{"id":31024,"date":"2021-12-15T20:38:04","date_gmt":"2021-12-15T12:38:04","guid":{"rendered":"https:\/\/swarma.org\/?p=31024"},"modified":"2021-12-15T20:38:04","modified_gmt":"2021-12-15T12:38:04","slug":"%e8%bf%9e%e6%8e%a5%e5%9b%be%e8%ae%ba%e5%92%8c%e4%bf%a1%e6%81%af%e8%ae%ba%ef%bc%8c%e9%ab%98%e7%bb%b4%e6%89%a9%e5%b1%95%e5%9b%be%e5%b8%ae%e5%8a%a9%e5%88%9b%e9%80%a0%e7%90%86%e6%83%b3%e7%bc%96%e7%a0%81","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=31024","title":{"rendered":"\u8fde\u63a5\u56fe\u8bba\u548c\u4fe1\u606f\u8bba\uff0c\u9ad8\u7ef4\u6269\u5c55\u56fe\u5e2e\u52a9\u521b\u9020\u7406\u60f3\u7f16\u7801"},"content":{"rendered":"
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<\/strong>\u4fe1\u606f\u4f20\u8f93\u4e0d\u53ef\u907f\u514d\u4f1a\u53d7\u5230\u5916\u90e8\u7684\u5e72\u6270\u7834\u574f\uff0c\u6211\u4eec\u662f\u5426\u53ef\u4ee5\u7f16\u7801\u4fe1\u606f\uff0c\u4f7f\u5f97\u63a5\u6536\u8005\u5728\u9605\u8bfb\u4e4b\u524d\u5c31\u80fd\u4e00\u773c\u8bc6\u522b\u4fe1\u606f\u662f\u5426\u88ab\u7be1\u6539\uff1f\u5728\u4e00\u9879\u6700\u65b0\u7814\u7a76\u4e2d\uff0c\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u548c\u6570\u5b66\u5bb6\u901a\u8fc7\u5c06\u6269\u5c55\u56fe\u63a8\u5e7f\u5230\u9ad8\u7ef4\u5f62\u5f0f\u6765\u8868\u793a\u7f16\u7801\uff0c\u4f7f\u4e4b\u5177\u6709\u7a00\u758f\u6027\u3001\u5173\u8054\u6027\uff0c\u548c\u4e30\u5bcc\u7684\u5c40\u90e8\u7ed3\u6784\u3002\u5bf9\u56fe\u4e2d\u4e00\u4e2a\u8282\u70b9\u8fdb\u884c\u6d4b\u8bd5\uff0c\u5c31\u53ef\u4ee5\u7ed9\u51fa\u8fdc\u5904\u8282\u70b9\u7684\u9519\u8bef\u4fe1\u606f\uff0c\u4ece\u800c\u5b9e\u73b0\u5c40\u90e8\u53ef\u6d4b\u8bd5\u6027\u3002\u8fd9\u662f\u4e00\u79cd\u65b0\u7684\u4fe1\u606f\u7f16\u7801\u65b9\u5f0f\uff0c\u8d85\u8d8a\u4e86\u4f20\u7edf\u4f9d\u9760\u968f\u673a\u6027\u7684\u7f16\u7801\uff0c\u786e\u7acb\u4e86\u7ea0\u9519\u7801\u7684\u6700\u65b0\u6280\u672f\u6c34\u5e73\u3002<\/strong><\/p>\n


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\u7814\u7a76\u9886\u57df\uff1a\u4fe1\u606f\u7f16\u7801\uff0c\u56fe\u8bba\uff0c\u4fe1\u606f\u8bba<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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Mordechai Rorvig<\/span> | \u4f5c\u8005<\/strong><\/span><\/p>\n

\u6f58\u4f73\u680b<\/span> | <\/strong><\/span>\u8bd1\u8005<\/strong><\/span><\/p>\n

\u6881\u91d1<\/span> | \u5ba1\u6821<\/strong><\/span><\/strong><\/span><\/p>\n

\u9093\u4e00\u96ea<\/span> | \u7f16\u8f91<\/strong><\/span><\/p>\n<\/section>\n


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\u5047\u8bbe\u4f60\u6b63\u8bd5\u56fe\u4f20\u8f93\u4fe1\u606f\u3002\u8ba1\u7b97\u673a\u5c06\u6bcf\u4e2a\u5b57\u7b26\u8f6c\u6362\u6210\u6bd4\u7279\uff0c\u5c06\u6bcf\u4e2a\u6bd4\u7279\u8f6c\u6362\u6210\u4fe1\u53f7\uff0c\u7136\u540e\u901a\u8fc7\u94dc\u5bfc\u7ebf\u3001\u5149\u7ea4\u6216\u7a7a\u6c14\u53d1\u9001\u3002\u5c3d\u7ba1\u4f60\u5c3d\u53ef\u80fd\u5730\u5c0f\u5fc3\u7ffc\u7ffc\uff0c\u4f46\u53e6\u4e00\u8fb9\u6536\u5230\u7684\u4fe1\u606f\u5c06\u4e0e\u4f60\u53d1\u9001\u7684\u4fe1\u606f\u4e0d\u4e00\u6837\uff0c\u566a\u58f0\u603b\u662f\u4f1a\u9020\u6210\u4e00\u4e9b\u7834\u574f\u3002<\/span><\/section>\n
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\u572820\u4e16\u7eaa40\u5e74\u4ee3\uff0c\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u9996\u6b21\u9762\u5bf9\u4e0d\u53ef\u907f\u514d\u7684\u566a\u58f0\u95ee\u9898\u3002\u4e94\u5341\u5e74\u540e\uff0c\u4ed6\u4eec\u60f3\u51fa\u4e86\u4e00\u4e2a\u4f18\u96c5\u7684\u65b9\u6cd5\u6765\u89e3\u51b3\u95ee\u9898\uff1a\u662f\u4e0d\u662f\u53ef\u4ee5\u5bf9\u4e00\u6761\u4fe1\u606f\u8fdb\u884c\u7f16\u7801\uff0c\u4f7f\u5f97\u5728\u6536\u4ef6\u4eba\u9605\u8bfb\u4e4b\u524d\u5c31\u80fd\u660e\u663e\u770b\u51fa\u4fe1\u606f\u662f\u5426\u88ab\u7be1\u6539\uff1f\u4eba\u4eec\u4e0d\u80fd\u901a\u8fc7\u4e00\u672c\u4e66\u7684\u5c01\u9762\u6765\u5224\u65ad\u91cc\u9762\u7684\u5185\u5bb9\uff0c\u4f46\u8fd9\u79cd\u7f16\u7801\u7684\u4fe1\u606f\u53ef\u4ee5\u3002<\/span><\/section>\n
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\u4ed6\u4eec\u5c06\u4fe1\u606f\u7684\u8fd9\u4e00\u7279\u6027\u79f0\u4e3a\u5c40\u90e8\u53ef\u6d4b\u8bd5\u6027<\/strong><\/span>\uff08local testability\uff09<\/span>\uff0c\u4eba\u4eec\u53ef\u4ee5\u5728\u5176\u4e2d\u4ec5\u4ec5\u51e0\u4e2a\u5730\u65b9\u5bf9\u4fe1\u606f\u8fdb\u884c\u8d85\u5feb\u901f\u6d4b\u8bd5\uff0c\u4ee5\u786e\u5b9a\u4fe1\u606f\u7684\u6b63\u786e\u6027\u3002\u5728\u63a5\u4e0b\u6765\u768430\u5e74\u91cc\uff0c\u7814\u7a76\u4eba\u5458\u5728\u521b\u5efa\u8fd9\u79cd\u6d4b\u8bd5\u65b9\u9762\u53d6\u5f97\u4e86\u5b9e\u8d28\u6027\u7684\u8fdb\u5c55\uff0c\u4f46\u4ed6\u4eec\u7684\u52aa\u529b\u603b\u662f\u6ca1\u6709\u56de\u62a5\u3002\u8bb8\u591a\u4eba\u8ba4\u4e3a\uff0c\u5c40\u90e8\u53ef\u6d4b\u8bd5\u6027\u5c06\u6c38\u8fdc\u4e0d\u4f1a\u4ee5\u5176\u7406\u60f3\u7684\u5f62\u5f0f\u5b9e\u73b0\u3002<\/span><\/section>\n
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\u572811\u67088\u65e5\u53d1\u5e03\u7684\u4e00\u4efd\u9884\u5370\u672c\u8bba\u6587[1]\u4e2d\uff0c\u4ee5\u8272\u5217\u9b4f\u5179\u66fc\u79d1\u5b66\u7814\u7a76\u6240\u7684\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u4f0a\u96f7\u7279\u00b7\u8fea\u52aa\u5c14<\/span>\uff08Irit Dinur\uff09<\/span>[2]\u548c\u8036\u8def\u6492\u51b7\u5e0c\u4f2f\u6765\u5927\u5b66\u7684\u56db\u4f4d\u6570\u5b66\u5bb6\u8c22\u00b7\u57c3\u5f17\u62c9<\/span>\uff08Shai Evra\uff09<\/span>[3]\u3001\u7f57\u6069\u00b7\u5229\u592b\u5185<\/span>\uff08Ron Livne\uff09<\/span>[4]\u3001\u4e9a\u5386\u514b\u65af\u00b7\u5362\u535a\u8328\u57fa<\/span>\uff08Alex Lubotzky\uff09<\/span>[5]\u548c\u6c99\u54c8\u5c14\u00b7\u83ab\u5179<\/span>\uff08Shahar Mozes\uff09<\/span>[6]\u627e\u5230\u4e86\u5b9e\u73b0\u5c40\u90e8\u53ef\u6d4b\u8bd5\u6027\u7684\u65b9\u6cd5\u3002<\/span><\/section>\n
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\u56fe1\uff1a\u9b4f\u8328\u66fc\u79d1\u5b66\u7814\u7a76\u9662\u7684 Irit Dinur \u5e2e\u52a9\u6784\u5efa\u4e86\u4e00\u79cd\u5177\u6709\u4e00\u7cfb\u5217\u7406\u60f3\u6027\u8d28\u7684\u7ea0\u9519\u7801\uff0c\u5373\u4f7f\u5728\u7801\u5b57\u89c4\u6a21\u6269\u5927\u65f6\uff0c\u7ea0\u9519\u7801\u4e5f\u4fdd\u6301\u4e0d\u53d8\u3002| \u6765\u6e90\uff1aHadar Dveer Benyamini<\/span><\/p>\n

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\u201c\u8fd9\u662f\u6211\u6240\u77e5\u9053\u7684\u6570\u5b66\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u9886\u57df\u6700\u4e86\u4e0d\u8d77\u7684\u6210\u5c31\u4e4b\u4e00\uff0c\u5b83\u4e00\u76f4\u662f\u6574\u4e2a\u9886\u57df\u7684\u5723\u676f\u3002\u201d\u534e\u5a01\u5927\u5b66\u7684\u6c64\u59c6\u00b7\u53e4\u5c14<\/span>\uff08Tom Gur\uff09<\/span>\u8bf4 [7]\u3002<\/span><\/section>\n
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\u4ed6\u4eec\u7684\u65b0\u6280\u672f\u5c06\u4e00\u6761\u4fe1\u606f\u8f6c\u5316\u4e3a\u4e00\u4e2a\u201c\u8d85\u7ea7\u544a\u5bc6\u8005\u201d<\/span>\uff08super-canary\uff09<\/span>\uff0c\u5b83\u6bd4\u5df2\u77e5\u7684\u5176\u4ed6\u4efb\u4f55\u4fe1\u606f\u90fd\u80fd\u66f4\u597d\u5730\u68c0\u67e5\u4fe1\u606f\u7684\u5b8c\u597d\u72b6\u6001\u3002\u53ea\u9700\u8981\u901a\u8fc7\u51e0\u4e2a\u70b9\u7684\u7b80\u5355\u6d4b\u8bd5\uff0c\u57cb\u85cf\u5728\u5176\u4e0a\u5c42\u7ed3\u6784\u4e2d\u4efb\u4f55\u5730\u65b9\u7684\u4efb\u4f55\u91cd\u8981\u9519\u8bef\u90fd\u4f1a\u663e\u793a\u51fa\u6765\u3002<\/span><\/section>\n
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\u54c8\u4f5b\u5927\u5b66\u7684\u9a6c\u675c\u00b7\u82cf\u4e39<\/span>\uff08Madhu Sudan\uff09<\/span>[8] \u8bf4\uff0c\u201c\u8fd9\u770b\u8d77\u6765\u5e76\u4e0d\u5408\u7406\uff0c\u4f46\u662f\u7ed3\u679c\u7a81\u7136\u544a\u8bc9\u4f60\u53ef\u4ee5\u505a\u5230\u3002\u201d<\/span><\/section>\n
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\u5927\u591a\u6570\u4e4b\u524d\u7684\u6570\u636e\u7f16\u7801\u65b9\u6cd5\u90fd\u4f9d\u8d56\u4e8e\u67d0\u79cd\u5f62\u5f0f\u7684\u968f\u673a\u6027\u3002\u4f46\u5bf9\u4e8e\u5c40\u90e8\u53ef\u6d4b\u8bd5\u6027\u6765\u8bf4\uff0c\u968f\u673a\u6027\u65e0\u80fd\u4e3a\u529b\u3002\u76f8\u53cd\uff0c\u7814\u7a76\u4eba\u5458\u4e0d\u5f97\u4e0d\u8bbe\u8ba1\u51fa\u4e00\u79cd\u6570\u5b66\u4e0a\u5168\u65b0\u7684\u9ad8\u5ea6\u975e\u968f\u673a\u7684\u56fe\u7ed3\u6784\uff0c\u4ed6\u4eec\u7684\u65b0\u65b9\u6cd5\u5c31\u57fa\u4e8e\u6b64\u3002\u8fd9\u65e2\u662f\u4e00\u79cd\u7406\u8bba\u7684\u597d\u5947\u5fc3\uff0c\u4e5f\u662f\u5c3d\u53ef\u80fd\u4f7f\u4fe1\u606f\u4f20\u8f93\u66f4\u53ef\u9760\u7684\u5b9e\u8df5\u8fdb\u6b65\u3002<\/span><\/section>\n

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\u566a\u58f0\u5728\u901a\u4fe1\u4e2d\u65e0\u5904\u4e0d\u5728\u3002\u4e3a\u4e86\u7cfb\u7edf\u5730\u5206\u6790\u5b83\uff0c\u7814\u7a76\u4eba\u5458\u9996\u5148\u5c06\u4fe1\u606f\u8868\u793a\u4e3a\u6bd4\u7279<\/span>\uff08\u53731\u548c0\uff09<\/span>\u7684\u5e8f\u5217\u3002\u7136\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u566a\u58f0\u89c6\u4e3a\u7ffb\u8f6c\u67d0\u4e9b\u6bd4\u7279\u7684\u968f\u673a\u5f71\u54cd\u3002<\/span><\/section>\n
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\u6709\u8bb8\u591a\u65b9\u6cd5\u6765\u5904\u7406\u566a\u58f0\uff0c\u8457\u540d\u6570\u5b66\u5bb6\u51af\u00b7\u8bfa\u4f0a\u66fc\u63d0\u51fa\u4e00\u79cd\u65b9\u6cd5\uff0c\u5229\u7528\u5197\u4f59\u6765\u7ea0\u9519\u3002\u8003\u8651\u4e00\u6761\u7b80\u77ed\u7684\u4fe1\u606f\uff0c\u6bd4\u598201\u3002\u5982\u679c\u8ba1\u7b97\u673a\u5c06\u6bcf\u4e00\u4e2a\u6bd4\u7279\u590d\u5236\u4e09\u4efd\uff0c\u5f97\u5230 000 111\u3002\u7136\u540e\uff0c\u5373\u4f7f\u566a\u58f0\u78b0\u5de7\u7834\u574f\u4e86\u4e09\u4e2a\u62f7\u8d1d\u4e2d\u7684\u4e00\u4e2a<\/span>\uff08\u6bd4\u5982\u7b2c2\u548c\u7b2c6\u4f4d\uff09<\/span>\uff0c\u4f7f\u4fe1\u606f\u53d8\u4e3a 010 110\uff0c\u63a5\u6536\u8005\u4ecd\u7136\u53ef\u4ee5\u901a\u8fc7\u4e24\u6b21\u591a\u6570\u6295\u7968\u6765\u7ea0\u6b63\u9519\u8bef\uff0c\u5982\u5c06\u7b2c2\u4f4d\u6bd4\u7279\u7ffb\u8f6c\u56de0\uff0c\u7b2c6\u4f4d\u7ffb\u8f6c\u56de1\u3002<\/span><\/section>\n
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\u8fd9\u6837\u4e00\u79cd\u4fee\u6539\u4fe1\u606f\u7684\u65b9\u6cd5\u88ab\u79f0\u4e3a\u7ea0\u9519\u7801<\/strong><\/span>\uff08error-correcting code\uff09<\/span>\uff0c\u5728\u7f16\u7801\u6709\u6548\u4fe1\u606f\u7684\u57fa\u7840\u4e0a\uff0c\u7801\u5b57<\/span>\uff08codeword\uff09<\/span>\u8fd8\u4f1a\u9644\u5e26\u4e00\u4e2a\u4fee\u590d\u9519\u8bef\u7684\u7a0b\u5e8f\u3002\u7f16\u7801\u5c31\u50cf\u5b57\u5178\uff0c\u6bcf\u4e00\u4e2a\u5b57\u5178\u90fd\u5b9a\u4e49\u4e86\u4e00\u5957\u7279\u5b9a\u7684\u7801\u5b57\uff0c\u5982 000 111\u3002<\/span><\/section>\n
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\u4e3a\u4e86\u8fd0\u884c\u987a\u5229\uff0c\u7ea0\u9519\u7801\u5fc5\u987b\u6709\u51e0\u4e2a\u7279\u6027\u3002\u9996\u5148\uff0c\u7ea0\u9519\u7801\u4e2d\u7684\u5b57\u7b26\u4e0d\u5e94\u8be5\u592a\u76f8\u4f3c\uff1a\u5982\u679c\u4e00\u4e2a\u7f16\u7801\u5305\u542b\u7801\u5b570000\u548c0001\uff0c\u53ea\u9700\u8981\u4e00\u4e2a\u6bd4\u7279\u7ffb\u8f6c\uff0c\u5c31\u53ef\u4ee5\u6df7\u6dc6\u8fd9\u4e24\u4e2a\u5b57\u7b26\u3002\u7b2c\u4e8c\uff0c\u7801\u5b57\u4e0d\u5e94\u8be5\u592a\u957f\u3002\u91cd\u590d\u7684\u6bd4\u7279\u53ef\u80fd\u4f1a\u4f7f\u4fe1\u606f\u4f20\u8f93\u66f4\u53ef\u9760\uff0c\u4f46\u4e5f\u4f1a\u4f7f\u4fe1\u606f\u7684\u53d1\u9001\u65f6\u95f4\u66f4\u957f\u3002<\/span><\/section>\n
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\u8fd9\u4e24\u4e2a\u5c5e\u6027\u88ab\u79f0\u4e3a\u8ddd\u79bb<\/span>\uff08distance\uff09<\/span>\u548c\u901f\u7387<\/span>\uff08rate\uff09<\/span>\u3002\u4e00\u4e2a\u597d\u7684\u7f16\u7801\u5e94\u8be5\u540c\u65f6\u5177\u6709\u8f83\u5927\u7684\u8ddd\u79bb<\/strong><\/span>\uff08\u4e0d\u540c\u7801\u5b57\u4e4b\u95f4\uff09<\/span>\u548c\u8f83\u9ad8\u7684\u901f\u7387<\/strong><\/span>\uff08\u4f20\u8f93\u771f\u5b9e\u4fe1\u606f\uff09<\/span>\u3002\u4f46\u5982\u4f55\u624d\u80fd\u540c\u65f6\u83b7\u5f97\u8fd9\u4e24\u4e2a\u7279\u6027\u5462\uff1f1948\u5e74\uff0c\u514b\u52b3\u5fb7\u00b7\u9999\u519c<\/span>\uff08Claude Shannon\uff09<\/span>\u63d0\u51fa\uff0c\u4efb\u4f55\u7531\u968f\u673a\u9009\u62e9\u5f62\u6210\u7684\u7801\u5b57\u90fd\u4f1a\u5728\u8fd9\u4e24\u79cd\u7279\u6027\u4e4b\u95f4\u6709\u4e00\u4e2a\u8fd1\u4e4e\u6700\u4f73\u7684\u6743\u8861\u3002\u7136\u800c\uff0c\u5b8c\u5168\u968f\u673a\u5730\u9009\u62e9\u7801\u5b57\u4f1a\u4ea7\u751f\u4e00\u4e2a\u4e0d\u53ef\u9884\u6d4b\u7684\u5b57\u5178\uff0c\u5b83\u592a\u96be\u6574\u7406\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u9999\u519c\u8bc1\u660e\uff0c\u597d\u7684\u7f16\u7801\u662f\u5b58\u5728\u7684\uff0c\u4f46\u4ed6\u5236\u4f5c\u8fd9\u4e9b\u7f16\u7801\u7684\u65b9\u6cd5\u5e76\u4e0d\u53ef\u884c\u3002”\u8fd9\u53ea\u662f\u4e00\u4e2a\u4e8b\u5b9e\u4e0a\u5b58\u5728\u7684\u7ed3\u679c\uff0c”\u54e5\u4f26\u6bd4\u4e9a\u5927\u5b66\u7684\u4ea8\u5229\u00b7\u8881<\/span>\uff08Henry Yuen\uff09<\/span>[8]\u8bf4\u3002<\/span><\/section>\n
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\u5728\u63a5\u4e0b\u6765\u768440\u5e74\u91cc\uff0c\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u4eec\u52aa\u529b\u5bfb\u627e\u975e\u968f\u673a\u7684\u65b9\u6cd5\uff0c\u6765\u5b9e\u73b0\u63a5\u8fd1\u968f\u673a\u9009\u62e9\u7684\u6bd4\u7279\u6392\u5217\u3002\u523020\u4e16\u7eaa80\u5e74\u4ee3\u672b\uff0c\u4ed6\u4eec\u7684\u7f16\u7801\u88ab\u7528\u4e8e\u4ece\u5149\u76d8\u5230\u536b\u661f\u4f20\u8f93\u7684\u6240\u6709\u9886\u57df\u3002<\/span><\/section>\n
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1990\u5e74\uff0c\u7814\u7a76\u4eba\u5458\u63d0\u51fa\u4e86\u5c40\u90e8\u53ef\u6d4b\u8bd5\u6027\u7684\u60f3\u6cd5\u3002\u4f46\u5c40\u90e8\u53ef\u6d4b\u8bd5\u6027\u7684\u6027\u8d28\u662f\u4e0d\u540c\u7684\u3002\u5982\u679c\u50cf\u9999\u519c\u5efa\u8bae\u7684\u90a3\u6837\uff0c\u968f\u673a\u6311\u9009\u4e00\u4e2a\u7f16\u7801\uff0c\u90a3\u5b83\u5c31\u4e0d\u53ef\u80fd\u662f\u4e00\u4e2a\u5c40\u90e8\u53ef\u6d4b\u8bd5\u7684\u7f16\u7801\u3002\u5c40\u90e8\u53ef\u6d4b\u8bd5\u7684\u7f16\u7801\u662f\u968f\u673a\u7f16\u7801\u5b87\u5b99\u4e2d\u7684\u767d\u5316\u8774\u8776\u2014\u2014\u5f02\u5e38\u7f8e\u4e3d\uff0c\u5982\u679c\u5b83\u4eec\u5b58\u5728\u7684\u8bdd\u3002\u8881\u8bf4\uff1a\u201c\u4f60\u5b9e\u9645\u4e0a\u5fc5\u987b\u9996\u5148\u52aa\u529b\u8bc1\u660e\u5b83\u4eec\u7684\u5b58\u5728\uff0c\u66f4\u4e0d\u7528\u8bf4\u60f3\u51fa\u4e00\u4e2a\u660e\u786e\u7684\u4f8b\u5b50\u4e86\u3002\u201d<\/span><\/section>\n
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2. \u56fe\u4f5c\u4e3a\u7f16\u7801\uff0c\u7f16\u7801\u4f5c\u4e3a\u56fe<\/strong><\/strong><\/p>\n<\/section>\n

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\u4e3a\u4e86\u7406\u89e3\u4e3a\u4ec0\u4e48\u53ef\u6d4b\u8bd5\u6027\u5982\u6b64\u96be\u4ee5\u83b7\u5f97\uff0c\u6211\u4eec\u9700\u8981\u628a\u4fe1\u606f\u4e0d\u4ec5\u4ec5\u770b\u4f5c\u662f\u4e00\u4e32\u6bd4\u7279\uff0c\u800c\u662f\u4e00\u4e2a\u6570\u5b66\u4e0a\u7684\u56fe\uff1a\u4e00\u4e2a\u7531\u8fb9<\/span>\uff08\u7ebf\uff09<\/span>\u8fde\u63a5\u7684\u9876\u70b9<\/span>\uff08\u70b9\uff09<\/span>\u7684\u96c6\u5408\u3002\u5728\u9999\u519c\u7684\u8bc1\u660e\u63d0\u51fa\u4e24\u5e74\u540e\uff0c\u7406\u67e5\u5fb7\u00b7\u6c49\u660e<\/span>\uff08Richard Hamming\uff09<\/span>\u521b\u9020\u4e86\u7b2c\u4e00\u4e2a\u806a\u660e\u7684\u7f16\u7801\u2014\u2014\u6c49\u660e\u6821\u9a8c\u7801<\/strong><\/span>\uff08Hamming codes\uff09<\/span>\uff0c\u4f7f\u5f97\u7f16\u7801\u548c\u56fe\u7684\u7b49\u4ef7\u5173\u7cfb\u6210\u4e3a\u7406\u89e3\u7f16\u7801\u7684\u6838\u5fc3\u3002<\/span>\uff08\u5728R.\u8fc8\u514b\u5c14\u00b7\u5766\u7eb3\uff08R.Michael Tanner\uff09\u4e8e1981\u5e74\u53d1\u8868\u4e00\u7bc7\u8bba\u6587[9]\u4e4b\u540e\uff0c\u56fe\u7684\u89c2\u70b9\u53d8\u5f97\u5341\u5206\u6709\u5f71\u54cd\u529b\u3002\uff09<\/span><\/section>\n
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\u6c49\u660e\u7684\u5de5\u4f5c\u4e3a\u7ea0\u9519\u7801\u572820\u4e16\u7eaa80\u5e74\u4ee3\u83b7\u5f97\u666e\u904d\u5e94\u7528\u521b\u9020\u4e86\u6761\u4ef6\u3002\u4ed6\u63d0\u51fa\u4e86\u4e00\u6761\u89c4\u5219\uff1a\u6bcf\u6761\u4fe1\u606f\u90fd\u5e94\u4e0e\u4e00\u7ec4\u56de\u6267\u914d\u5bf9\uff0c\u8fd9\u4e9b\u56de\u6267\u8bb0\u5f55\u4e86\u4fe1\u606f\u6bd4\u7279\u3002\u66f4\u5177\u4f53\u5730\u8bf4\uff0c\u6bcf\u4e2a\u56de\u6267\u662f\u8fd9\u6761\u4fe1\u606f\u4e2d\u7cbe\u5fc3\u9009\u62e9\u7684\u6bd4\u7279\u5b50\u96c6\u7684\u603b\u548c\u3002\u5f53\u8fd9\u4e2a\u603b\u548c\u4e3a\u5076\u6570\u65f6\uff0c\u56de\u6267\u88ab\u6807\u8bb0\u4e3a0\uff0c\u5f53\u5b83\u4e3a\u5947\u6570\u65f6\uff0c\u56de\u6267\u88ab\u6807\u8bb0\u4e3a1\u3002\u6bcf\u4e2a\u56de\u6267\u7531\u5355\u4e00\u6bd4\u7279\u8868\u793a\uff0c\u7814\u7a76\u4eba\u5458\u79f0\u4e4b\u4e3a\u5947\u5076\u6821\u9a8c<\/strong>\u6216\u6821\u9a8c\u4f4d<\/strong>\u3002<\/span><\/section>\n
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\u6c49\u660e\u8bbe\u8ba1\u4e86\u4e00\u4e2a\u7a0b\u5e8f\u5c06\u6821\u9a8c\u4f4d\u9644\u52a0\u5230\u4fe1\u606f\u4e2d\u3002\u7136\u540e\uff0c\u63a5\u6536\u8005\u53ef\u4ee5\u901a\u8fc7\u5c1d\u8bd5\u590d\u5236\u6821\u9a8c\u4f4d\u3001\u8ba1\u7b97\u6bd4\u7279\u7684\u603b\u548c\u6765\u68c0\u6d4b\u9519\u8bef\u3002\u6c49\u660e\u7801\u7684\u6548\u679c\u975e\u5e38\u597d\uff0c\u8fd9\u662f\u5c06\u7f16\u7801\u89c6\u4e3a\u56fe\u3001\u5c06\u56fe\u89c6\u4e3a\u7f16\u7801<\/strong>\u8fd9\u4e00\u601d\u60f3\u7684\u51fa\u53d1\u70b9\u3002<\/span><\/section>\n
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\u56fe2\uff1a\u5c06\u7f16\u7801\u8868\u793a\u4e3a\u56fe\u3002\u4e3a\u4e86\u68c0\u67e5\u7f16\u7801\u7684\u771f\u5b9e\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u6dfb\u52a0\u4e00\u4e2a\u6821\u9a8c\u4f4d\uff0c\u8ddf\u8e2a\u7f16\u7801\u7684\u5177\u4f53\u5f62\u5f0f\u3002\u6bcf\u4e2a\u6821\u9a8c\u4f4d\u4f1a\u68c0\u67e5\u4fe1\u606f\u4e2d\u7684\u4e00\u4e2a\u6bd4\u7279\u5b50\u96c6\u3002\u5982\u679c\u8be5\u5b50\u96c6\u603b\u548c\u662f\u5076\u6570\uff0c\u90a3\u4e48\u6821\u9a8c\u4f4d\u5c31\u662f0\uff1b\u5982\u679c\u662f\u5947\u6570\uff0c\u6821\u9a8c\u4f4d\u5c31\u662f1\u3002\u8fd9\u4e9b\u65b0\u7684\u6bd4\u7279\u53ef\u4ee5\u8868\u793a\u4e3a\u56fe\u4e2d\u7684\u9876\u70b9\uff0c\u8fd9\u4e9b\u9876\u70b9\u5c06\u5b83\u4eec\u6240\u68c0\u67e5\u7684\u6bd4\u7279\u7684\u9876\u70b9\u8fde\u63a5\u8d77\u6765\u3002| \u6765\u6e90\uff1aSamuel Velasco\/Quanta Magazine<\/span><\/p>\n

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\u5fb7\u514b\u8428\u65af\u5927\u5b66\u5965\u65af\u6c40\u5206\u6821\u7684\u8fbe\u5a1c\u00b7\u83ab\u65af\u79d1\u7ef4\u8328<\/span>\uff08Dana Moshkovitz\uff09<\/span>[10]\u8bf4\uff1a\u201c\u5bf9\u6211\u4eec\u6765\u8bf4\uff0c\u601d\u8003\u56fe\u548c\u601d\u8003\u7f16\u7801\u662f\u540c\u4e00\u4ef6\u4e8b\u3002\u201d<\/span><\/section>\n
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\u6211\u4eec\u53ef\u4ee5\u4ece\u7f16\u7801\u5f00\u59cb\u521b\u9020\u56fe\u3002\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u4fe1\u606f\u6bd4\u7279\uff0c\u753b\u4e00\u4e2a\u9876\u70b9<\/span>\uff08\u6216\u8282\u70b9\uff09<\/span>\uff0c\u79f0\u4e3a\u6570\u5b57\u8282\u70b9<\/strong><\/span>\uff08digit node\uff09<\/span>\u3002\u7136\u540e\u4e3a\u6bcf\u4e2a\u5947\u5076\u6821\u9a8c\u4f4d\u753b\u4e00\u4e2a\u8282\u70b9\uff0c\u79f0\u4e3a\u5947\u5076\u6821\u9a8c\u8282\u70b9<\/strong><\/span>\uff08parity node\uff09<\/span>\u3002\u6700\u540e\uff0c\u4ece\u6bcf\u4e2a\u5947\u5076\u6821\u9a8c\u7ed3\u70b9\u5230\u76f8\u52a0\u4ea7\u751f\u5176\u5947\u5076\u6821\u9a8c\u503c\u7684\u6570\u5b57\u7ed3\u70b9\u8fde\u7ebf\uff0c\u5c31\u4ece\u7f16\u7801\u521b\u9020\u4e86\u56fe\u3002<\/span><\/section>\n
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\u5c06\u7f16\u7801\u548c\u56fe\u770b\u4f5c\u7b49\u4ef7\u7269\uff0c\u6210\u4e3a\u4e86\u5236\u4f5c\u7f16\u7801\u7684\u827a\u672f\u30021996\u5e74\uff0c\u8fc8\u514b\u5c14\u00b7\u897f\u666e\u65af<\/span>\uff08Michael Sipes\uff09<\/span>\u548c\u4e39\u5c3c\u5c14\u00b7\u65af\u76ae\u5c14\u66fc<\/span>\uff08Daniel Spielman\uff09<\/span>\u7528\u8fd9\u79cd\u65b9\u6cd5\u4ece\u6269\u5c55\u56fe<\/strong><\/span>\uff08expander graph\uff09<\/span>\u4e2d\u521b\u9020\u4e86\u4e00\u79cd\u7a81\u7834\u6027\u7684\u7f16\u7801\u3002\u5c3d\u7ba1\u4ed6\u4eec\u7684\u7f16\u7801\u4ecd\u7136\u4e0d\u80fd\u5b9e\u73b0\u5c40\u90e8\u53ef\u6d4b\u8bd5\u6027\uff0c\u4f46\u662f\u5b83\u5728\u5176\u4ed6\u65b9\u9762\u88ab\u8bc1\u660e\u662f\u6700\u4f73\u7684\uff0c\u5e76\u6700\u7ec8\u6210\u4e3a\u6700\u8fd1\u8fd9\u9879\u65b0\u6210\u679c\u7684\u57fa\u7840\u3002<\/span><\/section>\n
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3. \u62d3\u5c55\u56fe\u4e0e\u968f\u673a\u6027<\/strong><\/strong><\/p>\n<\/section>\n

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\u6269\u5c55\u56fe\u6709\u4e24\u4e2a\u770b\u4f3c\u77db\u76fe\u7684\u7279\u6027\u3002\u9996\u5148\uff0c\u5b83\u4eec\u662f\u7a00\u758f\u7684\uff0c\u6bcf\u4e2a\u8282\u70b9\u4e0e\u5176\u4ed6\u8282\u70b9\u7684\u8fde\u63a5\u90fd\u76f8\u5bf9\u8f83\u5c11\u3002\u5176\u6b21\uff0c\u5b83\u4eec\u6709\u4e00\u79cd\u88ab\u79f0\u4e3a\u6269\u5c55\u6027\u7684\u5c5e\u6027\u2014\u2014\u8fd9\u5c31\u662f\u5b83\u4eec\u540d\u5b57\u7684\u7531\u6765\uff0c\u8fd9\u610f\u5473\u7740\u6ca1\u6709\u4e00\u7ec4\u8282\u70b9\u662f\u5f88\u5c11\u6709\u8fb9\u7ecf\u8fc7\u7684\u74f6\u9888\u8282\u70b9\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6bcf\u4e2a\u8282\u70b9\u90fd\u4e0e\u5176\u4ed6\u8282\u70b9\u6709\u5f88\u597d\u7684\u8fde\u63a5\u2014\u2014\u5c3d\u7ba1\u5b83\u6240\u62e5\u6709\u7684\u8fde\u63a5\u5f88\u7a00\u5c11\u3002<\/span><\/section>\n
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“\u4e3a\u4ec0\u4e48\u8fd9\u6837\u7684\u56fe\u53ef\u4ee5\u5b58\u5728\uff1f”Evra\u95ee\u9053\uff0c”\u6211\u4eec\u901a\u5e38\u8ba4\u4e3a\uff0c\u5982\u679c\u56fe\u662f\u7a00\u758f\u7684\uff0c\u90a3\u4e48\u5b83\u4e0e\u5176\u4ed6\u8282\u70b9\u5c31\u6ca1\u6709\u90a3\u4e48\u591a\u8fde\u63a5\u3002”<\/span><\/section>\n
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\u4f46\u51fa\u4e4e\u610f\u6599\u7684\u662f\uff0c\u6269\u5c55\u56fe\u5b9e\u9645\u4e0a\u5f88\u5bb9\u6613\u6784\u5efa\u3002\u5982\u679c\u4f60\u4ee5\u968f\u673a\u7684\u65b9\u5f0f\u6784\u5efa\u4e00\u4e2a\u56fe\uff0c\u968f\u673a\u9009\u62e9\u8282\u70b9\u8fde\u63a5\uff0c\u5c31\u4f1a\u4e0d\u53ef\u907f\u514d\u5730\u5f97\u5230\u4e00\u4e2a\u6269\u5c55\u56fe\u3002\u8fd9\u4e9b\u56fe\u662f\u7eaf\u7cb9\u7684\u968f\u673a\u6027\u4e4b\u6e90\uff0c\u662f\u6784\u5efa\u9999\u519c\u6240\u8ba4\u4e3a\u7684\u597d\u7f16\u7801\u7684\u81ea\u7136\u4e4b\u9009\u3002<\/span><\/section>\n
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\u56fe3\uff1a\u6316\u6398\u968f\u673a\u6027\u3002\u6269\u5c55\u56fe\u7531\u8282\u70b9\u7684\u968f\u673a\u8fde\u63a5\u6784\u5efa\u800c\u6210\uff0c\u8fd9\u4e2a\u7279\u70b9\u4f7f\u5f97\u5b83\u4eec\u6210\u4e3a\u57fa\u4e8e\u968f\u673a\u6027\u83b7\u5f97\u7f16\u7801\u7684\u6700\u597d\u8d77\u70b9\u3002\u6269\u5c55\u56fe\u7684\u4e24\u4e2a\u4e3b\u8981\u6027\u8d28\uff1a\uff081\uff09\u7a00\u758f\u6027\uff1a\u6bcf\u4e2a\u8282\u70b9\u53ea\u6709\u5f88\u5c11\u7684\u76f8\u90bb\u8282\u70b9\uff1b\uff082\uff09\u6269\u5c55\u6027\uff1a\u8282\u70b9\u4e4b\u95f4\u6709\u826f\u597d\u8fde\u63a5\uff0c\u6ca1\u6709\u74f6\u9888\u8282\u70b9\u3002| \u6765\u6e90\uff1aSamuel Velasco\/Quanta Magazine<\/span><\/p>\n

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Sipser \u548c Spielman \u7814\u7a76\u51fa\u4e86\u5982\u4f55\u5c06\u6269\u5c55\u56fe\u53d8\u6210\u7f16\u7801\u3002\u4ed6\u4eec\u60f3\u51fa\u7684\u7801\u5b57\u7531\u6c49\u660e\u6821\u9a8c\u7801\u4ea7\u751f\u7684\u8bb8\u591a\u66f4\u77ed\u5b57\u7b26\u2014\u2014\u4ed6\u4eec\u79f0\u4e4b\u4e3a\u5c0f\u7801<\/span>\uff08small code\uff09<\/span>\u2014\u2014\u7ec4\u6210\u3002\u7801\u5b57\u7684\u6bd4\u7279\u8868\u793a\u4e3a\u6269\u5c55\u56fe\u7684\u8fb9\uff0c\u5c0f\u7801\u7684\u6240\u6709\u6821\u9a8c\u4f4d\u90fd\u8868\u793a\u4e3a\u8282\u70b9\u3002<\/span><\/section>\n
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\u5b9e\u9645\u4e0a\uff0cSipser \u548c Spielman \u8bc1\u660e\uff0c\u5982\u679c\u5728\u6bcf\u4e2a\u8282\u70b9\u4e0a\u5b9a\u4e49\u5177\u6709\u826f\u597d\u5c5e\u6027\u7684\u5c0f\u7801\uff0c\u90a3\u4e48\u7531\u4e8e\u6269\u5c55\u56fe\u5177\u6709\u826f\u597d\u7684\u8fde\u63a5\u6027\uff0c\u8fd9\u4e9b\u5c5e\u6027\u4f1a\u4f20\u64ad\u5230\u5168\u5c40\u7f16\u7801\u4e2d\u3002\u8fd9\u79cd\u4f20\u64ad\u7ed9\u4e86\u4ed6\u4eec\u4e00\u79cd\u521b\u5efa\u826f\u597d\u7f16\u7801\u7684\u65b9\u6cd5\u3002”\u6269\u5c55\uff0c\u6269\u5c55\uff0c\u518d\u6269\u5c55\u3002\u8fd9\u5c31\u662f\u6210\u529f\u7684\u79d8\u8bc0\u3002” Evra \u8bf4\u3002<\/span><\/section>\n
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\u7136\u800c\uff0c\u5c40\u90e8\u53ef\u6d4b\u8bd5\u6027\u662f\u4e0d\u53ef\u80fd\u7684\u3002\u5047\u8bbe\u4f60\u6709\u4e00\u4e2a\u6765\u81ea\u6269\u5c55\u56fe\u7f16\u7801\u7684\u6709\u6548\u7801\u5b57\uff0c\u4e4b\u540e\u4ece\u4e00\u4e2a\u5355\u4e00\u8282\u70b9\u4e0a\u53bb\u9664\u4e00\u4e2a\u5947\u5076\u6821\u9a8c\u4f4d\u3002\u8fd9\u5c06\u6784\u6210\u4e00\u4e2a\u65b0\u7684\u7f16\u7801\uff0c\u5b83\u6bd4\u7b2c\u4e00\u4e2a\u7f16\u7801\u6709\u66f4\u591a\u7684\u6709\u6548\u7801\u5b57\uff0c\u56e0\u4e3a\u5b83\u4eec\u9700\u8981\u6ee1\u8db3\u7684\u6821\u9a8c\u4f4d\u4f1a\u5c11\u4e00\u4e2a\u3002\u5bf9\u4e8e\u521b\u9020\u539f\u59cb\u7f16\u7801\u7684\u4eba\u6765\u8bf4\uff0c\u8fd9\u4e9b\u65b0\u7684\u7801\u5b57\u5c06\u6ee1\u8db3\u5927\u591a\u6570\u8282\u70b9\u7684\u6821\u9a8c\u4f4d\u2014\u2014\u6240\u6709\u8282\u70b9\uff0c\u9664\u4e86\u6821\u9a8c\u4f4d\u88ab\u62b9\u53bb\u7684\u90a3\u4e00\u4e2a\u8282\u70b9\u3002\u7136\u800c\uff0c\u7531\u4e8e\u8fd9\u4e24\u79cd\u7f16\u7801\u6709\u5f88\u5927\u7684\u8ddd\u79bb\uff0c\u770b\u4f3c\u6b63\u786e\u7684\u65b0\u7801\u5b57\u8ddd\u79bb\u539f\u6765\u7684\u7801\u5b57\u96c6\u6781\u5176\u9065\u8fdc\u3002\u5c40\u90e8\u53ef\u6d4b\u8bd5\u6027\u4e0e\u6269\u5c55\u56fe\u7f16\u7801\u6839\u672c\u4e0d\u76f8\u5bb9<\/strong>\u3002<\/span><\/section>\n
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\u4e3a\u4e86\u83b7\u5f97\u53ef\u6d4b\u8bd5\u6027\uff0c\u7814\u7a76\u4eba\u5458\u5fc5\u987b\u5f04\u6e05\u695a\u5982\u4f55\u4e0e\u66fe\u7ecf\u5f88\u6709\u5e2e\u52a9\u7684\u968f\u673a\u6027\u4f5c\u6597\u4e89\u3002\u6700\u540e\uff0c\u4ed6\u4eec\u9009\u62e9\u63a2\u7d22\u968f\u673a\u6027\u4e0d\u5b58\u5728\u7684\u5730\u65b9\uff1a\u66f4\u9ad8\u7ef4\u5ea6\u3002<\/span><\/section>\n
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\u56fe4\uff1a1996\u5e74\uff0cMichael Sipes \u548c Daniel Spielman \u521b\u5efa\u4e86\u4e00\u4e2a\u57fa\u4e8e\u6269\u5c55\u56fe\u7684\u7f16\u7801\uff0c\u5b83\u5177\u6709\u5f88\u597d\u7684\u7ec4\u5408\u7279\u6027\uff0c\u4f46\u5b8c\u5168\u672a\u80fd\u8fbe\u5230\u5c40\u90e8\u53ef\u6d4b\u8bd5\u3002| \u6765\u6e90\uff1aBryce Vickmark; John D. and Catherine T. MacArthur Foundation<\/span>
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\u7814\u7a76\u4eba\u5458\u63d0\u51fa\u731c\u60f3\uff0c\u53ef\u4ee5\u627e\u5230\u5177\u6709\u6700\u4f73\u901f\u7387\u3001\u8ddd\u79bb\u548c\u5c40\u90e8\u53ef\u6d4b\u8bd5\u6027\u7684\u7f16\u7801\u2014\u2014\u5373\u4f7f\u4fe1\u606f\u91cf\u589e\u5927\uff0c\u8fd9\u4e9b\u53c2\u6570\u90fd\u4fdd\u6301\u4e0d\u53d8\u2014\u2014\u8fd9\u88ab\u79f0\u4e3a c3<\/sup><\/span> \u731c\u60f3\u3002\u5148\u524d\u7684\u7ed3\u679c\u4f7f\u4e00\u4e9b\u7814\u7a76\u4eba\u5458\u8ba4\u4e3a\uff0c\u8fd9\u4e2a\u731c\u60f3\u5fc5\u7136\u4f1a\u88ab\u8bc1\u660e\u3002\u4f46\u5b9e\u9645\u4e0a\uff0c\u8fdb\u5c55\u5341\u5206\u7f13\u6162\uff0c\u5e76\u4e14\u5176\u4ed6\u7ed3\u679c\u8868\u660e\u8be5\u731c\u60f3\u53ef\u80fd\u662f\u9519\u8bef\u7684\u3002\u201c\u8fd9\u4e2a\u7814\u7a76\u9886\u57df\u4e2d\u7684\u8bb8\u591a\u4eba\u90fd\u8ba4\u4e3a\uff0c\u8fd9\u4e2a\u731c\u60f3\u662f\u4e00\u4e2a\u770b\u4f3c\u7f8e\u597d\uff0c\u4f46\u4e8b\u5b9e\u4e0a\u9065\u4e0d\u53ef\u53ca\u7684\u68a6\uff0c\u201dGur\u8bf4\uff0c\u201c\u4e8b\u60c5\u770b\u8d77\u6765\u76f8\u5f53\u4e25\u5cfb\u3002\u201d<\/span><\/section>\n
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\u4f46\u57282017\u5e74\uff0c\u65b0\u7684\u60f3\u6cd5\u51fa\u73b0\u4e86\u3002Dinur \u548c Lubotzky \u5728\u53c2\u52a0\u4ee5\u8272\u5217\u9ad8\u7b49\u7814\u7a76\u6240\u4e3a\u671f\u4e00\u5e74\u7684\u7814\u7a76\u9879\u76ee\u65f6\u5f00\u59cb\u5408\u4f5c\u3002\u4ed6\u4eec\u5f00\u59cb\u76f8\u4fe1\uff0c\u6570\u5b66\u5bb6\u970d\u534e\u5fb7\u00b7\u52a0\u5170<\/span>\uff08Howard Garland\uff09<\/span>\u57281973\u5e74\u7684\u4e00\u9879\u6210\u679c\u53ef\u80fd\u6b63\u662f\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u6240\u5bfb\u6c42\u7684\u3002\u666e\u901a\u7684\u6269\u5c55\u56fe\u672c\u8d28\u4e0a\u662f\u4e00\u7ef4\u7ed3\u6784\uff0c\u6bcf\u6761\u8fb9\u53ea\u5411\u4e00\u4e2a\u65b9\u5411\u5ef6\u4f38\uff0c\u800c Garland \u521b\u9020\u4e86\u4e00\u4e2a\u6570\u5b66\u5bf9\u8c61\uff0c\u53ef\u4ee5\u88ab\u89e3\u91ca\u4e3a\u4e00\u4e2a\u5f20\u5f00\u66f4\u9ad8\u7ef4\u5ea6\u7684\u6269\u5c55\u56fe\uff0c\u56fe\u7684\u8fb9\u88ab\u91cd\u65b0\u5b9a\u4e49\u4e3a\u6b63\u65b9\u5f62\u6216\u7acb\u65b9\u4f53\u3002<\/span><\/section>\n
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Garland \u7684\u9ad8\u7ef4\u6269\u5c55\u56fe<\/strong>\u4f3c\u4e4e\u662f\u5b9e\u73b0\u5c40\u90e8\u53ef\u6d4b\u8bd5\u6027\u7684\u7406\u60f3\u9009\u62e9\u3002\u5b83\u4eec\u5fc5\u987b\u88ab\u6709\u610f\u5730\u4ece\u5934\u5f00\u59cb\u6784\u5efa\uff0c\u56e0\u800c\u662f\u968f\u673a\u6027\u7684\u5bf9\u7acb\u9762\u3002\u800c\u4e14\u5b83\u4eec\u7684\u8282\u70b9\u5982\u6b64\u7d27\u5bc6\u7684\u76f8\u4e92\u8fde\u63a5\uff0c\u4ee5\u81f3\u4e8e\u5c40\u90e8\u7279\u5f81\u4e0e\u5168\u5c40\u7279\u5f81\u51e0\u4e4e\u6ca1\u6709\u533a\u522b\u3002\u201c\u200d<\/span>\u9ad8\u200d<\/span>\u200d<\/span>\u200d<\/span>\u200d<\/span>\u200d<\/span>\u200d<\/span>\u200d<\/span>\u200d<\/span>\u7ef4\u6269\u5c55\u56fe\u662f\u4e00\u4e2a\u5947\u8ff9\u3002\u53ea\u8981\u5bf9\u56fe\u7684\u4e00\u90e8\u5206\u505a\u5fae\u5c0f\u8c03\u6574\uff0c\u4e00\u5207\u90fd\u4f1a\u6539\u53d8\u3002\u201dGur \u8bf4\u3002<\/span><\/section>\n
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Lubotzky \u548c Dinur \u5f00\u59cb\u5c1d\u8bd5\u5728 Garland \u5de5\u4f5c\u7684\u57fa\u7840\u4e0a\u521b\u5efa\u4e00\u4e2a\u53ef\u80fd\u89e3\u51b3 c3<\/sup><\/span> \u731c\u60f3\u7684\u7f16\u7801\u3002Evra, Livne \u548c Mozes \u5f88\u5feb\u52a0\u5165\u4e86\u8fd9\u4e2a\u56e2\u961f\uff0c\u4ed6\u4eec\u6bcf\u4e2a\u4eba\u90fd\u662f\u9ad8\u7ef4\u6269\u5c55\u56fe\u4e0d\u540c\u65b9\u9762\u7684\u4e13\u5bb6\u3002\u5f88\u5feb\uff0c\u4ed6\u4eec\u5c31\u5728\u7814\u8ba8\u4f1a\u548c\u8bb2\u5ea7\u4e0a\u4ecb\u7ecd\u4e86\u81ea\u5df1\u7684\u5de5\u4f5c\uff0c\u4f46\u5e76\u4e0d\u662f\u6bcf\u4e2a\u4eba\u90fd\u76f8\u4fe1\u9ad8\u7ef4\u6269\u5c55\u56fe\u80fd\u591f\u89e3\u51b3\u95ee\u9898\u3002\u8981\u5b8c\u5168\u7406\u89e3\u9ad8\u7ef4\u6269\u5c55\u56fe\u9700\u8981\u6500\u8d8a\u4e00\u6761\u9661\u5ced\u7684\u5b66\u4e60\u66f2\u7ebf\u3002\u201c\u5f53\u65f6\u5b83\u770b\u8d77\u6765\u50cf\u662f\u9065\u8fdc\u672a\u6765\u7684\u6280\u672f\uff0c\u662f\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u4ece\u672a\u89c1\u8fc7\u7684\u590d\u6742\u800c\u5947\u7279\u7684\u6570\u5b66\u5de5\u5177\u3002\u8fd9\u4f3c\u4e4e\u6709\u4e9b\u5c0f\u9898\u5927\u505a\u3002\u201dGur \u8bf4\u3002<\/span><\/section>\n
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2020\u5e74\uff0c\u7814\u7a76\u4eba\u5458\u9677\u5165\u4e86\u56f0\u5883\uff0c\u76f4\u5230\u4ed6\u4eec\u610f\u8bc6\u5230\uff0c\u4e0d\u4f9d\u9760\u590d\u6742\u7684\u65b0\u5de5\u5177\u4e5f\u80fd\u89e3\u51b3\u95ee\u9898\u3002\u4ece\u9ad8\u7ef4\u6269\u5c55\u7406\u8bba\u4e2d\u83b7\u5f97\u7684\u7075\u611f\u5df2\u7ecf\u8db3\u591f\u3002<\/span><\/section>\n
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\u5728\u4ed6\u4eec\u7684\u65b0\u5de5\u4f5c\u4e2d\uff0c\u4f5c\u8005\u4eec\u63d0\u51fa\u5c06\u6269\u5c55\u56fe\u7ec4\u88c5\u8d77\u6765\u521b\u5efa\u4e00\u4e2a\u65b0\u7684\u56fe\uff0c\u8fd9\u4f1a\u4ea7\u751f\u5177\u6709\u6700\u4f73\u5f62\u5f0f\u7684\u5c40\u90e8\u53ef\u6d4b\u8bd5\u7f16\u7801\u3002\u4ed6\u4eec\u79f0\u4e4b\u4e3a\u5de6\u53f3Cayley\u590d\u5f62<\/span>\uff08left-right Cayley complex\uff09<\/span>\u3002<\/span><\/section>\n
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\u4e0e Garland \u7684\u5de5\u4f5c\u4e00\u6837\uff0c\u8fd9\u79cd\u56fe\u7684\u6784\u4ef6\u4e0d\u518d\u662f\u4e00\u7ef4\u7684\u8fb9\uff0c\u800c\u662f\u4e8c\u7ef4\u7684\u6b63\u65b9\u5f62\u3002\u7f16\u7801\u4e2d\u7684\u6bcf\u4e2a\u4fe1\u606f\u6bd4\u7279\u88ab\u5206\u914d\u5230\u4e00\u4e2a\u6b63\u65b9\u5f62\uff0c\u800c\u5947\u5076\u6821\u9a8c\u4f4d\u88ab\u5206\u914d\u5230\u8fb9\u548c\u89d2\uff08\u5373\u8282\u70b9\uff09<\/strong>\u3002\u56e0\u6b64\uff0c\u6bcf\u4e2a\u8282\u70b9\u90fd\u5b9a\u4e49\u4e86\u8fde\u63a5\u5230\u5b83\u7684\u6bd4\u7279<\/span>\uff08\u6216\u6b63\u65b9\u5f62\uff09<\/span>\u7684\u503c\u3002<\/span><\/section>\n
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\u4e3a\u4e86\u4e86\u89e3\u8fd9\u4e2a\u56fe\u5230\u5e95\u662f\u4ec0\u4e48\u6837\uff0c\u6211\u4eec\u53ef\u4ee5\u60f3\u8c61\u7ad9\u5728\u5176\u4e2d\u4e00\u6761\u8fb9\u4e0a\uff0c\u4ece\u56fe\u7684\u5185\u90e8\u8fdb\u884c\u89c2\u5bdf\u3002\u5728\u6784\u5efa\u56fe\u65f6\uff0c\u6bcf\u6761\u8fb9\u4e0a\u90fd\u8fde\u63a5\u6709\u56fa\u5b9a\u6570\u91cf\u7684\u6b63\u65b9\u5f62\u3002\u56e0\u6b64\uff0c\u4ece\u4f60\u7684\u4f4d\u7f6e\u770b\u6765\uff0c\u4f1a\u611f\u89c9\u50cf\u662f\u4ece\u5c0f\u518c\u5b50\u7684\u4e66\u810a\u5411\u5916\u770b\uff1b\u4f46\u662f\uff0c\u4ece\u4e66\u9875\u7684\u5176\u4ed6\u4e09\u8fb9\uff0c\u4e5f\u4f1a\u770b\u5230\u4ece\u4e2d\u5206\u51fa\u65b0\u5c0f\u518c\u5b50\u7684\u4e66\u810a\u3002\u5c0f\u518c\u5b50\u4f1a\u4ece\u6bcf\u4e2a\u8fb9\u7f18\u5206\u51fa\uff0c\u76f4\u81f3\u65e0\u7a77\u3002<\/span><\/section>\n
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\u56fe5. \u4e3a\u4e86\u521b\u9020\u4e00\u79cd\u6700\u4f73\u7684\u4fe1\u606f\u7f16\u7801\u65b9\u6cd5\uff0c\u7814\u7a76\u4eba\u5458\u7528\u56fe\u6765\u8868\u793a\u7f16\u7801\uff0c\u8fd9\u4e2a\u56fe\u7684\u5f62\u5f0f\u662f\u7531\u5c0f\u518c\u5b50\u7ec4\u6210\u7684\u76f8\u4e92\u8fde\u63a5\u7684\u7f51\u7edc\uff0c\u5b83\u5411\u5916\u6269\u5c55\uff0c\u76f4\u81f3\u65e0\u7a77\u3002\u56fe\u4e2d\u7684\u4e00\u4e2a\u6b63\u65b9\u5f62\u4ee3\u8868\u4fe1\u606f\u7684\u4e00\u4e2a\u6bd4\u7279\u3002| \u6765\u6e90\uff1aOlena Shmahalo for Quanta Magazine<\/span><\/p>\n

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\u201c\u4e0d\u53ef\u80fd\u770b\u5230\u8fd9\u6837\u7684\u56fe\u50cf\uff0c\u8fd9\u5c31\u662f\u95ee\u9898\u7684\u5173\u952e\uff0c\u4e5f\u662f\u4e3a\u4ec0\u4e48\u95ee\u9898\u5982\u6b64\u590d\u6742\u3002\u201dLubotzky \u8bf4\u3002<\/span><\/section>\n
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\u81f3\u5173\u91cd\u8981\u7684\u662f\uff0c\u8fd9\u79cd\u590d\u6742\u7684\u56fe\u4e5f\u5177\u6709\u6269\u5f20\u56fe\u7684\u5c5e\u6027\uff0c\u5982\u7a00\u758f\u6027\u548c\u5173\u8054\u6027\uff0c\u4f46\u5177\u6709\u66f4\u4e30\u5bcc\u7684\u5c40\u90e8\u7ed3\u6784<\/strong>\u3002\u4f8b\u5982\uff0c\u5750\u5728\u9ad8\u7ef4\u6269\u5c55\u56fe\u4e00\u4e2a\u9876\u70b9\u7684\u89c2\u5bdf\u8005\u53ef\u4ee5\u5229\u7528\u5c40\u90e8\u7ed3\u6784\u76f4\u63a5\u63a8\u65ad\u51fa\u6574\u4e2a\u56fe\u662f\u5f3a\u8fde\u63a5\u7684\u3002<\/span><\/section>\n
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\u201c\u968f\u673a\u6027\u7684\u5bf9\u7acb\u9762\u662f\u4ec0\u4e48\uff1f\u662f\u7ed3\u6784\u3002\u5c40\u90e8\u53ef\u6d4b\u8bd5\u6027\u7684\u5173\u952e\u662f\u7ed3\u6784\u3002\u201dEvra \u8bf4\u3002<\/span><\/section>\n
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\u4e3a\u4e86\u4e86\u89e3\u8fd9\u79cd\u65b0\u7684\u9ad8\u7ef4\u6269\u5c55\u56fe\u5982\u4f55\u5bfc\u81f4\u5c40\u90e8\u53ef\u6d4b\u8bd5\u7684\u7f16\u7801\uff0c\u9996\u5148\u8003\u8651\u4e00\u4e2a\u6269\u5c55\u56fe\u7684\u7f16\u7801\uff0c\u5982\u679c\u4e00\u4e2a\u6bd4\u7279<\/span>\uff08\u4e00\u6761\u8fb9\uff09<\/span>\u6709\u9519\u8bef\uff0c\u53ea\u80fd\u901a\u8fc7\u68c0\u6d4b\u5176\u7d27\u90bb\u8282\u70b9\u7684\u6821\u9a8c\u4f4d\u6765\u53d1\u73b0\u8fd9\u4e2a\u9519\u8bef\u3002\u4f46\u5728\u5de6\u53f3Cayley\u590d\u5f62\u4e2d\uff0c\u5982\u679c\u4e00\u4e2a\u6bd4\u7279<\/span>\uff08\u4e00\u4e2a\u6b63\u65b9\u5f62\uff09<\/span>\u6709\u9519\u8bef\uff0c\u90a3\u4e48\u8fd9\u4e2a\u9519\u8bef\u53ef\u4ee5\u4ece\u591a\u4e2a\u4e0d\u540c\u7684\u8282\u70b9\u770b\u5230\uff0c\u751a\u81f3\u5305\u62ec\u4e00\u4e9b\u6ca1\u6709\u4e92\u76f8\u8fde\u63a5\u7684\u8282\u70b9\u3002\u8fd9\u6837\u4e00\u6765\uff0c\u5bf9\u4e00\u4e2a\u8282\u70b9\u7684\u6d4b\u8bd5\u53ef\u4ee5\u7ed9\u51fa\u8fdc\u5904\u8282\u70b9\u7684\u9519\u8bef\u4fe1\u606f<\/strong>\u3002\u901a\u8fc7\u5229\u7528\u66f4\u9ad8\u7684\u7ef4\u5ea6\uff0c\u56fe\u4ee5\u8d85\u51fa\u6211\u4eec\u8ba4\u77e5\u7684\u65b9\u5f0f\u8fde\u63a5\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u9664\u4e86\u53ef\u6d4b\u8bd5\u6027\u4e4b\u5916\uff0c\u65b0\u7f16\u7801\u8fd8\u4fdd\u6301\u4e86\u901f\u7387\u3001\u8ddd\u79bb\u548c\u5176\u4ed6\u6240\u9700\u7684\u7279\u6027\uff0c\u751a\u81f3\u5728\u7801\u5b57\u6269\u5c55\u65f6\u4e5f\u662f\u5982\u6b64\uff0c\u8bc1\u660e\u4e86 c3<\/sup><\/span> \u731c\u60f3\u7684\u6b63\u786e\u6027\u3002\u5b83\u786e\u7acb\u4e86\u7ea0\u9519\u7801\u7684\u6700\u65b0\u6280\u672f\u6c34\u5e73\uff0c\u4e5f\u662f\u5c06\u9ad8\u7ef4\u6269\u5c55\u56fe\u5e94\u7528\u4e8e\u7f16\u7801\u7684\u7b2c\u4e00\u4e2a\u5b9e\u8d28\u6027\u56de\u62a5\u3002\u201c\u8fd9\u662f\u89c2\u5bdf\u8fd9\u4e9b\u7f16\u7801\u7684\u5168\u65b0\u65b9\u5f0f\u3002\u201dDinur \u8bf4\u3002<\/span><\/section>\n
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\u7b97\u6cd5\u5b9e\u8df5\u548c\u7406\u8bba\u4e0a\u7684\u5e94\u7528\u5e94\u8be5\u5f88\u5feb\u5c31\u4f1a\u51fa\u73b0\u3002\u4e0d\u540c\u5f62\u5f0f\u7684\u5c40\u90e8\u53ef\u68c0\u6d4b\u7f16\u7801\u73b0\u5728\u6b63\u88ab\u7528\u4e8e\u53bb\u4e2d\u5fc3\u5316\u7684\u91d1\u878d<\/strong>\uff0c\u800c\u4e00\u4e2a\u6700\u4f73\u7248\u672c\u5c06\u5e2e\u52a9\u5b9e\u73b0\u66f4\u597d\u7684\u53bb\u4e2d\u5fc3\u5316\u5de5\u5177\u3002\u6b64\u5916\uff0c\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u6709\u5b8c\u5168\u4e0d\u540c\u7684\u7406\u8bba\u6784\u9020\uff0c\u79f0\u4e3a\u6982\u7387\u53ef\u68c0\u6d4b\u8bc1\u660e<\/span>\uff08probabilistically checkable proofs\uff09<\/span>\uff0c\u5b83\u4e0e\u5c40\u90e8\u53ef\u68c0\u6d4b\u7f16\u7801\u6709\u76f8\u4f3c\u4e4b\u5904\u3002\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u627e\u5230\u4e86\u540e\u8005\u7684\u6700\u4f73\u5f62\u5f0f\uff0c\u524d\u8005\u7684\u65b0\u7248\u672c\u4f3c\u4e4e\u4e5f\u53ef\u80fd\u51fa\u73b0\u3002<\/span><\/section>\n
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\u6700\u7ec8\uff0c\u65b0\u7f16\u7801\u6807\u5fd7\u7740\u4e00\u4e2a\u6982\u5ff5\u4e0a\u7684\u91cc\u7a0b\u7891\uff0c\u8fd9\u662f\u8d85\u8d8a\u7531\u968f\u673a\u6027\u8bbe\u7f6e\u7684\u7f16\u7801\u754c\u9650\u7684\u6700\u5927\u4e00\u6b65\u3002\u5269\u4e0b\u7684\u552f\u4e00\u95ee\u9898\u662f\uff0c\u4fe1\u606f\u7684\u4f2a\u9020\u7a0b\u5ea6\u662f\u5426\u5b58\u5728\u771f\u6b63\u7684\u9650\u5236\u3002<\/span><\/section>\n
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\u53c2\u8003\u94fe\u63a5<\/span><\/strong><\/span><\/section>\n
[1]https:\/\/arxiv.org\/abs\/2111.04808<\/span><\/section>\n
[2]https:\/\/www.wisdom.weizmann.ac.il\/~dinuri\/<\/span><\/section>\n
[3]https:\/\/mathematics.huji.ac.il\/people\/shai-evra?ref_tid=4311<\/span><\/section>\n
[4]https:\/\/mathematics.huji.ac.il\/people\/ron-livne<\/span><\/section>\n
[5]http:\/\/www.ma.huji.ac.il\/~alexlub\/<\/span><\/section>\n
[6]https:\/\/mathematics.huji.ac.il\/people\/shahar-mozes<\/span><\/section>\n
[7]https:\/\/www.dcs.warwick.ac.uk\/~tomgur\/<\/span><\/section>\n
[8]http:\/\/www.henryyuen.net\/<\/span><\/section>\n
[9]https:\/\/ieeexplore.ieee.org\/abstract\/document\/1056404<\/span><\/section>\n
[10]https:\/\/www.cs.utexas.edu\/~danama\/<\/span><\/section>\n
 <\/span><\/section>\n
\u539f\u6587\u94fe\u63a5\uff1a<\/span><\/section>\n
https:\/\/www.quantamagazine.org\/researchers-defeat-randomness-to-create-ideal-code-20211124\/<\/span><\/section>\n


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\u96c6\u667a\u6591\u56fe\u9876\u520a\u8bba\u6587\u901f\u9012\u680f\u76ee\u4e0a\u7ebf\u4ee5\u6765\uff0c\u6301\u7eed\u6536\u5f55\u6765\u81eaNature\u3001Science<\/span>\u7b49\u9876\u520a\u7684\u6700\u65b0\u8bba\u6587\uff0c\u8ffd\u8e2a\u590d\u6742\u7cfb\u7edf\u3001\u7f51\u7edc\u79d1\u5b66\u3001\u8ba1\u7b97\u793e\u4f1a\u79d1\u5b66\u7b49\u9886\u57df\u7684\u524d\u6cbf\u8fdb\u5c55\u3002\u73b0\u5728\u6b63\u5f0f\u63a8\u51fa\u8ba2\u9605\u529f\u80fd\uff0c\u6bcf\u5468\u901a\u8fc7\u5fae\u4fe1\u670d\u52a1\u53f7\u300c\u96c6\u667a\u6591\u56fe\u300d\u63a8\u9001\u8bba\u6587\u4fe1\u606f\u3002\u626b\u63cf\u4e0b\u65b9\u4e8c\u7ef4\u7801\u5373\u53ef\u4e00\u952e\u8ba2\u9605\uff1a<\/span>
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