\u201d\u4e86\u86cb\u767d\u8d28\u6298\u53e0\u7684\u95ee\u9898\u4ecd\u5b58\u4e89\u8bae\uff0c\u5e76\u4e14\u73b0\u5728\u4fbf\u8bc4\u4f30\u5176\u5f71\u54cd\u529b\u8fd8\u4e3a\u65f6\u8fc7\u65e9\uff0c\u4f46\u4ece\u957f\u8fdc\u6765\u770b\uff0c\u5b83\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u4e00\u4e2a\u65b0\u7684\u6570\u5b57\u5316\u5de5\u5177\u6765\u7814\u7a76\u86cb\u767d\u8d28\uff0c\u7406\u89e3\u5b83\u4eec\u662f\u5982\u4f55\u76f8\u4e92\u4f5c\u7528\uff0c\u5e76\u5b66\u4e60\u5982\u4f55\u8bbe\u8ba1\u86cb\u767d\u8d28\u6765\u5bf9\u6297\u75be\u75c5\u3002<\/span><\/section>\n

<\/section>\n
P\/NP\u4e4b\u5916\uff1a\u8c61\u68cb\u4e0e\u56f4\u68cb <\/strong>NP\u95ee\u9898\u5c31\u50cf\u89e3\u8c1c\u6e38\u620f\u3002\u6570\u72ec\u95ee\u9898\u5c31\u662fNP\u5b8c\u5907\u7684\uff1a\u5728\u4e00\u4e2a\u4efb\u610f\u5927\u5c0f\u7684\u5bab\u683c\u4e0a\uff0c\u7ed9\u5b9a\u4e00\u4e9b\u521d\u59cb\u6570\u5b57\uff0c\u7136\u540e\u6c42\u89e3\u5176\u4f59\u7a7a\u683c\u4e2d\u6570\u5b57\u3002\u4f46\u662f\u5bf9\u4e8e\u4e24\u4f4d\u73a9\u5bb6\u8f6e\u6d41\u6267\u5b50\u7684\u56de\u5408\u5236\u6e38\u620f\uff0c\u6bd4\u5982\u8c61\u68cb\u548c\u56f4\u68cb\uff0c\u5982\u679c\u6211\u4eec\u60f3\u77e5\u9053\u8c01\u4f1a\u5728\u7ed9\u5b9a\u68cb\u5c40\u4e0b\u83b7\u80dc\uff0c\u60c5\u51b5\u53c8\u4f1a\u600e\u4e48\u6837\u5462\uff1f\u4e8b\u5b9e\u4e0a\uff0c\u5373\u4fbf\u662fP=NP\uff0c\u6211\u4eec\u4e5f\u672a\u5fc5\u53ef\u4ee5\u627e\u5230\u5b8c\u7f8e\u7684\u68cb\u7c7b\u7b97\u6cd5\u3002\u6211\u4eec\u4e0d\u5f97\u4e0d\u8003\u8651\u5bf9\u4e8e\u9ed1\u5b50\u7684\u6bcf\u4e00\u6b65\uff0c\u767d\u5b50\u90fd\u53ef\u4ee5\u8d70\u51fa\u5408\u9002\u7684\u4e00\u6b65\uff0c\u5e76\u4e0d\u65ad\u5faa\u73af\u76f4\u5230\u767d\u68cb\u80dc\u5229\u3002\u800c\u8bbe\u8ba1\u8fd9\u79cd\u4ea4\u66ff\u7684\u7b97\u6cd5\u4ec5\u4ec5\u4f9d\u9760P=NP\u662f\u4e0d\u591f\u7684\u3002\u8fd9\u4e00\u7c7b\u6e38\u620f\u7684\u7b97\u6cd5\u8bbe\u8ba1\u88ab\u79f0\u4e3aPSPACE-hard\u2014\u2014\u5728\u6ca1\u6709\u65f6\u95f4\u9650\u5236\u4e0b\uff0c\u4f7f\u7528\u5408\u7406\u7684\u5b58\u50a8\u5bb9\u91cf\u8fdb\u884c\u8ba1\u7b97\u662f\u56f0\u96be\u7684\u3002\u6839\u636e\u5177\u4f53\u7684\u89c4\u5219\u8bbe\u5b9a\uff0c\u8c61\u68cb\u548c\u56f4\u68cb\u7684\u7b97\u6cd5\u8bbe\u8ba1\u4f1a\u66f4\u6709\u96be\u5ea6\u3002<\/span>\uff08\u611f\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u4ee5\u9605\u8bfb\u5fb7\u8fc8\u7eb3\u4e0e\u8d6b\u6069\u7684\u6587\u7ae0<\/span><\/span>[11]<\/span>\u3002\uff09<\/span><\/section>\n

<\/section>\n
\u4e0d\u8fc7\uff0c\u8fd9\u5e76\u4e0d\u610f\u5473\u7740\u5728\u5047\u8bbeP=NP\u7684\u524d\u63d0\u4e0b\uff0c\u6211\u4eec\u4e0d\u80fd\u627e\u5230\u4e00\u4e2a\u597d\u7684\u68cb\u7c7b\u7b97\u6cd5\u3002\u4f60\u53ef\u80fd\u505a\u51fa\u4e00\u4e2a\u5927\u5c0f\u5408\u9002\u7684\u9ad8\u6548\u8ba1\u7b97\u673a\u7a0b\u5e8f\uff0c\u4f7f\u5176\u4f18\u4e8e\u6240\u6709\u6bd4\u5b83\u4f53\u91cf\u7565\u5c0f\u7684\u9ad8\u6548\u7a0b\u5e8f\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5373\u4fbf\u6ca1\u6709P=NP\u8fd9\u4e00\u5047\u8bbe\uff0c\u8ba1\u7b97\u673a\u5728\u68cb\u7c7b\u65b9\u9762\u5df2\u7ecf\u8db3\u591f\u5f3a\u5927\u3002\u57281997\u5e74\uff0cIBM\u7684\u8d85\u7ea7\u7535\u8111\u201c\u6df1\u84dd\u201d\u51fb\u8d25\u4e86\u5f53\u65f6\u7684\u56fd\u9645\u8c61\u68cb\u4e16\u754c\u51a0\u519b\u52a0\u91cc\u00b7\u5361\u65af\u5e15\u7f57\u592b<\/span>\uff08Gary Kasparov\uff09<\/span>\uff0c\u7136\u800c\u5728\u5f53\u65f6\uff0c\u5373\u4fbf\u662f\u4e0e\u6709\u5b9e\u529b\u7684\u4e1a\u4f59\u9009\u624b\u7684\u5bf9\u51b3\uff0c\u56f4\u68cb\u7a0b\u5e8f\u4e5f\u96be\u4ee5\u53d6\u80dc\u3002\u5728\u8fd9\u4e4b\u540e\uff0c\u673a\u5668\u5b66\u4e60\u5728\u8ba1\u7b97\u673a\u6e38\u620f\u7684\u7b97\u6cd5\u8bbe\u8ba1\u65b9\u9762\u53d6\u5f97\u4e86\u5de8\u5927\u7684\u8fdb\u6b65\u3002\u8ba9\u6211\u4eec\u76f4\u63a5\u8df3\u8fc7\u8fd9\u6bb5\u60a0\u4e45\u7684\u5386\u53f2\uff0c\u6765\u770b\u770b2017\u5e74DeepMind\u5f00\u53d1\u7684AlphaZe<\/span><\/span>ro[35]<\/span>\u3002<\/span><\/section>\n

<\/section>\n
AlphaZero\u4f7f\u7528\u4e86\u4e00\u79cd\u88ab\u79f0\u4e3a\u8499\u7279\u5361\u6d1b\u6811\u641c\u7d22<\/span>\uff08MCTS\uff09<\/span>\u7684\u6280\u672f\u2014\u2014\u8ba9\u53cc\u65b9\u73a9\u5bb6\u968f\u673a\u5730\u843d\u5b50\u4ece\u800c\u51b3\u5b9a\u6700\u4f73\u7684\u68cb\u8def\u65b9\u6848\u3002AlphaZero\u4f7f\u7528\u6df1\u5ea6\u5b66\u4e60\u6765\u9884\u6d4b\u68cb\u5c40\u7684\u6700\u4f73\u5206\u5e03\uff0c\u4ee5\u4f18\u5316\u4f7f\u7528MCTS\u83b7\u80dc\u7684\u673a\u4f1a\u3002\u867d\u7136AlphaZero\u5e76\u4e0d\u662f\u7b2c\u4e00\u4e2a\u4f7f\u7528MCTS\u7684\u7a0b\u5e8f\uff0c\u4f46\u662f\u5b83\u6ca1\u6709\u4efb\u4f55\u5185\u7f6e\u7b56\u7565\u6216\u8005\u8bbf\u95ee\u4e4b\u524d\u7684\u68cb\u7c7b\u6570\u636e\u5e93\u2014\u2014\u5b83\u4ec5\u4ec5\u5047\u8bbe\u4e86\u6e38\u620f\u7684\u89c4\u5219\u3002\u8fd9\u4e5f\u4f7f\u5f97AlphaZero\u5728\u56fd\u9645\u8c61\u68cb\u548c\u56f4\u68cb\u4e0a\u90fd\u8868\u73b0\u5f97\u51fa\u8272\uff0c\u8fd9\u4e24\u79cd\u6e38\u620f\u9664\u4e86\u4ea4\u66ff\u56de\u5408\u5236\u548c\u56fa\u5b9a\u5927\u5c0f\u7684\u68cb\u76d8\u4e4b\u5916\u622a\u7136\u4e0d\u540c\u3002DeepMind\u6700\u8fd1\u8fdb\u4e00\u6b65\u5730\u7814\u7a76\u4e86MuZ<\/span><\/span>ero[33]\u2014\u2014<\/span>\u5b83\u751a\u81f3\u6ca1\u6709\u5b8c\u6574\u7684\u89c4\u5219\uff0c\u4ec5\u4ec5\u6709\u4e00\u4e9b\u68cb\u76d8\u4f4d\u7f6e\u7684\u8868\u793a\uff0c\u4e00\u7cfb\u5217\u7b26\u5408\u89c4\u5219\u7684\u843d\u5b50\uff0c\u4ee5\u53ca\u54ea\u4e9b\u60c5\u51b5\u662f\u8d62\u3001\u8f93\u6216\u8005\u5e73\u5c40\u3002\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u660e\u767d\uff0c\u5728\u56fd\u9645\u8c61\u68cb\u548c\u56f4\u68cb\u4e2d\uff0c\u7eaf\u7cb9\u7684\u673a\u5668\u5b66\u4e60\u53ef\u4ee5\u5f88\u8f7b\u6613\u5730\u51fb\u8d25\u4eba\u7c7b\u6216\u8005\u5176\u4ed6\u7b97\u6cd5\u3002\u800c\u4eba\u4e3a\u5730\u5e72\u9884\u53ea\u4f1a\u59a8\u788d\u5b83\u3002\u5bf9\u4e8e\u8c61\u68cb\u548c\u56f4\u68cb\u8fd9\u7c7b\u6e38\u620f\uff0c\u5373\u4fbfP=NP\u4e0d\u8db3\u4ee5\u89e3\u51b3\u8fd9\u7c7b\u95ee\u9898\uff0c\u4f46\u673a\u5668\u5b66\u4e60\u5374\u53ef\u4ee5\u53d6\u5f97\u6210\u529f\u3002<\/span><\/section>\n

<\/section>\n

\u53ef\u89e3\u91ca\u7684\u4eba\u5de5\u667a\u80fd <\/strong>\u5f88\u591a\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u4f3c\u4e4e\u5df2\u7ecf\u90fd\u8fd0\u884c\u5f97\u5f88\u597d\uff0c\u4f46\u662f\u6211\u4eec\u5374\u4e0d\u7406\u89e3\u4e3a\u4ec0\u4e48\u3002\u5982\u679c\u4f60\u53bb\u89c2\u5bdf\u4e3a\u4e86\u8bed\u97f3\u8bc6\u522b\u800c\u8bad\u7ec3\u7684\u795e\u7ecf\u7f51\u7edc\uff0c\u4f60\u901a\u5e38\u4f1a\u96be\u4ee5\u7406\u89e3\u5b83\u4e3a\u4f55\u505a\u51fa\u8fd9\u6837\u7684\u9009\u62e9\u3002\u6211\u4eec\u4e3a\u4ec0\u4e48\u8981\u5173\u5fc3\u8fd9\u4e2a\u95ee\u9898\u5462\uff1f\u4ee5\u4e0b\u662f\u4e00\u4e9b\u539f\u56e0\uff1a<\/span><\/p>\n

1. \u7f6e\u4fe1<\/strong>\uff1a\u6211\u4eec\u5982\u4f55\u77e5\u9053\u795e\u7ecf\u7f51\u7edc\u8fd0\u884c\u6b63\u786e\uff1f\u9664\u4e86\u68c0\u67e5\u8f93\u5165\u548c\u8f93\u51fa\uff0c\u6211\u4eec\u4e0d\u4f1a\u505a\u5176\u4ed6\u4efb\u4f55\u7684\u5206\u6790\u3002\u4e0d\u540c\u7684\u5e94\u7528\u573a\u666f\u4f1a\u6709\u4e0d\u540c\u7684\u7f6e\u4fe1\u6c34\u5e73\uff1aNetflix\u63a8\u8350\u4e86\u4e00\u90e8\u6c34\u5e73\u4e0d\u9ad8\u7684\u7535\u5f71\u6ca1\u4ec0\u4e48\u5173\u7cfb\uff0c\u4f46\u5982\u679c\u662f\u81ea\u52a8\u9a7e\u9a76\u7684\u6c7d\u8f66\u9009\u62e9\u4e86\u4e00\u4e2a\u9519\u8bef\u7684\u8f6c\u5f2f\uff0c\u7ed3\u679c\u5c31\u5f88\u4e25\u91cd\u3002<\/span><\/p>\n

2. \u516c\u5e73<\/strong>\uff1a\u6709\u5f88\u591a\u4f8b\u5b50\u8868\u660e\uff0c\u901a\u8fc7\u6570\u636e\u8bad\u7ec3\u7684\u7b97\u6cd5\u53d7\u5230\u4e86\u6570\u636e\u4e2d\u6709\u610f\u6216\u65e0\u610f\u7684\u504f\u5dee\u7684\u5f71\u54cd\u3002\u5982\u679c\u6211\u4eec\u4e0d\u7406\u89e3\u7a0b\u5e8f\uff0c\u6211\u4eec\u5982\u4f55\u53d1\u73b0\u8fd9\u4e9b\u6570\u636e\u4e2d\u7684\u504f\u5dee\uff1f<\/span><\/p>\n

3. \u5b89\u5168<\/strong>\uff1a\u5982\u679c\u4f7f\u7528\u673a\u5668\u5b66\u4e60\u6765\u76d1\u7ba1\u5b89\u5168\u7cfb\u7edf\uff0c\u6211\u4eec\u5c06\u4e0d\u77e5\u9053\u54ea\u4e9b\u6f0f\u6d1e\u4ecd\u7136\u5b58\u5728\uff0c\u7279\u522b\u662f\u5f53\u6211\u4eec\u7684\u654c\u624b\u662f\u4e0d\u65ad\u53d8\u5316\u7684\u65f6\u5019\u3002\u4f46\u5982\u679c\u6211\u4eec\u7406\u89e3\u4ee3\u7801\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u53d1\u73b0\u5e76\u4fee\u8865\u5b89\u5168\u6f0f\u6d1e\u3002\u5f53\u7136\uff0c\u5982\u679c\u654c\u624b\u83b7\u5f97\u4e86\u4ee3\u7801\uff0c\u4ed6\u4eec\u4e5f\u53ef\u4ee5\u53d1\u73b0\u6f0f\u6d1e\u3002<\/span><\/p>\n

4. \u56e0\u679c\u5173\u7cfb<\/strong>\uff1a\u76ee\u524d\u6211\u4eec\u6700\u591a\u53ea\u80fd\u68c0\u67e5\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u662f\u5426\u4e0e\u6211\u4eec\u60f3\u8981\u7684\u8f93\u51fa\u7c7b\u578b\u76f8\u5173\u3002\u7406\u89e3\u4ee3\u7801\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u6570\u636e\u4e2d\u7684\u56e0\u679c\u5173\u7cfb\uff0c\u4ece\u800c\u5728\u79d1\u5b66\u4e0e\u533b\u5b66\u65b9\u9762\u53d6\u5f97\u65b0\u7684\u8fdb\u6b65\u3002<\/span><\/section>\n

<\/section>\n
\u5982\u679cP=NP\uff0c\u6211\u4eec\u4f1a\u5f97\u5230\u4e00\u4e2a\u66f4\u597d\u7684\u60c5\u51b5\u5417\uff1f\u5982\u679c\u6211\u4eec\u6709\u4e00\u4e2aNP\u5b8c\u5168\u95ee\u9898\u7684\u5feb\u901f\u7b97\u6cd5\uff0c\u4f60\u53ef\u4ee5\u5c06\u5176\u7528\u4e8e\u5339\u914d\u95ee\u9898\u6216\u65c5\u884c\u5546\u95ee\u9898\uff0c\u627e\u5230\u53ef\u80fd\u7684\u6700\u5c0f\u56de\u8def\uff0c\u4f46\u4f60\u4e0d\u4f1a\u77e5\u9053\u4e3a\u4ec0\u4e48\u8fd9\u4e2a\u56de\u8def\u662f\u5bf9\u7684\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u6211\u4eec\u60f3\u8981\u4e00\u4e2a\u53ef\u89e3\u91ca\u7b97\u6cd5\u7684\u539f\u56e0\u662f\u6211\u4eec\u5e0c\u671b\u53ef\u4ee5\u7406\u89e3\u5b83\u7684\u6027\u8d28\uff0c\u4f46\u5982\u679cP=NP\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u5bfc\u51fa\u8fd9\u4e9b\u6027\u8d28\u3002\u73b0\u5728\u7814\u7a76\u53ef\u89e3\u91ca\u7684\u4eba\u5de5\u667a\u80fd\u4f1a\u8bae\u6d8c\u73b0\u51fa\u6765\uff0c\u4f8b\u5982ACM FAccT\u4f1a\u8bae\u3002<\/span><\/section>\n

<\/section>\n
\u673a\u5668\u5b66\u4e60\u7684\u5c40\u9650\u6027 <\/strong>\u867d\u7136\u5728\u8fc7\u53bb\u5341\u5e74\u4e2d\uff0c\u673a\u5668\u5b66\u4e60\u5df2\u7ecf\u5c55\u73b0\u4e86\u8bb8\u591a\u4ee4\u4eba\u60ca\u5947\u7684\u7ed3\u679c\uff0c\u4f46\u5f88\u591a\u7cfb\u7edf\u8fd8\u8fdc\u672a\u8fbe\u5230\u5b8c\u7f8e\u7684\u6c34\u5e73\uff0c\u5728\u5927\u591a\u6570\u5e94\u7528\u573a\u666f\u4e2d\uff0c\u4eba\u7c7b\u4ecd\u7136\u66f4\u80dc\u4e00\u7b79\u3002\u4eba\u4eec\u4e5f\u5c06\u7ee7\u7eed\u901a\u8fc7\u65b0\u7684\u4f18\u5316\u7b97\u6cd5\u3001\u6570\u636e\u6536\u96c6\u4e0e\u4e13\u4e1a\u786c\u4ef6\u6765\u63d0\u9ad8\u673a\u5668\u5b66\u4e60\u7684\u80fd\u529b\u3002\u4e0d\u8fc7\uff0c\u673a\u5668\u5b66\u4e60\u4f3c\u4e4e\u786e\u5b9e\u6709\u5176\u5c40\u9650\u6027\u3002\u6b63\u5982\u6211\u4eec\u4e0a\u6587\u63d0\u5230\u8fc7\u7684\uff0c\u673a\u5668\u5b66\u4e60\u8ba9\u6211\u4eec\u4e00\u5b9a\u7a0b\u5ea6\u7684\u63a5\u8fd1P=NP\uff0c\u4f46\u5374\u6c38\u8fdc\u65e0\u6cd5\u66ff\u4ee3P=NP\u2014\u2014\u673a\u5668\u5b66\u4e60\u5728\u5bc6\u7801\u7834\u89e3\u65b9\u9762\u8fdb\u5c55\u751a\u5fae\uff0c\u6211\u4eec\u4e5f\u5c06\u5728\u672c\u6587\u540e\u9762\u770b\u5230\u8fd9\u4e00\u70b9\u3002<\/span><\/section>\n

<\/section>\n
\u673a\u5668\u5b66\u4e60\u4f3c\u4e4e\u65e0\u6cd5\u5b66\u4e60\u7b80\u5355\u7684\u7b97\u672f\u2014\u2014\u4f8b\u5982\u5bf9\u5927\u91cf\u7684\u6570\u5b57\u6c42\u548c\u6216\u8005\u5927\u6570\u4e4b\u95f4\u76f8\u4e58\u3002\u4eba\u4eec\u53ef\u4ee5\u60f3\u5230\u5c06\u673a\u5668\u5b66\u4e60\u4e0e\u7b26\u53f7\u8fd0\u7b97\u7684\u6570\u5b66\u5de5\u5177\u7ed3\u5408\u8d77\u6765\u3002\u7136\u800c\uff0c\u5c3d\u7ba1\u5728\u5b9a\u7406\u8bc1\u660e\u65b9\u9762\u6211\u4eec\u53d6\u5f97\u4e86\u4e00\u4e9b\u4ee4\u4eba\u77a9\u76ee\u7684<\/span>\u8fdb\u5c55[19]\uff0c<\/span>\u4f46\u8fd9\u4e0e\u6211\u4eec\u671f\u5f85\u4e2d\u7684\u5b9e\u9645\u79d1\u7814\u4efb\u52a1\u4ecd\u8ddd\u79bb\u9065\u8fdc\uff0c\u5373\u9009\u53d6\u4e00\u7bc7\u79d1\u7814\u6587\u7ae0\uff0c\u6587\u4e2d\u8bc1\u660e\u8fd8\u672a\u6b63\u5f0f\u5b8c\u6210\uff0c\u4f7f\u7528AI\u7cfb\u7edf\u8865\u5145\u7ec6\u8282\u5e76\u68c0\u9a8c\u8bc1\u660e\u3002<\/span><\/section>\n

<\/section>\n
\u800cP=NP\u5c06\u4f7f\u8fd9\u4e9b\u4efb\u52a1\u53d8\u5f97\u7b80\u5355\uff0c\u6216\u8005\u81f3\u5c11\u6613\u4e8e\u5904\u7406\u3002\u673a\u5668\u5b66\u4e60\u5728\u9762\u5bf9\u4e0d\u5c5e\u4e8e\u5176\u8bad\u7ec3\u5206\u5e03\u7684\u4efb\u52a1\u65f6\u53ef\u80fd\u8868\u73b0\u4e0d\u4f73\u3002\u4f46\u8fd9\u53ef\u80fd\u662f\u6982\u7387\u8f83\u4f4e\u7684\u6781\u7aef\u60c5\u51b5\uff0c\u4f8b\u5982\u8bad\u7ec3\u6570\u636e\u4e2d\u5e76\u672a\u83b7\u5f97\u5f88\u597d\u4ee3\u8868\u67d0\u4e2a\u79cd\u65cf\u7684\u4eba\u8138\u8bc6\u522b\uff1b\u6216\u8005\u53ef\u80fd\u662f\u4e00\u79cd\u5bf9\u6297\u6027\u7684\u5c1d\u8bd5\u2014\u2014\u901a\u8fc7\u5bf9\u8f93\u5165\u8fdb\u884c\u5fae\u5c0f\u7684\u66f4\u6539\u6765\u5f3a\u884c\u83b7\u5f97\u4e0d\u540c\u7684\u8f93\u51fa\uff0c\u6bd4\u5982\u628a\u505c\u8f66\u6807\u5fd7\u4fee\u6539\u51e0\u4e2a\u50cf\u7d20\uff0c\u4ece\u800c\u8ba9\u7b97\u6cd5\u5c06\u5176\u8bc6\u522b\u4e3a\u4e00\u4e2a\u9650\u901f\u6807<\/span>\u5fd7[12]\u3002<\/span>\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7b97\u6cd5\u53ef\u80fd\u6709\u6570\u767e\u4e07\u4e2a\u53c2\u6570\uff0c\u56e0\u6b64\u5b83\u4eec\u5728\u5206\u5e03\u4e4b\u5916\u7684\u6cdb\u5316\u6548\u679c\u53ef\u80fd\u4e0d\u7406\u60f3\u3002\u5982\u679cP=NP\uff0c\u6211\u4eec\u53ef\u4ee5\u83b7\u5f97\u6700\u5c0f\u5c3a\u5bf8\u7684\u6a21\u578b\u4ece\u800c\u6709\u671b\u5b9e\u73b0\u66f4\u597d\u7684\u6cdb\u5316\uff0c\u4f46\u5982\u679c\u6ca1\u6709\u76f8\u5e94\u7684\u5b9e\u9a8c\uff0c\u6211\u4eec\u6c38\u8fdc\u4e5f\u65e0\u6cd5\u9a8c\u8bc1\u3002<\/span><\/section>\n

<\/section>\n
\u5c3d\u7ba1\u673a\u5668\u5b66\u4e60\u4ee4\u4eba\u5370\u8c61\u6df1\u523b\uff0c\u4f46\u6211\u4eec\u8fd8\u6ca1\u6709\u83b7\u5f97\u4efb\u4f55\u63a5\u8fd1\u4e8e\u901a\u7528\u4eba\u5de5\u667a\u80fd\u7684\u4e1c\u897f\u2014\u2014\u8fd9\u4e2a\u672f\u8bed\u6307\u7684\u662f\u5bf9\u4e8e\u4e00\u4e2a\u4e3b\u9898\u6709\u771f\u6b63\u7684\u7406\u89e3\uff0c\u6216\u662f\u5b9e\u73b0\u771f\u6b63\u7684\u610f\u8bc6\u6216\u81ea\u6211\u8ba4\u77e5\u7684\u4eba\u5de5\u7cfb\u7edf\u3002\u5b9a\u4e49\u8fd9\u4e9b\u672f\u8bed\u53ef\u80fd\u662f\u68d8\u624b\u7684\u3001\u6709\u4e89\u8bae\u7684\uff0c\u751a\u81f3\u662f\u4e0d\u53ef\u80fd\u7684\u3002\u4e8e\u6211\u4e2a\u4eba\u800c\u8a00\uff0c\u6211\u4ece\u672a\u89c1\u5230\u8fc7\u4e00\u4e2a\u5173\u4e8e\u610f\u8bc6\u7684\u6b63\u5f0f\u5b9a\u4e49\uff0c\u80fd\u591f\u4f53\u73b0\u6211\u5bf9\u4e8e\u610f\u8bc6\u7684\u76f4\u89c2\u8ba4\u8bc6\u3002\u6211\u6000\u7591\u5373\u4f7fP=NP\uff0c\u6211\u4eec\u4e5f\u6c38\u8fdc\u65e0\u6cd5\u5b9e\u73b0\u5f3a\u610f\u4e49\u4e0b\u7684\u901a\u7528\u4eba\u5de5\u667a\u80fd\u3002<\/span><\/section>\n

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<\/svg><\/section>\n<\/section>\n<\/section>\n
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\u5bc6\u7801\u5b66<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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


<\/p>\n

\u867d\u7136\u6211\u4eec\u5728\u89e3\u51b3NP\u95ee\u9898\u65b9\u9762\u53d6\u5f97\u4e86\u5f88\u5927\u8fdb\u5c55\uff0c\u4f46\u662f\u5bc6\u7801\u5b66\u7684\u591a\u79cd\u7406\u8bba\uff0c\u5305\u62ec\u5355\u5411\u51fd\u6570<\/span>\uff08one-way functions\uff09<\/span>\u3001\u5b89\u5168\u6563\u5217\u7b97\u6cd5<\/span>\uff08secure hashes\uff09<\/span>\u4ee5\u53ca\u516c\u94a5\u5bc6\u7801\u5b66\u4f3c\u4e4e\u90fd\u5b8c\u597d\u65e0\u635f\u3002\u5982\u679cNP\u95ee\u9898\u5b58\u5728\u4e00\u4e2a\u9ad8\u6548\u7684\u7b97\u6cd5\uff0c\u90a3\u4e48\u9664\u4e86\u90a3\u4e9b\u5728\u4fe1\u606f\u5b66\u4e0a\u5b89\u5168\u7684\u5bc6\u7801\u7cfb\u7edf\uff0c\u6bd4\u5982\u4e00\u6b21\u6027\u5bc6\u7801\u7c3f\u548c\u4e00\u4e9b\u57fa\u4e8e\u91cf\u5b50\u7269\u7406\u5b66\u7684\u5bc6\u7801\u7cfb\u7edf\uff0c\u5176\u4ed6\u6240\u6709\u5bc6\u7801\u7cfb\u7edf\u90fd\u4f1a\u88ab\u7834\u89e3\u3002\u6211\u4eec\u5df2\u7ecf\u89c1\u8bc1\u4e86\u5f88\u591a\u6210\u529f\u7684\u7f51\u7edc\u5b89\u5168\u653b\u51fb\uff0c\u4f46\u5b83\u4eec\u901a\u5e38\u6e90\u4e8e\u7cdf\u7cd5\u7684\u4ee3\u7801\u6f0f\u6d1e\u3001\u5f88\u5f31\u7684\u968f\u673a\u6570\u751f\u6210\u5668\u6216\u8005\u4eba\u4e3a\u758f\u6f0f\uff0c\u5f88\u5c11\u662f\u56e0\u4e3a\u5bc6\u7801\u5b66\u7406\u8bba\u7684\u95ee\u9898\u3002<\/span><\/span><\/section>\n

<\/section>\n
\u73b0\u5728\u5927\u591a\u6570CPU\u82af\u7247\u90fd\u5185\u7f6e\u4e86AES<\/span>\uff08Advanced Encryption Standard\uff09<\/span>\uff0c\u56e0\u6b64\u4e00\u65e6\u6211\u4eec\u4f7f\u7528\u4e86\u516c\u94a5\u52a0\u5bc6\u7cfb\u7edf\u8bbe\u7f6e\u79c1\u94a5\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u50cf\u53d1\u9001\u666e\u901a\u6587\u672c\u4e00\u6837\u8f7b\u677e\u5730\u53d1\u9001\u52a0\u5bc6\u540e\u7684\u6570\u636e\u3002\u52a0\u5bc6\u6280\u672f\u4e3a\u533a\u5757\u94fe\u548c\u52a0\u5bc6\u8d27\u5e01\u7684\u53d1\u5c55\u63d0\u4f9b\u4e86\u52a8\u529b\uff0c\u8fd9\u610f\u5473\u7740\u4eba\u4eec\u5bf9\u4e8e\u52a0\u5bc6\u6280\u672f\u7684\u4fe1\u4efb\u8db3\u4ee5\u8ba9\u4ed6\u4eec\u613f\u610f\u628a\u8d27\u5e01\u6362\u6210\u6bd4\u7279\u3002\u8fc8\u514b\u5c14\u00b7\u5361\u6069\u65af<\/span>\uff08Michael Kearns\uff09<\/span>\u548c\u83b1\u65af\u5229\u00b7\u74e6\u5229\u5b89\u7279<\/span>\uff08Leslie Valiant\uff09<\/span>\u57281994\u5e74<\/span><\/span>\u8bc1\u660e[24]\uff0c<\/span>\u5982\u679c\u53ef\u4ee5\u5b66\u4e60\u5230\u6700\u5c0f\u7684\u56de\u8def\uff0c\u751a\u81f3\u53ea\u662f\u5b66\u5230\u4e86\u6700\u5c0f\u7684\u6709\u754c\u5c42\u7684\u795e\u7ecf\u7f51\u7edc\uff0c\u90a3\u4e48\u5b83\u4eec\u5c31\u53ef\u4ee5\u88ab\u7528\u6765\u5206\u89e3\u8d28\u56e0\u6570\u5e76\u7834\u89e3\u516c\u94a5\u52a0\u5bc6\u7cfb\u7edf\u3002\u800c\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u8fd8\u4ece\u672a\u6210\u529f\u7834\u89e3\u8fc7\u52a0\u5bc6\u534f\u8bae\uff0c\u4e0d\u8fc7\u4e5f\u6ca1\u6709\u4eba\u671f\u671b\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u53ef\u4ee5\u6210\u529f\u3002<\/span><\/section>\n

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\u4e3a\u4ec0\u4e48\u6211\u4eec\u5728\u8bb8\u591a\u5176\u4ed6NP\u95ee\u9898\u53d6\u5f97\u4e86\u8fdb\u5c55\uff0c\u800c\u52a0\u5bc6\u7cfb\u7edf\u4ecd\u53ef\u4ee5\u8868\u73b0\u826f\u597d\uff1f\u5728\u5bc6\u7801\u5b66\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u9009\u62e9\u95ee\u9898\uff0c\u7279\u522b\u662f\u53ef\u4ee5\u5c06\u5176\u8bbe\u8ba1\u6210\u96be\u4ee5\u8ba1\u7b97\u5e76\u53ef\u88ab\u5e7f\u4e3a\u6d4b\u8bd5\u7684\u3002\u800c\u5176\u4ed6\u7684NP\u95ee\u9898\u901a\u5e38\u6765\u81ea\u5e94\u7528\u95ee\u9898\u6216\u81ea\u7136\u754c\u3002\u5b83\u4eec\u5f80\u5f80\u4e0d\u662f\u6700\u56f0\u96be\u7684\uff0c\u4e5f\u66f4\u5bb9\u6613\u6298\u670d\u4e8e\u5f53\u4e0b\u6280\u672f\u3002<\/span><\/section>\n

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\u91cf\u5b50\u8ba1\u7b97\u4f3c\u4e4e\u5a01\u80c1\u7740\u5f53\u4e0b\u4fdd\u62a4\u6211\u4eec\u4e92\u8054\u7f51\u4ea4\u6613\u7684\u516c\u94a5\u52a0\u5bc6\u534f\u8bae\u3002\u79c0\u5c14\u7b97\u6cd5<\/span>\uff08Shor\u2019s algorithm\uff09<\/span><\/span>[34]\u53ef\u4ee5<\/span>\u8fdb\u884c\u8d28\u56e0\u6570\u5206\u89e3\u4e0e\u5176\u4ed6\u6570\u8bba\u8ba1\u7b97\u3002\u8fd9\u79cd\u5fe7\u8651\u53ef\u4ee5\u901a\u8fc7\u51e0\u79cd\u65b9\u5f0f\u6765\u7f13\u548c\u3002\u5c3d\u7ba1\u91cf\u5b50\u8ba1\u7b97\u53d6\u5f97\u4e86\u4e00\u4e9b\u4ee4\u4eba\u5370\u8c61\u6df1\u523b\u7684\u8fdb\u5c55\uff0c\u4f46\u8981\u5f00\u53d1\u51fa\u80fd\u5904\u7406\u8db3\u591f\u591a\u7ea0\u7f20\u6bd4\u7279\u7684\u91cf\u5b50\u8ba1\u7b97\u673a\uff0c\u4ece\u800c<\/span>\u5728\u4e00\u5b9a\u89c4\u6a21\u4e0a\u5b9e\u73b0\u79c0\u5c14\u7b97\u6cd5\uff0c\u6211\u4eec\u53ef\u80fd\u4ecd\u9700\u8981\u51e0\u5341\u5e74\u751a\u81f3\u51e0\u4e2a\u4e16\u7eaa\u7684\u65f6\u95f4\u3002\u6b64\u5916\uff0c\u7814\u7a76\u8005\u4eec\u4e5f\u5728\u5f00\u53d1\u53ef\u62b5\u6297\u91cf\u5b50\u653b\u51fb\u7684\u516c\u94a5\u5bc6\u7801\u7cfb\u7edf\u5e76\u53d6\u5f97\u4e86\u4e00\u5b9a\u7684\u8fdb\u5c55\u3002\u66f4\u591a\u91cf\u5b50\u8ba1\u7b97\u5185\u5bb9\u6211\u4eec\u5c06\u5728\u540e\u6587\u8be6\u7ec6\u8ba8\u8bba\u3002<\/span><\/span><\/section>\n

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\u6211\u4eec\u4e0d\u77e5\u9053\u56e0\u5f0f\u5206\u89e3\u95ee\u9898\u662f\u5426\u662fNP\u5b8c\u5907\u7684\uff0c\u6240\u4ee5\u5373\u4fbf\u6211\u4eec\u6ca1\u6709\u5927\u89c4\u6a21\u7684\u91cf\u5b50\u8ba1\u7b97\u673a\uff0c\u6570\u5b66\u4e0a\u7684\u7a81\u7834\u4e5f\u6709\u53ef\u80fd\u4f1a\u5e26\u6765\u9ad8\u6548\u7684\u7b97\u6cd5\u3002\u4f46\u65e0\u8bba\u4f60\u5bf9\u91cf\u5b50\u9886\u57df\u7684\u672a\u6765\u6709\u4ec0\u4e48\u6837\u7684\u770b\u6cd5\uff0c\u5982\u679c\u62e5\u6709\u591a\u79cd\u65b9\u6cd5\u6765\u4f18\u5316\u516c\u94a5\u52a0\u5bc6\u7cfb\u7edf\uff0c\u5b83\u4eec\u53ef\u80fd\u90fd\u4f1a\u6d3e\u4e0a\u7528\u573a\u3002<\/span><\/section>\n

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\u5982\u6469\u64e6\u529b\u822c\u7684\u590d\u6742\u6027<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u6211\u4eec\u53ef\u4ee5\u4ece\u8ba1\u7b97\u590d\u6742\u6027\u4e2d\u83b7\u5f97\u4ec0\u4e48\uff1f\u6b64\u65f6\uff0c\u5bc6\u7801\u5b66\u53ef\u80fd\u4f1a\u4ece\u4f60\u7684\u8111\u6d77\u6d6e\u73b0\u3002\u4f46\u6216\u8bb8\u5c31\u50cf\u5b58\u5728\u6469\u64e6\u529b\u4e00\u6837\uff0c\u5b87\u5b99\u4f7f\u5f97\u67d0\u4e9b\u8ba1\u7b97\u5f88\u56f0\u96be\u662f\u6709\u539f\u56e0\u7684\u3002\u5728\u7269\u7406\u4e16\u754c\u4e2d\uff0c\u514b\u670d\u6469\u64e6\u529b\u901a\u5e38\u4ee5\u6d88\u8017\u80fd\u91cf\u4e3a\u4ee3\u4ef7\uff0c\u4f46\u662f\u5982\u679c\u6ca1\u6709\u6469\u64e6\u529b\uff0c\u6211\u4eec\u5bf8\u6b65\u96be\u884c\u3002\u5728\u8ba1\u7b97\u4e16\u754c\u4e2d\uff0c\u9519\u7efc\u590d\u6742\u7684\u8ba1\u7b97\u4e00\u822c\u4f1a\u4f7f\u8ba1\u7b97\u8fc7\u7a0b\u7f13\u6162\u800c\u4f4e\u6548\uff0c\u4f46\u5982\u679c\u6ca1\u6709\u590d\u6742\u6027\uff0c\u5c31\u50cf\u6ca1\u6709\u6469\u64e6\u529b\u4e00\u6837\uff0c\u6211\u4eec\u4e5f\u4f1a\u6709\u5f88\u591a\u5176\u4ed6\u7684\u95ee\u9898\u3002\u800cP=NP\u5728\u5f88\u591a\u60c5\u51b5\u4e0b\uff0c\u4f1a\u8ba9\u6211\u4eec\u6d88\u9664\u201c\u6469\u64e6\u529b\u201d\u3002<\/span><\/section>\n

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\u8ba1\u7b97\u9886\u57df\u7684\u6700\u65b0\u8fdb\u5c55\u8868\u660e\uff0c\u6d88\u9664\u201c\u6469\u64e6\u529b\u201d\u6709\u65f6\u4f1a\u4ea7\u751f\u8d1f\u9762\u5f71\u54cd\u3002\u4f8b\u5982\u4eba\u4eec\u4e0d\u80fd\u76f4\u63a5\u9605\u8bfb\u522b\u4eba\u601d\u60f3\uff0c\u53ea\u80fd\u770b\u5230\u5176\u91c7\u53d6\u7684\u884c\u52a8\u3002\u7ecf\u6d4e\u5b66\u5bb6\u6709\u4e00\u4e2a\u672f\u8bed\uff0c\u201c\u504f\u597d\u63ed\u793a\u201d<\/span>\uff08preference revelation\uff09<\/span>\uff0c\u65e8\u5728\u6839\u636e\u4eba\u4eec\u7684\u884c\u4e3a\u6765\u786e\u5b9a\u5176\u504f\u597d\u3002\u5728\u8fc7\u53bb\uff0c\u7531\u4e8e\u7f3a\u4e4f\u6570\u636e\u4e0e\u8db3\u591f\u7684\u7b97\u529b\uff0c\u8fd9\u4e00\u9886\u57df\u4e00\u76f4\u88ab\u8ba4\u4e3a\u6700\u591a\u53ea\u662f\u975e\u5e38\u4e0d\u7cbe\u786e\u7684\u4e00\u79cd\u827a\u672f\u3002<\/span><\/span><\/section>\n

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\u800c\u5982\u4eca\uff0c\u6211\u4eec\u5df2\u7ecf\u6536\u96c6\u5230\u4e86\u76f8\u5f53\u53ef\u89c2\u7684\u6570\u636e\u2014\u2014\u6765\u81ea\u4eba\u4eec\u7684\u7f51\u7edc\u641c\u7d22\u3001\u76f8\u7247\u4e0e\u89c6\u9891\u3001\u7f51\u8d2d\u8bb0\u5f55\u3001\u865a\u62df\u4e0e\u73b0\u5b9e\u4e16\u754c\u4e2d\u7684\u8bbf\u95ee\u8bb0\u5f55\u3001\u793e\u4ea4\u5a92\u4f53\u4e0a\u7684\u6d3b\u52a8\u7b49\u7b49\u3002\u800c\u4e14\uff0c\u673a\u5668\u5b66\u4e60\u53ef\u4ee5\u5904\u7406\u8fd9\u4e9b\u5e9e\u6742\u7684\u4fe1\u606f\uff0c\u5e76\u5bf9\u4eba\u4eec\u7684\u884c\u4e3a\u505a\u51fa\u5f02\u5e38\u7cbe\u786e\u7684\u9884\u6d4b\u3002\u5982\u4eca\uff0c\u8ba1\u7b97\u673a\u6bd4\u6211\u4eec\u66f4\u4e86\u89e3\u6211\u4eec\u81ea\u5df1\u3002<\/span><\/section>\n

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\u8ba1\u7b97\u4e0a\u7684\u201c\u6469\u64e6\u529b\u201d\u4e0d\u4ec5\u4f53\u73b0\u5728\u9690\u79c1\u8fd9\u4e00\u65b9\u9762\u3002\u57281978\u5e74\uff0c\u7f8e\u56fd\u653f\u5e9c\u89e3\u9664\u4e86\u5bf9\u822a\u7a7a\u516c\u53f8\u7684\u5b9a\u4ef7\u7ba1\u5236\uff0c\u4f46\u5982\u679c\u60f3\u8981\u627e\u5230\u4e00\u6761\u822a\u7ebf\u7684\u6700\u4f73\u4ef7\u683c\uff0c\u4eba\u4eec\u5f80\u5f80\u9700\u8981\u7ed9\u591a\u5bb6\u822a\u7a7a\u516c\u53f8\u6253\u7535\u8bdd\u54a8\u8be2\uff0c\u6216\u8005\u901a\u8fc7\u65c5\u884c\u793e\u4ee3\u7406\u8d2d\u7968\uff0c\u5f53\u7136\u65c5\u884c\u793e\u4e5f\u5e76\u4e0d\u603b\u662f\u6709\u52a8\u529b\u53bb\u5bfb\u627e\u6700\u4f4e\u7684\u4ef7\u683c\u3002\u56e0\u6b64\u822a\u7a7a\u516c\u53f8\u81f4\u529b\u4e8e\u6253\u9020\u58f0\u8a89\uff0c\u4e00\u4e9b\u516c\u53f8\u4fa7\u91cd\u4f18\u8d28\u7684\u670d\u52a1\uff0c\u53e6\u4e00\u4e9b\u516c\u53f8\u53ef\u4ee5\u63d0\u4f9b\u66f4\u4f4e\u7684\u4ef7\u683c\u3002\u4eca\u5929\uff0c\u6211\u4eec\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u627e\u5230\u6700\u4fbf\u5b9c\u7684\u822a\u73ed\uff0c\u56e0\u6b64\u822a\u7a7a\u516c\u53f8\u5728\u4ef7\u683c\u8fd9\u4e2a\u5355\u4e00\u7ef4\u5ea6\u4e0a\u6295\u5165\u4e86\u76f8\u5f53\u5927\u7684\u52aa\u529b\uff0c\u4ed6\u4eec\u901a\u8fc7\u8ba1\u7b97\u4f18\u5316\u5b9a\u4ef7\u5e76\u4ee5\u727a\u7272\u98de\u884c\u4f53\u9a8c\u7684\u4ee3\u4ef7\u6765\u5b89\u6392\u5ea7\u4f4d\u3002<\/span><\/section>\n

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\u8fd9\u79cd\u201c\u6469\u64e6\u529b\u201d\u5728\u4ee5\u524d\u4e5f\u6709\u52a9\u4e8e\u6253\u51fb\u5b66\u751f\u7684\u4f5c\u5f0a\u884c\u4e3a\u3002\u5728\u4e0a\u4e16\u7eaa80\u5e74\u4ee3\uff0c\u6211\u8bfb\u5927\u5b66\u65f6\u5fc5\u987b\u8ba1\u7b97\u4f5c\u7b54\u7684\u5fae\u79ef\u5206\u95ee\u9898\uff0c\u73b0\u5728\u5df2\u7ecf\u53ef\u4ee5\u88abMathematica\u8f6f\u4ef6\u8f7b\u677e\u89e3\u51b3\u3002\u5728\u6211\u7684\u5165\u95e8\u7406\u8bba\u8bfe\u7a0b\u4e2d\uff0c\u6211\u5728\u4e3a\u5b66\u751f\u51c6\u5907\u4f5c\u4e1a\u4e0e\u8003\u9898\u7684\u65f6\u5019\u9047\u5230\u4e86\u9ebb\u70e6\u2014\u2014\u7b54\u6848\u90fd\u53ef\u4ee5\u5728\u7f51\u4e0a\u627e\u5230\u3002\u968f\u7740GPT-3\u548c\u5176\u540e\u7eed\u7248\u672c\u80fd\u529b\u65e5\u76ca\u5f3a\u5927\uff0c\u751a\u81f3\u8fde\u8bba\u6587\u4e0e\u4ee3\u7801\u90fd\u53ef\u4ee5\u81ea\u52a8\u751f\u6210\uff0c\u5982\u679cGPT\u8fd9\u7c7b\u7684\u5de5\u5177\u5df2\u7ecf\u53ef\u4ee5\u89e3\u51b3\u5bf9\u4e8e\u5b66\u751f\u6765\u8bf4\u6700\u590d\u6742\u7684\u95ee\u9898\uff0c\u6211\u4eec\u8981\u5982\u4f55\u6fc0\u53d1\u5b66\u751f\uff1f<\/span><\/section>\n

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\u4ee5\u4e0a\u63d0\u5230\u7684\u8fd9\u4e9b\u53ea\u662f\u8bb8\u591a\u53ef\u80fd\u7684\u573a\u666f\u4e2d\u7684\u4e00\u5c0f\u90e8\u5206\u3002\u4f5c\u4e3a\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\uff0c\u6211\u4eec\u7684\u76ee\u6807\u662f\u4f7f\u8ba1\u7b97\u5c3d\u53ef\u80fd\u7684\u9ad8\u6548\u548c\u7b80\u5355\uff0c\u4f46\u6211\u4eec\u4e5f\u5fc5\u987b\u7262\u8bb0\u51cf\u5c11\u201c\u6469\u64e6\u529b\u201d\u7684\u4ee3\u4ef7\u3002<\/span><\/section>\n

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2019\u5e74\uff0c\u8c37<\/span>\u6b4c[1]\u5ba3\u5e03<\/span>\u5176\u4f7f\u7528\u4e86\u4e00\u53f0\u62e5\u670953\u4e2a\u91cf\u5b50\u6bd4\u7279\u7684\u91cf\u5b50\u8ba1\u7b97\u673a\u5b9e\u73b0\u4e86\u201c\u91cf\u5b50\u9065\u9065\u9886\u5148\u201d\uff0c\u89e3\u51b3\u4e86\u5f53\u524d\u4f20\u7edf\u8ba1\u7b97\u65e0\u6cd5\u89e3\u51b3\u7684\u8ba1\u7b97\u4efb\u52a1\u3002\u5c3d\u7ba1\u6709\u4e9b\u4eba\u8d28\u7591\u8fd9\u4e00\u8bf4\u6cd5\uff0c\u4f46\u6211\u4eec\u786e\u5b9e\u6b63\u5904\u5728\u91cf\u5b50\u8ba1\u7b97\u65b0\u65f6\u4ee3\u7684\u8fb9\u7f18\u3002\u7136\u800c\u6211\u4eec\u8fd8\u8fdc\u6ca1\u6709\u8fbe\u5230\u5b9e\u73b0\u76ae\u7279\u00b7\u79c0\u5c14<\/span>\uff08Peter Shor\uff09<\/span>\u7b97<\/span><\/span>\u6cd5[34]\u6240<\/span>\u9700\u8981\u7684\u6570\u4e07\u4e2a\u91cf\u5b50\u6bd4\u7279\u7684\u6c34\u5e73\uff0c\u4ece\u800c\u89e3\u51b3\u5f53\u4eca\u8ba1\u7b97\u673a\u8ba1\u7b97\u8d28\u56e0\u6570\u5206\u89e3\u95ee\u9898\u3002\u901a\u5e38\u6765\u8bf4\uff0c\u91cf\u5b50\u8ba1\u7b97\u88ab\u63cf\u8ff0\u4e3a\u7531\u6bd4\u7279\u8868\u793a\u7684\u72b6\u6001\u6570\uff0c\u6bd4\u598253\u91cf\u5b50\u6bd4\u7279\u7684\u673a\u5668\u6709253<\/sup>\u4e2a\u72b6\u6001\u3002\u8fd9\u4f3c\u4e4e\u8868\u660e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u91cf\u5b50\u8ba1\u7b97\u901a\u8fc7\u521b\u5efa\u8db3\u591f\u591a\u7684\u72b6\u6001\u6765\u89e3\u51b3NP\u5b8c\u5168\u95ee\u9898\u2014\u2014\u4f8b\u5982\uff0c\u5728\u4e00\u4e2a\u56fe\u7ed3\u6784\u4e2d\uff0c\u68c0\u9a8c\u6240\u6709\u53ef\u80fd\u6ee1\u8db3\u6761\u4ef6\u7684\u56e2\u4f53\u3002\u53ef\u60dc\u7684\u662f\uff0c\u91cf\u5b50\u7b97\u6cd5\u64cd\u63a7\u8fd9\u4e9b\u72b6\u6001\u662f\u53d7\u9650\u7684\uff0c\u800c\u4e14\u6240\u6709\u7684\u8bc1\u636e\u90fd\u8868\u660e\uff0c\u9664\u4e86\u7531\u683c\u7f57\u5f17<\/span>\uff08Grover\uff09<\/span>\u7b97<\/span><\/span>\u6cd5[18]\u7ed9<\/span>\u51fa\u7684\u4e8c\u6b21\u52a0\u901f\u6539\u5584\uff0c\u91cf\u5b50\u8ba1\u7b97\u673a\u65e0\u6cd5\u89e3\u51b3NP\u5b8c\u5907\u95ee<\/span>\u9898[3]<\/span>\u3002<\/span><\/section>\n

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\u5df4\u62dc\u7684\u8bc1\u660e\u662f\u4e00\u4efd\u5c06\u7ec4\u5408\u5b66\u4e0e\u7fa4\u8bba\u7ed3\u5408\u7684\u6770\u51fa\u5de5\u4f5c\u3002\u5c3d\u7ba1\u8ba9\u7b97\u6cd5\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u8fd0\u884c\u7ed3\u675f\u4ecd\u9700\u8981\u5f88\u591a\u65b0\u7684\u7a81\u7834\uff0c\u4f46\u5df4\u62dc\u7ed9\u51fa\u4e86\u4e00\u4e2a\u91cd\u8981\u7684\u7406\u8bba\u7ed3\u679c\uff0c\u662fP\u4e0eNP\u5b8c\u5907\u4e4b\u95f4\u6700\u91cd\u8981\u95ee\u9898\u4e4b\u4e00\u7684\u91cd\u5927\u8fdb\u5c55\u3002<\/span><\/section>\n

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\u7535\u8def\u8bbe\u8ba1\uff1a<\/strong>\u5982\u679c\u5728\u5b8c\u5907\u7684\u57fa<\/span>\uff08\u4e0e\u95e8\u3001\u6216\u95e8\u3001\u975e\u95e8\uff09<\/span>\u4e0b\uff0c\u5c0f\u578b\u7535\u8def\u4e0d\u80fd\u6c42\u89e3NP\u95ee\u9898\uff0c\u5219P\u2260NP\u3002\u867d\u7136\u4e0a\u4e16\u7eaa80\u5e74\u4ee3\u6709\u5f88\u591a\u5173\u4e8e\u7535\u8def\u590d\u6742\u5ea6\u7684\u7814\u7a76\u6210\u679c\u95ee\u4e16\uff0c\u4f46\u5b83\u4eec\u90fd\u6ca1\u80fd\u63a5\u8fd1\u4e8e\u8bc1\u660eP\u2260<\/span>NP\u30022009\u5e74\u7684\u7efc\u8ff0\u6587\u7ae0\u6307\u51fa\uff0c\u5728\u6b64\u524d\u768420\u5e74\u91cc\uff0c\u7535\u8def\u590d\u6742\u6027\u9886\u57df\u6ca1\u6709\u53d6\u5f97\u65b0\u7684\u91cd\u5927\u6210\u679c\u3002\u8fd9\u79cd\u60c5\u51b5\u4e00\u76f4\u6301\u7eed\u52302010\u5e74\u30021987\u5e74\uff0c\u62c9\u5179\u6ce2\u6d1b\u592b<\/span>\uff08Razborov\uff09<\/span><\/span>[32]\u548c<\/span>\u65af\u83ab\u4f26\u65af\u57fa<\/span>\uff08Smolensky\uff09<\/span><\/span>[36]\u8bc1\u660e<\/span>\u4e86\u5bf9\u4e8e\u56fa\u5b9a\u7d20\u6570p\u5bf9\u5e94\u7684\u5e38\u6570\u6df1\u5ea6\u7535\u8def\u2014\u2014\u7531\u53d6\u4f59\u7535\u8def<\/span>\uff08Modp<\/sub>\uff09<\/span>\u3001\u4e0e\u95e8\u3001\u6216\u95e8\u3001\u975e\u95e8\u7535\u8def\u7ec4\u6210\u2014\u2014\u662f\u4e0d\u53ef\u80fd\u8ba1\u7b97\u5927\u591a\u6570\u51fd\u6570\u7684\u3002\u4e0d\u8fc7\uff0c\u5982\u679c\u662f\u67096\u5bf9\u5e94\u7684\u53d6\u4f59\u7535\u8def\uff08Mod6<\/sub>\uff09<\/span>\uff0c\u5b58\u5728\u5c11\u91cf\u7684\u4e00\u4e9b\u8bc1\u660e\u5de5\u4f5c\u3002\u4f46\u5373\u4f7f\u662f\u8bc1\u660eNEXP<\/span>\uff08\u4e00\u79cdNP\u7684\u6307\u6570\u65f6\u95f4\u7248\u672c\uff09<\/span>\u4e0d\u80fd\u88ab\u5e38\u6570\u6df1\u5ea6\u7684\u3001\u7531\u4e0e\u6216\u975e\u95e8\u7535\u8def\u4ee5\u53ca6\u5bf9\u5e94\u7684\u53d6\u4f59\u7535\u8def\u7ec4\u6210\u7684\u5c0f\u578b\u7535\u8def\u8ba1\u7b97\u8fd9\u4e00\u95ee\u9898\uff0c\u5176\u4ecd\u5728\u51e0\u5341\u5e74\u4e2d\u672a\u88ab\u89e3\u51b3\u3002\u56e0\u6b64\u5e38\u6570\u6df1\u5ea6\u7684\u7535\u8def\u88ab\u8ba4\u4e3a\u5728\u8ba1\u7b97\u4e0a\u80fd\u529b\u5f88\u5f31\u3002\u5728\u8fd9\u65b9\u9762\u5de5\u4f5c\u7684\u7f3a\u4e4f\u4e5f\u53cd\u6620\u4e86\u6211\u4eec\u5728\u9610\u91ca\u8ba1\u7b97\u6a21\u578b\u5c40\u9650\u6027\u8fd9\u4e00\u9886\u57df\u53d6\u5f97\u7684\u8fdb\u5c55\u5341\u5206\u6709\u9650\u3002<\/span><\/span><\/section>\n

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\u57282010\u5e74\uff0c\u745e\u6069\u00b7\u5a01\u5ec9\u59c6\u65af<\/span>\uff08Ryan Williams\uff09<\/span>[39]\u8bc1\u660e<\/span>\u4e86NEXP\u786e\u5b9e\u4e0d\u80fd\u88ab\u5e38\u6570\u6df1\u5ea6\u3001\u75316\u5bf9\u5e94\u7684\u53d6\u4f59\u7535\u8def\u6216\u4efb\u610f\u5176\u4ed6\u53d6\u4f59\u7535\u8def\u7684\u5c0f\u578b\u7535\u8def\u8ba1\u7b97\u6c42\u89e3\u3002\u4ed6\u6784\u9020\u4e86\u4e00\u79cd\u65b0\u6280\u672f\uff0c\u5e94\u7528\u4e86\u53ef\u6ee1\u8db3\u6027\u7b97\u6cd5\u3002\u8fd9\u79cd\u7b97\u6cd5\u6bd4\u5c1d\u8bd5\u6240\u6709\u8d4b\u503c\u5e76\u4f7f\u7528\u51e0\u79cd\u590d\u6742\u5de5\u5177\u6765\u83b7\u5f97\u4e0b\u754c\u8981\u597d\u4e00\u4e9b\u3002\u540e\u6765\uff0c\u5a01\u5ec9\u59c6\u65af\u548c\u4ed6\u7684\u5b66\u751f\u79d1\u8fea\u00b7\u9ed8\u91cc<\/span>\uff08Cody Murray\uff09<\/span><\/span>[29]\u5728<\/span>\u6b64\u7ed3\u679c\u4e0a\u66f4\u8fdb\u4e00\u6b65\uff0c\u8bc1\u660e\u4e86\u5373\u4fbf\u662f\u4e0d\u786e\u5b9a\u7684\u62df\u591a\u9879\u5f0f\u65f6\u95f4\u7684\u7b97\u6cd5\uff0c\u4e5f\u4e0d\u5b58\u5728\u5bf9\u5e94\u7684\u5e38\u6570\u6df1\u5ea6\u7684\u3001\u5e26\u6709\u56fa\u5b9am\u5bf9\u5e94\u7684\u53d6\u4f59\u7535\u8def\uff08Modm<\/sub>\uff09<\/span>\u7684\u5c0f\u578b\u7535\u8def\u3002\u7136\u800c\u8bc1\u660e\u4e0d\u5b58\u5728\u4efb\u610f\u6df1\u5ea6\u7684\u5c0f\u578b\u7535\u8def\u53ef\u4ee5\u6c42\u89e3NP\u95ee\u9898<\/span>\uff08\u8fd9\u6b63\u662f\u8bc1\u660eP\u2260NP\u6240\u9700\u8981\u7684\uff09<\/span>\u4ecd\u7136\u9065\u4e0d\u53ef\u53ca\u3002<\/span><\/span><\/section>\n

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\u590d\u6742\u6027\u7684\u53cd\u51fb\uff1a<\/strong>\u57282009\u5e74\u7684\u7efc\u8ff0\u6587\u7ae0\u4e2d\uff0c\u6709\u4e00\u8282\u9898\u4e3a\u201c<\/span>\u65b0\u5e0c\u671b\u201d[13]\u3002<\/span>\u5728\u8fd9\u4e00\u8282\u4e2d\uff0c\u6211\u4eec\u57fa\u4e8e\u514b\u5766\u00b7\u7a46\u7a46\u5229<\/span>\uff08Ketan Mulmuley\uff09<\/span>\u548c\u7c73\u6797\u5fb7\u00b7\u7d22\u970d\u5c3c<\/span>\uff08Milind Sohoni\uff09<\/span>\u63d0\u51fa\u7684\u4ee3\u6570\u51e0\u4f55\u4e0e\u8868\u793a\u7406\u8bba\uff0c\u8ba8\u8bba\u4e86\u4e00\u79cd\u65b0\u7684\u51e0\u4f55\u590d\u6742\u6027\u7406\u8bba\u6765\u653b\u7834P\/NP\u95ee\u9898\u3002\u7b80\u800c\u8a00\u4e4b\uff0c\u7a46\u7a46\u5229\u548c\u7d22\u970d\u5c3c\u8bd5\u56fe\u6784\u9020\u9ad8\u7ef4\u591a\u8fb9\u5f62\uff0c\u4ee5\u4f53\u73b0\u4ee3\u6570\u5f62\u5f0f\u7684NP\u95ee\u9898\u7684\u6027\u8d28\uff0c\u5e76\u8868\u660e\u5b83\u5177\u6709\u4efb\u610f\u4e0eP\u95ee\u9898\u7684\u4ee3\u6570\u6027\u8d28\u76f8\u5bf9\u5e94\u591a\u8fb9\u5f62\u4e0d\u540c\u7684\u6027\u8d28\u3002\u4ed6\u4eec\u7684\u731c\u60f3\u4e4b\u4e00\u662f\u8ba4\u4e3a\u591a\u8fb9\u5f62\u5305\u542b\u67d0\u79cd\u8868\u793a\u8bba\u7684\u7ed3\u6784\u3002\u7136\u800c\u57282016\u5e74\uff0c\u5f7c\u5f97\u00b7\u5e03\u5c14\u5409\u745f<\/span>\uff08Peter B\u00fcrgisser\uff09<\/span>\uff0c\u514b\u91cc\u65af\u8482\u5b89\u00b7\u827e\u80af\u8fc8\u5c14<\/span>\uff08Christian Ikenmeyer\uff09<\/span>\uff0c\u548c\u683c\u857e\u5854\u00b7\u5e15\u8bfa\u5a03<\/span>\uff08Greta Panova\uff09<\/span><\/span>[6]\u8bc1<\/span>\u660e\u8fd9\u79cd\u65b9\u6cd5\u4e0d\u4f1a\u6210\u529f\u3002<\/span><\/section>\n

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\u5c3d\u7ba1\u5e03\u5c14\u5409\u745f\u3001\u827e\u80af\u8fc8\u5c14\u3001\u4e0e\u5e15\u8bfa\u5a03\u7684\u5de5\u4f5c\u5426\u5b9a\u4e86\u51e0\u4f55\u590d\u6742\u6027\u7406\u8bba<\/span>\uff08GCT\uff09<\/span>\u533a\u5206P\u4e0eNP\u95ee\u9898\u7684\u53ef\u80fd\uff0c\u4eba\u4eec\u4ecd\u7136\u6709\u53ef\u80fd\u6839\u636e\u8868\u793a\u8bba\u7ed3\u6784\u7684\u6570\u91cf\u6784\u9020\u4e0d\u540c\u7684\u591a\u8fb9\u5f62\u3002\u53ea\u4e0d\u8fc7\u6211\u4eec\u4e0d\u518d\u5e94\u8be5\u671f\u5f85GCT\u7406\u8bba\u53ef\u4ee5\u5728\u4e0d\u4e45\u7684\u5c06\u6765\u89e3\u51b3P\/NP\u95ee\u9898\u3002<\/span><\/span><\/section>\n


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\u5f53\u6211\u4eec\u601d\u8003P\/NP\u95ee\u9898\u65f6\uff0c\u6211\u4eec\u53d1\u73b0\u5b83\u6709\u8bb8\u591a\u4e0d\u540c\u7684\u542b\u4e49\u3002P\/NP\u662f\u6b63\u5f0f\u5b9a\u4e49\u7684\u3001\u957f\u65f6\u95f4\u60ac\u800c\u672a\u51b3\u3001\u4ecd\u6709\u767e\u4e07\u7f8e\u5143\u60ac\u8d4f\u7684\u4e00\u4e2a\u6570\u5b66\u95ee\u9898\u3002\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u770b\u5230\u901a\u8fc7\u53ef\u8ba1\u7b97\u6027\u7406\u8bba\u3001\u7535\u8def\u8bbe\u8ba1\u3001\u8bc1\u660e\u548c\u4ee3\u6570\u51e0\u4f55\u7b49\u5de5\u5177\u8bd5\u56fe\u89e3\u51b3P\/NP\u95ee\u9898\u7684\u52aa\u529b\u3002\u76ee\u524d\u6211\u4eec\u8fd8\u6ca1\u6709\u4e00\u79cd\u5f3a\u6709\u529b\u7684\u65b9\u6cd5\u89e3\u51b3P\/NP\u95ee\u9898\u3002\u751a\u81f3\u4ece\u67d0\u79cd\u610f\u4e49\u4e0a\u8bf4\uff0c\u6211\u4eec\u5230\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u7684\u8ddd\u79bb\u6bd4\u4ee5\u524d\u4efb\u4f55\u65f6\u5019\u90fd\u8981\u8fdc\u3002<\/span><\/section>\n

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\u8fd8\u6709\u4e00\u4e9bNP\u95ee\u9898\u662f\u6211\u4eec\u5e0c\u671b\u6216\u9700\u8981\u89e3\u51b3\u7684\u3002\u57281976\u5e74\u7684\u7ecf\u5178\u6587\u732e\u300a\u8ba1\u7b97\u673a\u4e0e\u96be\u89e3\u6027\uff1a\u4e00\u672cNP\u5b8c\u5907\u6027\u7406\u8bba\u7684\u6307<\/span>\u5357\u300b\u4e2d[16]<\/span>\uff0c\u52a0\u91cc<\/span>\uff08Garey\uff09<\/span>\u4e0e\u7ea6\u7ff0\u900a<\/span>\uff08Johnson\uff09<\/span>\u4e3e\u4e86\u4e00\u4e2a\u4f8b\u5b50\uff1a\u4e00\u4f4d\u5012\u9709\u7684\u5458\u5de5\u88ab\u8981\u6c42\u89e3\u51b3\u4e00\u4e2aNP\u5b8c\u5907\u7684\u4f18\u5316\u95ee\u9898\u3002\u6700\u540e\u8fd9\u4f4d\u5458\u5de5\u627e\u5230\u8001\u677f\u8bf4\uff1a\u201c\u6211\u627e\u4e0d\u5230\u4e00\u4e2a\u9ad8\u6548\u7684\u7b97\u6cd5\uff0c\u4f46\u8fd9\u4e16\u754c\u4e0a\u7684\u5929\u624d\u540d\u6d41\u4e5f\u4e00\u6837\u627e\u4e0d\u5230\u3002\u201c\u8a00\u5916\u4e4b\u610f\u662f\u8001\u677f\u4e0d\u5e94\u8be5\u89e3\u96c7\u8fd9\u4f4d\u5458\u5de5\uff0c\u56e0\u4e3a\u96c7\u4f63\u5176\u4ed6\u4eba\u4e5f\u65e0\u6cd5\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002<\/span><\/span><\/section>\n

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\u5728P\/NP\u95ee\u9898\u7684\u7814\u7a76\u65e9\u671f\uff0c\u6211\u4eec\u5c06NP\u5b8c\u5907\u6027\u770b\u4f5c\u4e00\u79cd\u969c\u788d\u2014\u2014\u8fd9\u4e9b\u95ee\u9898\u662f\u6211\u4eec\u65e0\u6cd5\u89e3\u51b3\u7684\u3002\u4f46\u968f\u7740\u8ba1\u7b97\u673a\u4e0e\u7b97\u6cd5\u7684\u53d1\u5c55\uff0c\u4eba\u4eec\u53d1\u73b0\u901a\u8fc7\u542f\u53d1\u5f0f\u7b97\u6cd5\u3001\u8fd1\u4f3c\u7b97\u6cd5\u548c\u66b4\u529b\u8ba1\u7b97\u7684\u7ed3\u5408\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u5728NP\u95ee\u9898\u4e0a\u53d6\u5f97\u8fdb\u5c55\u3002\u5728\u52a0\u91cc\u548c\u7ea6\u7ff0\u900a\u7684\u6545\u4e8b\u4e2d\uff0c\u5982\u679c\u6211\u662f\u8001\u677f\uff0c\u6211\u4e0d\u4f1a\u89e3\u96c7\u8fd9\u4f4d\u5458\u5de5\uff0c\u800c\u662f\u5efa\u8bae\u5c1d\u8bd5\u4f7f\u7528\u6df7\u5408\u6574\u6570\u89c4\u5212\u3001\u673a\u5668\u5b66\u4e60\u6216\u8005\u66b4\u529b\u641c\u7d22\u7b49\u65b9\u6cd5\u3002NP\u5b8c\u5907\u610f\u5473\u7740\u4e0d\u53ef\u80fd\u7684\u65f6\u4ee3\u5df2\u7ecf\u8fc7\u53bb\u4e86\u3002\u73b0\u5728NP\u5b8c\u5907\u4ec5\u4ec5\u610f\u5473\u7740\u53ef\u80fd\u6ca1\u6709\u4e00\u79cd\u7b97\u6cd5\u53ef\u4ee5\u6c38\u8fdc\u6709\u6548\u548c\u53ef\u6269\u5c55\u3002<\/span><\/section>\n

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\u5728\u62112013\u5e74\u5173\u4e8eP\/NP\u95ee\u9898\u7684<\/span>\u4e66\u4e2d[14]\uff0c<\/span>\u6709\u4e00\u7ae0\u540d\u4e3a\u201c\u7f8e\u4e3d\u7684\u4e16\u754c\u201d\u3002\u5728\u8fd9\u4e00\u7ae0\u4e2d\uff0c\u6211\u60f3\u8c61\u4e86\u4e00\u4e2a\u7406\u60f3\u5316\u7684\u4e16\u754c\uff1a\u4e00\u4f4d\u6377\u514b\u6570\u5b66\u5bb6\u5728\u8fd9\u4e2a\u4e16\u754c\u4e2d\u8bc1\u660e\u4e86P=NP\uff0c\u4ece\u800c\u5f97\u51fa\u4e00\u4e2a\u5bf9\u4e8e\u6240\u6709\u7684NP\u95ee\u9898\u90fd\u975e\u5e38\u9ad8\u6548\u7684\u7b97\u6cd5\u3002\u5c3d\u7ba1\u6211\u4eec\u73b0\u5728\u6ca1\u6709\uff0c\u4e5f\u5f88\u53ef\u80fd\u6c38\u8fdc\u4e0d\u4f1a\u751f\u6d3b\u5728\u8fd9\u6837\u7406\u60f3\u7684\u4e16\u754c\uff0c\u4f46\u662f\u968f\u7740\u6211\u4eec\u5728\u8ba1\u7b97\u4e0a\u4e00\u6b65\u4e00\u6b65\u5730\u524d\u8fdb\uff0c\u6211\u4eec\u5df2\u7ecf\u5b9e\u73b0\u4e86\u5f88\u591a\u533b\u5b66\u8fdb\u6b65\uff0c\u6253\u9020\u51fa\u4e0e\u73b0\u5b9e\u96be\u4ee5\u533a\u5206\u7684\u865a\u62df\u4e16\u754c\uff0c\u53d1\u660e\u51fa\u521b\u9020\u65b0\u827a\u672f\u4f5c\u54c1\u7684\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\uff0cP=NP\u6240\u5e26\u6765\u7684\u7f8e\u5999\u6216\u6ca1\u90a3\u4e48\u7f8e\u5999\u7684\u7ed3\u679c\u4f3c\u4e4e\u4e0d\u518d\u9065\u4e0d\u53ef\u53ca\u3002<\/span><\/section>\n

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\u611f\u8c22\u4e54\u5e0c\u00b7\u683c\u7f57\u4e54\uff08Josh Grochow\uff09\u4e0e\u6211\u5bf9GCT\u95ee\u9898\u975e\u5e38\u6709\u5e2e\u52a9\u7684\u8ba8\u8bba\uff0c\u4ee5\u53ca\u5e93\u514b\u5141\u8bb8\u6211\u4eec\u4f7f\u7528\u76f8\u5173\u56fe\u7247\u3002\u540c\u6837\u611f\u8c22\u4e54\u5e0c\u4ee5\u53ca\u5ba1\u7a3f\u4eba\u5bf9\u4e8e\u672c\u6587\u7684\u5efa\u8bae\u4e0e\u5e2e\u52a9\u3002\u672c\u6587\u7684\u4e00\u4e9b\u6750\u6599\u6539\u7f16\u81ea\u4f5c\u8005\u7684\u535a\u5ba2\u3002<\/span><\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n


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[1] <\/span>Arute, F., Arya, K., Babbus, R., Bacon, D., Bardin, J.C., Barends, R., Biswas, R., Boxio, S., Brandao, F.G.S.L., Buell, D.A., et al. Quantum supremacy using a programmable superconducting processor. Nature 574, 7779 (2019), 505\u2013510. https:\/\/doi.org\/10.1038\/s41586-019-1666-5<\/span><\/span><\/p>\n

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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>
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\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/strong><\/section>\n
1. <\/strong>\u8ba1\u7b97\u590d\u6742\u6027\u7406\u8bba50\u5e74\uff1a\u4eceP\u4e0eNP\u95ee\u9898\u5230\u5143\u590d\u6742\u6027<\/a><\/strong><\/span><\/section>\n
2. <\/strong>\u65f6\u95f4\u3001\u4fe1\u606f\u4e0e\u4eba\u5de5\u667a\u80fd\uff1a\u4ece\u4fe1\u606f\u52a8\u529b\u5b66\u89d2\u5ea6\u770b\u5927\u6a21\u578b\u7684\u672a\u6765<\/a><\/strong><\/span><\/section>\n
3.<\/strong> \u4ec0\u4e48\u662fP\u95ee\u9898\u3001NP\u95ee\u9898\u548cNPC\u95ee\u9898\uff1f<\/a><\/strong><\/span><\/section>\n
4. <\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
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


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\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/strong><\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u5bfc\u8bed \u6838\u5fc3\u89c2\u70b9\uff1a 1. \u81f32021\u5e74\uff0cP\/NP\u95ee\u9898\u5df2\u7ecf50\u5c81\u4e86\uff0c\u4f46\u5176\u89e3\u51b3\u65b9\u6848\u4ecd\u9065\u4e0d\u53ef\u53ca\u3002\u5c3d\u7ba1\u7b97\u6cd5\u4e0e\u786c\u4ef6\u7684\u5353\u8d8a\u8fdb\u6b65\u4f7f\u6211\u4eec\u53ef\u4ee5\u89e3\u51b3\u8bb8\u591aNP\u5b8c\u5168\u95ee\u9898\uff0c\u4f46\u5728\u5bc6\u7801\u7cfb\u7edf\u7684\u7834\u89e3\u65b9\u9762\u4ecd\u8fdb\u5c55\u751a\u5fae\u3002 2. \u968f\u7740\u6211\u4eec\u6301\u7eed\u5730\u5728\u673a\u5668\u5b66\u4e60\u4ee5\u53ca\u4ee5\u6570\u636e\u4e3a\u4e2d\u5fc3\u7684\u8ba1\u7b97\u9886\u57df\u53d6\u5f97\u6fc0\u52a8\u4eba\u5fc3\u7684\u8fdb\u6b65\uff0cP\/NP\u95ee\u9898\u5411\u6211\u4eec\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5b9d\u8d35\u7684\u89c6\u89d2\uff0c\u53bb\u4e86…<\/p>\n","protected":false},"author":0,"featured_media":51021,"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\/51026"}],"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=51026"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/51026\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/51021"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=51026"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=51026"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=51026"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=51026"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}