{"id":34921,"date":"2022-06-02T21:11:24","date_gmt":"2022-06-02T13:11:24","guid":{"rendered":"https:\/\/swarma.org\/?p=34921"},"modified":"2022-06-02T21:11:24","modified_gmt":"2022-06-02T13:11:24","slug":"%e4%ba%92%e4%bf%a1%e6%81%af%e7%9a%84%e5%be%ae%e7%a7%af%e5%88%86","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=34921","title":{"rendered":"\u4e92\u4fe1\u606f\u7684\u201c\u5fae\u79ef\u5206\u201d"},"content":{"rendered":"
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\u4f17\u6240\u5468\u77e5\uff0cShannon\u7684\u4fe1\u606f\u8bba\u5728\u7ecf\u5178\u7684\u901a\u8baf\u5de5\u7a0b\u4e2d\u8d77\u5230\u4e86\u5f02\u5e38\u91cd\u8981\u7684\u4f5c\u7528\u3002\u8fdb\u516521\u4e16\u7eaa\uff0c\u4fe1\u606f\u8bba\u5728\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u5e94\u7528\u53c8\u6709\u4e86\u957f\u8db3\u7684\u53d1\u5c55\u3002\u5176\u4e2d\uff0c\u5f88\u591a\u8fdb\u5c55\u90fd\u662f\u4e0e\u4e92\u4fe1\u606f\uff08Mutual Information\uff09\u8fd9\u4e00\u6307\u6807\u7684\u7ec6\u5316\u548c\u53d1\u5c55\u6709\u7740\u5bc6\u5207\u5173\u7cfb\u7684\u3002\u4f20\u7edf\u7684\u89c2\u70b9\u8ba4\u4e3a\uff0c\u4e92\u4fe1\u606f\u523b\u753b\u7684\u662f\u968f\u673a\u4e8b\u4ef6\u4e4b\u95f4\u7684\u975e\u7ebf\u6027\u5173\u8054\uff0c\u800c\u975e\u7ebf\u6027\u5f80\u5f80\u662f\u65e0\u6cd5\u8fdb\u884c\u62c6\u5206\u7684\u3002\u7136\u800c\uff0c2010\u5e74\u7684\u7ecf\u5178\u8bba\u6587 \u201cNonnegative Decomposition of Multivariate Information\u201d\u5374\u627e\u5230\u4e86\u4e00\u4e2a\u53ef\u4ee5\u5c06\u590d\u6742\u591a\u53d8\u91cf\u4f53\u7cfb\u7684\u4e92\u4fe1\u606f\u8fdb\u884c\u539f\u5b50\u5316\u62c6\u5206\u7684\u65b9\u5f0f\u3002\u8fd9\u4e00\u62c6\u5206\u4e0d\u4ec5\u80fd\u591f\u7cbe\u51c6\u5730\u5c06\u591a\u7ef4\u5ea6\u53d8\u91cfX\u5bf9\u5355\u4e00\u53d8\u91cfY\u7684\u4e92\u4fe1\u606f\u62c6\u5206\u4e3a\u5197\u4f59\u3001\u534f\u540c\uff0c\u4ee5\u53ca\u72ec\u7acb\u4fe1\u606f\uff0c\u8fd8\u80fd\u4e3a\u6211\u4eec\u7406\u89e3\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u6d8c\u73b0\u7279\u6027\u4ee5\u53ca\u56e0\u679c\u7279\u6027\u63d0\u4f9b\u6df1\u523b\u6d1e\u5bdf\uff0c\u7279\u522b\u662f\uff0c\u8be5\u7406\u8bba\u53ef\u80fd\u4e3a\u666e\u904d\u5b58\u5728\u4e8e\u590d\u6742\u7cfb\u7edf\u5206\u6790\u4e2d\u7684\u91cd\u6574\u5316\/\u7c97\u7c92\u5316\u64cd\u4f5c\u63d0\u4f9b\u4fe1\u606f\u8bba\u65b9\u9762\u7684\u7406\u8bba\u57fa\u7840\u3002<\/span><\/strong><\/p>\n


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\u7814\u7a76\u9886\u57df\uff1a\u590d\u6742\u7cfb\u7edf\uff0c\u591a\u53d8\u91cf\u76f8\u4e92\u4f5c\u7528\uff0c\u4fe1\u606f\u8bba<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u8bba\u6587\u9898\u76ee\uff1a<\/span><\/p>\n

<\/span>Nonnegative Decomposition of Multivariate Information<\/span><\/p>\n

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\u4ece\u67d0\u79cd\u89c6\u89d2\u6765\u770b\uff0c\u590d\u6742\u7cfb\u7edf\u53ef\u4ee5\u770b\u505a\u5b58\u5728\u76f8\u4e92\u4f5c\u7528\u7684\u591a\u53d8\u91cf\u7cfb\u7edf\u3002\u800c\u4fe1\u606f\u8bba\u89c6\u89d2\u662f\u7406\u89e3\u53d8\u91cf\u4e4b\u95f4\u76f8\u5e94\u5173\u7cfb\u7684\u91cd\u8981\u89c6\u89d2\uff0c\u56e0\u6b64\u4eba\u4eec\u53d1\u660e\u5e76\u62d3\u5c55\u4e86\u4e00\u7cfb\u5217\u65b9\u6cd5\uff0c\u5c06\u4fe1\u606f\u8bba\u7684\u601d\u7ef4\u5e94\u7528\u5230\u5bf9\u590d\u6742\u7cfb\u7edf\u7684\u7406\u89e3\u4e0a\u3002\u4f8b\u5982\uff0c\u9488\u5bf9\u4e24\u4e2a<\/strong>\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e92\u4fe1\u606f\uff08Mutual Information\uff09<\/strong>\u6765\u8861\u91cf\u5f53\u4e00\u4e2a\u53d8\u91cf\u88ab\u89c2\u6d4b\u540e\uff0c\u53e6\u4e00\u4e2a\u53d8\u91cf\u7684\u4e0d\u786e\u5b9a\u6027<\/span>\uff08\u71b5\uff09<\/span>\u7684\u51cf\u5c11\u3002\u4f46\u8fd9\u79cd\u5de5\u5177\u7684\u9002\u7528\u573a\u666f\u76f8\u5f53\u6709\u9650\uff0c\u5f53\u53d8\u91cf\u6570\u91cf\u589e\u591a\uff0c\u5176\u76f8\u4e92\u4f5c\u7528\u673a\u5236\u53d8\u5f97\u590d\u6742\u65f6\uff0c\u7531\u4e8e\u5927\u91cf\u53d8\u91cf\u4e4b\u95f4\u6709\u53ef\u80fd\u5b58\u5728\u534f\u540c\u6548\u5e94<\/span>\uff08synergy\uff09<\/span>\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u9664\u4e86\u8ba1\u7b97\u539f\u59cb\u53d8\u91cf\u4e4b\u95f4\u7684\u4e92\u4fe1\u606f\uff0c\u8fd8\u8981\u8ba1\u7b97\u53d8\u91cf\u7684\u4e24\u4e24\u7ec4\u5408\uff0c\u751a\u81f3\u66f4\u591a\u7ec4\u5408\u4e4b\u95f4\u7684\u4e92\u4fe1\u606f\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5728\u9884\u6d4b\u95ee\u9898\u4e2d\uff0c\u4e0d\u540c\u81ea\u53d8\u91cf\u4e4b\u95f4\u6709\u53ef\u80fd\u5171\u4eab\u76f8\u4f3c\u7684\u4fe1\u606f\uff0c\u90a3\u4e48\u4e0d\u540c\u53d8\u91cf\u4e4b\u95f4\u5171\u4eab\u7684\u8fd9\u90e8\u5206\u4fe1\u606f\u5230\u5e95\u5bf9\u9884\u6d4b\u8d77\u5230\u4e86\u591a\u5927\u4f5c\u7528\u5462\uff1f<\/span><\/p>\n


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\u4e3a\u4e86\u7406\u89e3\u591a\u53d8\u91cf\u76f8\u4e92\u4f5c\u7528<\/strong>\u60c5\u51b5\u4e0b\u7684\u4fe1\u606f\u7ed3\u6784\uff0c\u4eba\u4eec\u5bf9\u4e92\u4fe1\u606f\u505a\u4e86\u4e00\u7cfb\u5217\u62d3\u5c55\uff0c\u53d1\u660e\u4e86\u591a\u79cd\u65b0\u7684\u5de5\u5177\u4ee5\u5206\u6790\u590d\u6742\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u5e76\u8bd5\u56fe\u5c06\u8fd9\u4e9b\u5de5\u5177\u5e94\u7528\u4e8e\u5bf9\u590d\u6742\u7cfb\u7edf\u7684\u7406\u89e3\u4e2d\u3002<\/span><\/p>\n


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\u672c\u6587\u5c06\u4ecb\u7ecd\u591a\u4e2a\u6e90<\/span>\uff08source\uff09<\/span>\u53d8\u91cf\u4f5c\u7528\u4e8e\u4e00\u4e2a\u76ee\u6807<\/span>\uff08target\uff09<\/span>\u53d8\u91cf\u65f6\u7684\u4e00\u4e9b\u4fe1\u606f\u5206\u89e3\u5de5\u5177\uff0c\u6211\u4eec\u5c06\u4ece\u4e92\u4fe1\u606f\u51fa\u53d1\uff0c\u8fdb\u4e00\u6b65\u8ba8\u8bba\u591a\u53d8\u91cf\u60c5\u51b5\u4e0b\u7684\u4e92\u4fe1\u606f\u9762\u4e34\u7684\u56f0\u5883\uff0c\u5e76\u5f15\u5165\u4fe1\u606f\u7684\u975e\u8d1f\u5206\u89e3\u65b9\u6cd5\u6765\u66f4\u597d\u5730\u7406\u89e3\u591a\u5bf9\u4e00\u60c5\u51b5\u4e0b\u7684\u4fe1\u606f\u7ed3\u6784\u3002<\/span><\/p>\n


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\u4fe1\u606f\u8bba\u5960\u57fa\u4eba\u9999\u519c<\/span>\uff08Shannon\uff09<\/span>\u8ba4\u4e3a\uff0c\u201c\u4fe1\u606f\u662f\u7528\u6765\u6d88\u9664\u968f\u673a\u4e0d\u786e\u5b9a\u6027\u7684\u4e1c\u897f\u201d\u3002\u4e5f\u5c31\u662f\u8bf4\u8861\u91cf\u4fe1\u606f\u91cf\u5927\u5c0f\u5c31\u770b\u8fd9\u4e2a\u4fe1\u606f\u6d88\u9664\u4e0d\u786e\u5b9a\u6027\u7684\u7a0b\u5ea6\u3002\u901a\u8fc7\u5c06\u4fe1\u606f\u4e0e\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u7ed3\u5408\u5728\u4e00\u8d77\uff0c\u9999\u519c\u7387\u5148\u5bf9\u4fe1\u606f\u91cf\u8fdb\u884c\u4e86\u5ea6\u91cf\uff1a\u5373\u4fe1\u606f\u91cf<\/sub><\/span><\/span>\uff0cx \u4e3a\u968f\u673a\u53d8\u91cf X \u7684\u4e00\u4e2a\u53ef\u80fd\u53d6\u503c\uff0cp(x) \u8868\u793a X \u53d6\u503c\u4e3a x \u7684\u6982\u7387\uff0ch(x) \u4ee3\u8868 X \u53d6\u503c\u4e3a x \u8fd9\u4e00\u4e8b\u4ef6\u7684\u4fe1\u606f\u91cf\u3002\u8fdb\u4e00\u6b65\uff0c\u9999\u519c\u63d0\u51fa\u4e86\u4fe1\u606f\u71b5<\/strong>\u7684\u6982\u5ff5\u6765\u8861\u91cf\u4e00\u4e2a\u968f\u673a\u53d8\u91cf\u53ef\u80fd\u4ea7\u751f\u7684\u4fe1\u606f\u91cf\u7684\u671f\u671b\uff0c\u5373<\/sub><\/span><\/span>\u3002\u6211\u4eec\u4e5f\u53ef\u4ee5\u5c06\u4fe1\u606f\u71b5\u7406\u89e3\u4e3a\u5bf9\u4e8b\u7269\u7684\u4e0d\u786e\u5b9a\u6027\u7684\u5ea6\u91cf\uff1a\u4fe1\u606f\u71b5\u8d8a\u5927\uff0c\u4e8b\u7269\u8d8a\u5177\u6709\u4e0d\u786e\u5b9a\u6027\uff0c\u4fe1\u606f\u71b5\u7684\u5355\u4f4d\u4e3a bit\u3002<\/span><\/p>\n


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<\/p>\n

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

<\/p>\n


<\/p>\n

<\/p>\n

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<\/p>\n

\u5f53\u76f8\u4e92\u4f5c\u7528\u7684\u53d8\u91cf\u6570\u91cf\u589e\u591a\u65f6\uff0c\u4e92\u4fe1\u606f\u7684\u4f7f\u7528\u4fbf\u4f1a\u5e26\u6765\u4e00\u5b9a\u7684\u95ee\u9898\uff0c\u60f3\u8c61\u8fd9\u6837\u7684\u573a\u666f\uff1a\u5b58\u5728\u4e09\u4e2a\u53d8\u91cfR1<\/sub><\/span>, R2<\/sub><\/span>, S<\/span>\uff0c\u5b83\u4eec\u90fd\u4ee5\u7b49\u6982\u7387\u53d60\u62161\uff0c\u4f46\u5f7c\u6b64\u4e4b\u95f4\u5e76\u4e0d\u72ec\u7acb\uff0c\u5176\u5173\u7cfb\u4e3a\uff1a<\/span><\/p>\n


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

R<\/span>1<\/sub><\/span>=R<\/span>2<\/sub><\/span>=<\/span>S<\/span><\/p>\n


<\/p>\n

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<\/p>\n

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

<\/sub><\/span>\uff08\u5f02\u6216\uff09<\/span><\/p>\n


<\/p>\n

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


<\/p>\n

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<\/p>\n

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\u4e09\u3001\u591a\u53d8\u91cf\u4fe1\u606f\u5206\u89e3 <\/span><\/strong><\/strong><\/p>\n<\/section>\n

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

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

1. \u8ba1\u7b97\u5197\u4f59\u4fe1\u606f<\/strong><\/span><\/p>\n


<\/section>\n
\u63a5\u4e0b\u6765\u6211\u4eec\u5c06\u4ecb\u7ecd\u4e00\u79cd\u5197\u4f59\u4fe1\u606f\u7684\u8ba1\u7b97\u65b9\u6cd5\uff0c\u8fd9\u4e00\u65b9\u6cd5\u6765\u6e90\u4e8e\u8bba\u6587\u201cNonnegative Decomposition of Multivariate Information\u201d\uff0c\u8fd9\u4e00\u7ecf\u5178\u8bba\u6587\u53d1\u8868\u4e8e2010\u5e74\uff0c\u63d0\u4f9b\u4e86\u4e00\u79cd\u591a\u53d8\u91cf\u4f5c\u7528\u4e8e\u5355\u53d8\u91cf\u60c5\u51b5\u4e0b\u7684\u4fe1\u606f\u7ed3\u6784\u7406\u89e3\u65b9\u6cd5\uff0c\u5e76\u542f\u53d1\u4e86\u540e\u7eed\u4e00\u7cfb\u5217\u5de5\u4f5c<\/span>\uff08\u5982\u591a\u53d8\u91cf\u4f5c\u7528\u4e8e\u591a\u53d8\u91cf\u7684\u4fe1\u606f\u7ed3\u6784\u5206\u89e3\u65b9\u6cd5\uff09<\/span>\uff0c\u73b0\u5728\u8fd9\u4e00\u8bba\u6587\u53ca\u5176\u8ddf\u968f\u8005\u5df2\u7ecf\u5f00\u53d1\u51fa\u4e86\u4e00\u7cfb\u5217\u5de5\u5177\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u591a\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u4e92\u5f71\u54cd\uff0c\u4ece\u800c\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u4fe1\u606f\u6d41\u52a8\u3002\u5728\u8fd9\u7bc7\u8bba\u6587\u4e2d\uff0c\u5197\u4f59\u4fe1\u606f\u7684\u8ba1\u7b97\u65b9\u6cd5\u662f\u6240\u6709\u65b9\u6cd5\u7684\u6838\u5fc3\uff0c\u6211\u4eec\u5c06\u7387\u5148\u5b66\u4e60\u5982\u4f55\u8ba1\u7b97\u5197\u4f59\u4fe1\u606f\uff0c\u5e76\u6839\u636e\u5197\u4f59\u4fe1\u606f\u8fdb\u4e00\u6b65\u5b9a\u4e49\u5355\u72ec<\/span>\uff08Unique\uff09<\/span>\u548c\u534f\u540c<\/span>\uff08Synergistic\uff09<\/span>\u4fe1\u606f\u3002<\/span><\/section>\n

<\/section>\n
\u5373\u4f7f\u662f\u5728R<\/span>1<\/sub><\/span>\u548cR2<\/sub><\/span>\u5171\u540c\u4f5c\u7528\u4e8e\u53d8\u91cfS\u7684\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u4ecd\u7136\u53ef\u4ee5\u5206\u522b\u8ba1\u7b97R<\/span>1<\/sub><\/span>\u548cS\uff0c\u4ee5\u53caR2<\/sub><\/span>\u548cS\u7684\u4e92\u4fe1\u606f\u3002R<\/span>1<\/sub><\/span>\u548cS\u7684\u4e92\u4fe1\u606f\u53ef\u4ee5\u88ab\u7406\u89e3\u4e3aR<\/span>1<\/sub><\/span>\u53ef\u89c2\u6d4b\u7684\u72b6\u6001\u4e0b\uff0c\u5bf9S\u7684\u6240\u6709\u53ef\u80fd\u53d6\u503c\u7684\u4e0d\u786e\u5b9a\u51cf\u5c0f\u7a0b\u5ea6\u7684\u671f\u671b\u3002\u56e0\u6b64R<\/span>1<\/sub><\/span>\u548cS\u7684\u4e92\u4fe1\u606f\u53ef\u4ee5\u5199\u6210<\/span><\/section>\n

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\u5176\u4e2d<\/sub><\/span>\u8868\u793a\u4e86\u89c2\u6d4bR<\/span>1<\/sub><\/span>\u5bf9S\u53d6\u503c\u4e3as\u8fd9\u4e00\u4e8b\u4ef6\u7684\u4e0d\u786e\u5b9a\u6027\u7684\u51cf\u5c11\uff0c\u5f53\u7136\uff0c\u89c2\u6d4bR2<\/sub><\/span>\u540c\u6837\u53ef\u80fd\u51cf\u5c11S\u53d6\u503c\u4e3as\u7684\u4e0d\u786e\u5b9a\u6027\uff0c\u6211\u4eec\u53d6\u4ee5\u4e0a\u4e24\u4e2a\u4e0d\u786e\u5b9a\u6027\u7684\u6700\u5c0f\u503c\uff0c\u53731<\/sub><\/span>\uff0c\u4f5c\u4e3aR<\/span>1<\/sub><\/span>\u548cR<\/span>2<\/sub><\/span>\u5173\u4e8eS\u53d6s\u7684\u5197\u4f59\u4fe1\u606f\u91cf\u3002\u6ce8\u610f\uff0c\u8fd9\u91cc\u6307\u7684\u662f\u5bf9S\u53d6\u503c\u4e3as\u8fd9\u4e00\u4e8b\u4ef6\uff0cR<\/span>1<\/sub><\/span>\u548cR<\/span>2<\/sub><\/span>\u5747\u53ef\u63d0\u4f9b\u7684\u4fe1\u606f\u91cf\uff0c\u56e0\u6b64\u8fd9\u4e00\u4fe1\u606f\u91cf\u5177\u6709\u5197\u4f59\u7684\u6027\u8d28\u3002\u8fdb\u4e00\u6b65\uff0c\u5197\u4f59\u4fe1\u606f\u7684\u671f\u671b\u53ef\u4ee5\u88ab\u5199\u6210<\/span><\/section>\n

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<\/p>\n


<\/span><\/section>\n
\u66f4\u4e00\u822c\u5730\uff0c\u5047\u8bbe\u76ee\u6807\u53d8\u91cfZ\u53ef\u4ee5\u88ab\u591a\u4e2a\u6e90\u53d8\u91cf\u5f71\u54cd\uff0c\u6e90\u53d8\u91cf\u6784\u6210\u7684\u96c6\u5408\u4e3aR = {R1<\/sub><\/span>, R2<\/sub><\/span>,…,Rn<\/sub><\/span>}\uff0c\u6211\u4eec\u5047\u8bbeA = {A1<\/sub><\/span>, A2<\/sub><\/span>,…,Ak<\/sub><\/span>}\u4e3a\u4e00\u7cfb\u5217\u975e\u7a7a\u7684\u3001\u53ef\u80fd\u76f8\u4ea4\u7684R\u7684\u5b50\u96c6\u3002\u6211\u4eec\u636e\u6b64\u53ef\u4ee5\u5199\u51fa\u6700\u4e00\u822c\u5316\u7684\u5197\u4f59\u4fe1\u606f\u8ba1\u7b97\u65b9\u6cd5<\/strong>\uff1a<\/span><\/section>\n

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<\/p>\n

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

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\u5b83\u7684\u542b\u4e49\u662f\uff0c\u6211\u4eec\u6293\u4f4f\u4e86\u5bf9\u4e8eS\u7684\u6bcf\u4e00\u4e2a\u53ef\u80fd\u53d6\u503cs\uff0c\u6240\u6709\u7684Ai<\/sub><\/span>\u90fd\u80fd\u63d0\u4f9b\u7684\u6700\u5c0f\u4fe1\u606f\u3002<\/span><\/section>\n

<\/section>\n
\u8ba9\u6211\u4eec\u7528\u51e0\u4e2a\u5c0f\u4f8b\u5b50\u6765\u7406\u89e3\u5197\u4f59\u4fe1\u606f\uff0c\u5047\u8bbe\u5b58\u5728\u4e09\u4e2a\u53d8\u91cfR<\/span>1<\/sub><\/span>, R2<\/sub><\/span>, S\uff0c\u5176\u4e2dS\u4e3a\u76ee\u6807\u53d8\u91cf\uff0c\u5176\u4f59\u4e3a\u6e90\u53d8\u91cf\uff0c\u5176\u5173\u7cfb\u4e3aS=R<\/span>1<\/sub><\/span>=R2<\/sub><\/span>\u3002\u5219\u7cfb\u7edf\u7684\u53ef\u80fd\u72b6\u6001\u5206\u5e03\u5f8b\u5982\u4e0b\u8868\u6240\u793a\uff1a<\/span><\/section>\n

<\/span><\/section>\n\n\n\n\n\n
\n
R1<\/sub><\/span><\/span><\/section>\n<\/td>\n
\n
R2<\/sub><\/span><\/span><\/section>\n<\/td>\n
\n
S<\/span><\/section>\n<\/td>\n
\n
P<\/span><\/section>\n<\/td>\n<\/tr>\n
\n
0<\/span><\/section>\n<\/td>\n
\n
0<\/span><\/section>\n<\/td>\n
\n
0<\/span><\/section>\n<\/td>\n
\n
1\/2<\/span><\/section>\n<\/td>\n<\/tr>\n
\n
1<\/span><\/section>\n<\/td>\n
\n
1<\/span><\/section>\n<\/td>\n
\n
1<\/span><\/section>\n<\/td>\n
\n
1\/2<\/span><\/section>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
<\/span><\/section>\n

<\/section>\n
\u5728\u8be5\u7cfb\u7edf\u4e2d\uff0c\u5bb9\u6613\u77e5\u9053\u76ee\u6807\u53d8\u91cfS\u7684\u71b5\u4e3a1 bit\uff0c\u4ece\u76f4\u89c2\u89d2\u5ea6\u6765\u7406\u89e3\u8be5\u7cfb\u7edf\uff0c\u6211\u4eec\u4f1a\u53d1\u73b0\u82e5R1<\/sub><\/span>\u88ab\u89c2\u6d4b\uff0c\u5219S\u5c31\u6ca1\u6709\u4efb\u4f55\u4e0d\u786e\u5b9a\u6027\u4e86\uff0cS\u7684\u71b5\u964d\u4e3a0\uff0c\u5373R1<\/sub><\/span>\u4e3aS\u63d0\u4f9b\u4e861 bit\u7684\u4fe1\u606f\uff0c\u82e5R2<\/sub><\/span>\u88ab\u89c2\u6d4b\uff0c\u5219\u6211\u4eec\u4e5f\u80fd\u5b8c\u5168\u77e5\u9053S\u7684\u53d6\u503c\uff0cS\u6240\u9700\u7684\u4fe1\u606f\u65e2\u88abR1<\/sub><\/span>\u63d0\u4f9b\u53c8\u88abR2<\/sub><\/span>\u63d0\u4f9b\uff0c\u5219\u6211\u4eec\u8ba4\u4e3aR1<\/sub><\/span>\u548cR2<\/sub><\/span>\u4e3aS\u63d0\u4f9b\u4e861 bit \u7684\u5197\u4f59\u4fe1\u606f\u3002\u6211\u4eec\u5e26\u5165\u516c<\/sub><\/span>\u53ef\u77e5\uff0c\u5176\u8ba1\u7b97\u7ed3\u679c\u4e5f\u4e3a1 bit\uff0c\u53ef\u89c1\u6211\u4eec\u7684\u76f4\u89c2\u5206\u6790\u662f\u6b63\u786e\u7684\u3002<\/span><\/section>\n

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2. \u5197\u4f59\u4fe1\u606f\u7684\u6027\u8d28<\/span><\/strong><\/span>
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\u5197\u4f59\u4fe1\u606f\u6709\u5982\u4e0b\u4e09\u6761\u91cd\u8981\u7684\u6027\u8d28\uff1a<\/span><\/p>\n