{"id":28312,"date":"2021-04-18T13:00:12","date_gmt":"2021-04-18T13:00:12","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28312"},"modified":"2024-09-04T19:22:37","modified_gmt":"2024-09-04T19:22:37","slug":"%e8%8c%83%e5%bc%8f%e5%8f%8a%e5%85%b6%e6%80%a7%e8%b4%a8","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e8%8c%83%e5%bc%8f%e5%8f%8a%e5%85%b6%e6%80%a7%e8%b4%a8\/","title":{"rendered":"\u8303\u5f0f\u53ca\u5176\u6027\u8d28"},"content":{"rendered":"<p><center><\/p>\n<h1>\u8303\u5f0f\u53ca\u5176\u6027\u8d28<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u6458\u8981<\/strong><br \/><em>\u547d\u9898\u903b\u8f91\u662f\u6570\u5b66\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u7684\u4e00\u9879\u57fa\u672c\u5de5\u5177\u3002\u5728\u672c\u8bfe\u4e2d\uff0c\u5c06\u4ecb\u7ecd\u4e00\u4e2a\u4e0e\u8303\u5f0f\u76f8\u5173\u7684\u6709\u8da3\u4e14\u6709\u7528\u7684\u7ed3\u679c\u3002\u4e3a\u6b64\uff0c\u5c06\u5b9a\u4e49\u6587\u5b57\u3001\u5408\u53d6\u8303\u5f0f\uff08CNF\uff09\u548c\u6790\u53d6\u8303\u5f0f\uff08DNF\uff09\u7684\u6982\u5ff5\u3002\u6b64\u5916\uff0c\u8fd8\u5c06\u8bc1\u660e\u8303\u5f0f\u5b9a\u7406\uff0c\u5373\u6240\u6709\u547d\u9898\u903b\u8f91\u8868\u8fbe\u5f0f\u90fd\u7b49\u4ef7\u4e8eCNF\u548cDNF\u8868\u8fbe\u5f0f\u3002\u8bc1\u660e\u5c06\u901a\u8fc7\u5bf9\u516c\u5f0f\u590d\u6742\u6027\u7684\u5f52\u7eb3\u8fdb\u884c\uff0c\u4ece\u800c\u8868\u660e\u6240\u6709\u547d\u9898\u903b\u8f91\u8868\u8fbe\u5f0f\u90fd\u53ef\u4ee5\u7528CNF\u548cDNF\u8868\u793a\u3002\u672c\u8bfe\u5c06\u5bf9\u7406\u89e3\u547d\u9898\u903b\u8f91\u7684\u57fa\u7840\u5e76\u5c06\u5176\u5e94\u7528\u4e8e\u5404\u4e2a\u77e5\u8bc6\u9886\u57df\u5927\u6709\u5e2e\u52a9\u3002<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5b8c\u6210\u672c\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a\n<\/p>\n<ol>\n<li><strong>\u56de\u5fc6<\/strong>\u6587\u5b57\u4ee5\u53ca\u5408\u53d6\u8303\u5f0f\u548c\u6790\u53d6\u8303\u5f0f\u7684\u5b9a\u4e49\u3002<\/li>\n<li><strong>\u8bc6\u522b<\/strong>CNF\u548cDNF\u8868\u8fbe\u5f0f\u7684\u7ed3\u6784\u3002<\/li>\n<li><strong>\u4f7f\u7528<\/strong>CNF\u6216DNF\u7b80\u5316\u547d\u9898\u903b\u8f91\u8868\u8fbe\u5f0f\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>\u76ee\u5f55<\/strong><br \/>\n<a href=\"#1\">\u6587\u5b57\u5b9a\u4e49<\/a><br \/>\n<a href=\"#2\">\u8303\u5f0f\u5b9a\u4e49<\/a><br \/>\n<a href=\"#3\">\u8303\u5f0f\u5b9a\u7406<\/a><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/CrTcmmE4Q6c\" title=\"YouTube\u89c6\u9891\u64ad\u653e\u5668\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p style=\"text-align: justify;\">\u547d\u9898\u903b\u8f91\u7684\u4e00\u4e2a\u6709\u8da3\u4e14\u6709\u7528\u7684\u7ed3\u679c\u4e0e\u8303\u5f0f\u6709\u5173\u3002\u8981\u6df1\u5165\u63a2\u8ba8\u8fd9\u4e9b\u95ee\u9898\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u56de\u987e\u4e00\u4e9b\u6982\u5ff5\u3002<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u6587\u5b57\u5b9a\u4e49<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=CrTcmmE4Q6c&amp;t=309s\" target=\"_blank\" rel=\"noopener\"><strong>\u6587\u5b57\u662f\u4efb\u4f55<\/strong><\/a>\u539f\u5b50\u8868\u8fbe\u5f0f\u6216\u539f\u5b50\u8868\u8fbe\u5f0f\u7684\u5426\u5b9a\u3002\u57fa\u4e8e\u6b64\uff0c\u6211\u4eec\u8c08\u8bba\u6b63\u6587\u5b57\u6216\u8d1f\u6587\u5b57\uff0c\u53d6\u51b3\u4e8e\u539f\u5b50\u8868\u8fbe\u5f0f\u662f\u5426\u6709\u5426\u5b9a\u524d\u7f00\u3002\u4f8b\u5982\uff1a<span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u662f\u4e00\u4e2a\u6b63\u6587\u5b57\uff0c\u800c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg A<\/span><\/span> \u662f\u4e00\u4e2a\u8d1f\u6587\u5b57\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u8303\u5f0f\u5b9a\u4e49<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=CrTcmmE4Q6c&amp;t=337s\" target=\"_blank\" rel=\"noopener\"><strong>\u4e00\u4e2a\u8868\u8fbe\u5f0f <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span> \u5728\u8303\u5f0f\u4e2d<\/strong><\/a>\u662f\u5408\u53d6\u8303\u5f0f\uff08CNF\uff09\uff0c\u5f53\u5b83\u53ef\u4ee5\u8868\u793a\u4e3a\u6587\u5b57\u7684\u6790\u53d6\u7684\u5408\u53d6\u5f62\u5f0f\uff0c\u5373\uff1a<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle F=\\bigwedge_{i=1}^n \\left( \\bigvee_{j=1}^m L_{ij}\\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u540c\u6837\uff0c\u82e5\u4e00\u4e2a\u8868\u8fbe\u5f0f\u8868\u793a\u4e3a\u6587\u5b57\u5408\u53d6\u7684\u6790\u53d6\u5f62\u5f0f\uff0c\u5219\u4e3a\u6790\u53d6\u8303\u5f0f\uff08DNF\uff09\uff1a<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle F=\\bigvee_{i=1}^n \\left(\\bigwedge_{j=1}^m L_{ij}\\right)<\/span><\/span><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u8303\u5f0f\u5b9a\u7406<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=CrTcmmE4Q6c&amp;t=446s\" target=\"_blank\" rel=\"noopener\"><strong>\u6240\u6709\u547d\u9898\u903b\u8f91\u8868\u8fbe\u5f0f<\/strong><\/a> \u90fd\u7b49\u4ef7\u4e8eCNF\u548cDNF\u8868\u8fbe\u5f0f\u3002<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000080;\"><strong>\u8bc1\u660e\uff1a<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\">\u8fd9\u53ef\u4ee5\u901a\u8fc7\u5bf9\u516c\u5f0f <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span> \u590d\u6742\u6027\u7684\u5f52\u7eb3\u8fdb\u884c\u8bc1\u660e\u3002<\/p>\n<ul style=\"text-align: justify;\">\n<li><strong>\u521d\u59cb\u60c5\u51b5\uff1a<\/strong>\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span> \u662f\u4e00\u4e2a\u539f\u5b50\u8868\u8fbe\u5f0f\uff0c\u90a3\u4e48\u5b83\u53ef\u4ee5\u540c\u65f6\u4ee5CNF\u548cDNF\u8868\u793a\uff0c\u56e0\u4e3a\uff1a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F\\equiv F_D \\equiv F_C<\/span><\/span>\uff0c\u5176\u4e2d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_C:=((F\\vee F)\\wedge (F\\vee F)) <\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_D:=((F\\wedge F)\\vee (F\\wedge F)) <\/span><\/span><\/li>\n<li><strong>\u5f52\u7eb3\u6b65\u9aa4\uff1a<\/strong>\u8bbe <span class=\"katex-eq\" data-katex-display=\"false\">G<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">H<\/span> \u662f\u4efb\u610f\u4e24\u4e2a\u8868\u8fbe\u5f0f\uff0c\u5bf9\u5b83\u4eec\u6210\u7acb\u7684\u7ed3\u679c\u662f\uff1a\u5b58\u5728 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">H_C<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">G_C<\/span><\/span> \u5728CNF\u4e2d\uff0c\u4e14\u5b58\u5728 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">H_D<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">G_D<\/span><\/span> \u5728DNF\u4e2d\uff0c\u4f7f\u5f97\uff1a\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">G\\equiv G_D \\equiv G_D<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">H\\equiv H_D \\equiv H_D<\/span><\/span><\/p>\n<p>    \u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5199\uff1a<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle G_D := \\bigvee_{i=1}^n \\bigwedge_{j=1}^m L_{ij}^{GD}<\/span><\/span>\uff1b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle G_C := \\bigwedge_{i=1}^n \\bigvee_{j=1}^m L_{ij}^{GC}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle H_D := \\bigvee_{i=1}^n \\bigwedge_{j=1}^m L_{ij}^{HD}<\/span><\/span>\uff1b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle H_C := \\bigwedge_{i=1}^n \\bigvee_{j=1}^m L_{ij}^{HC}<\/span><\/span><\/p>\n<p>    \u4e0d\u5931\u4e00\u822c\u6027\uff0c\u5982\u679c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F:= \\neg G<\/span><\/span>\uff0c\u5219\u6839\u636e<strong>\u66ff\u4ee3\u5b9a\u7406<\/strong> \u548c <strong>\u5e7f\u4e49\u6469\u6839\u5b9a\u5f8b<\/strong> \u6211\u4eec\u6709\uff1a<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle F:= \\neg G \\equiv \\left\\{ \\begin{matrix}\n\n    \\neg G_D := \\neg \\bigvee_{i=1}^n \\bigwedge_{j=1}^m L_{ij}^{GD} \\equiv\\bigwedge_{i=1}^n \\neg \\bigwedge_{j=1}^m L_{ij}^{GD} \\equiv \\bigwedge_{i=1}^n \\bigvee_{j=1}^m \\neg L_{ij}^{GD} \\\\ \\\\ \\neg G_C := \\neg \\bigwedge_{i=1}^n \\bigvee_{j=1}^m L_{ij}^{GC} \\equiv \\bigvee_{i=1}^n \\neg \\bigvee_{j=1}^m L_{ij}^{GC} \\equiv \\bigvee_{i=1}^n \\bigwedge_{j=1}^m \\neg L_{ij}^{GC} \\end{matrix}\\right. <\/span>\n<p>    \u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F:=G\\wedge H<\/span><\/span>\uff0c\u5219\u6839\u636e\u66ff\u4ee3\u5b9a\u7406\uff1a<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle F:=G\\wedge H \\equiv G_C \\wedge H_C := \\bigwedge_{i=1}^n \\bigvee_{j=1}^m L_{ij}^{GC} \\wedge \\bigwedge_{i=1}^{n^\\prime} \\bigvee_{j=1}^{m^\\prime} L_{ij}^{HC} <\/span><\/span><\/p>\n<p>    \u8fd9\u662f\u4e00\u4e2a\u5408\u53d6\u8303\u5f0f\u3002\u540c\u7406\uff0c\u5982\u679c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F:=H\\vee G,<\/span><\/span>\u90a3\u4e48\uff1a<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle F:=G\\wedge H \\equiv G_D \\vee H_D := \\bigvee_{i=1}^n \\bigwedge_{j=1}^m L_{ij}^{GD} \\vee \\bigvee_{i=1}^{\\overline{n}} \\bigwedge_{j=1}^{\\overline{m}} L_{ij}^{HD} <\/span><\/span><\/p>\n<p>    \u5373\u4e3a\u4e00\u4e2a\u6790\u53d6\u8303\u5f0f\u3002<\/p>\n<p>    \u56e0\u6b64\uff0c\u5f52\u7eb3\u5b8c\u6210\uff0c\u6240\u6709\u547d\u9898\u903b\u8f91\u8868\u8fbe\u5f0f\u90fd\u53ef\u4ee5\u7528FND\u548cFNC\u8868\u793a\u3002<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u7814\u7a76\u547d\u9898\u903b\u8f91\u7684\u5408\u53d6\u8303\u5f0f\uff08CNF\uff09\u548c\u6790\u53d6\u8303\u5f0f\uff08DNF\uff09\u5bf9\u4e8e\u7b80\u5316\u548c\u89e3\u51b3\u6570\u5b66\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u7684\u590d\u6742\u95ee\u9898\u81f3\u5173\u91cd\u8981\u3002\u8be5\u5b9a\u7406\u8868\u660e\u4efb\u4f55\u903b\u8f91\u8868\u8fbe\u5f0f\u90fd\u53ef\u4ee5\u540c\u65f6\u7528FND\u548cFNC\u8868\u793a\uff0c\u8fd9\u4e00\u7ed3\u679c\u5177\u6709\u91cd\u8981\u610f\u4e49\uff0c\u56e0\u4e3a\u5b83\u4f7f\u5f97\u547d\u9898\u7684\u7ed3\u6784\u66f4\u52a0\u6613\u4e8e\u7ba1\u7406\u548c\u6807\u51c6\u5316\uff0c\u4ece\u800c\u6709\u5229\u4e8e\u5176\u5206\u6790\u548c\u64cd\u4f5c\u3002\u8fd9\u4e2a\u7ed3\u679c\u7684\u91cd\u8981\u6027\u5728\u4e8e\u5b83\u4e3a\u7b97\u6cd5\u8bbe\u8ba1\u3001\u903b\u8f91\u8868\u8fbe\u5f0f\u7684\u4f18\u5316\u4ee5\u53ca\u5728\u5404\u4e2a\u77e5\u8bc6\u9886\u57df\uff08\u5982\u4eba\u5de5\u667a\u80fd\u548c\u8f6f\u4ef6\u9a8c\u8bc1\uff09\u4e2d\u9ad8\u6548\u89e3\u51b3\u95ee\u9898\u63d0\u4f9b\u4e86\u575a\u5b9e\u7684\u57fa\u7840\u3002\u6b64\u5916\uff0c\u7528\u5f52\u7eb3\u6cd5\u8bc1\u660e\u8be5\u5b9a\u7406\u7684\u6280\u5de7\u5f3a\u5316\u4e86\u5bf9\u903b\u8f91\u8868\u8fbe\u5f0f\u57fa\u672c\u6027\u8d28\u7684\u7406\u89e3\uff0c\u5e76\u5c55\u793a\u4e86\u5176\u5728\u5176\u4ed6\u6570\u5b66\u80cc\u666f\u4e2d\u7684\u5e94\u7528\u53ef\u80fd\u6027\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8303\u5f0f\u53ca\u5176\u6027\u8d28 \u6458\u8981\u547d\u9898\u903b\u8f91\u662f\u6570\u5b66\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u7684\u4e00\u9879\u57fa\u672c\u5de5\u5177\u3002\u5728\u672c\u8bfe\u4e2d\uff0c\u5c06\u4ecb\u7ecd\u4e00\u4e2a\u4e0e\u8303\u5f0f\u76f8\u5173\u7684\u6709\u8da3\u4e14\u6709\u7528\u7684\u7ed3\u679c\u3002\u4e3a\u6b64\uff0c\u5c06\u5b9a\u4e49\u6587\u5b57\u3001\u5408\u53d6\u8303\u5f0f\uff08CNF\uff09\u548c\u6790\u53d6\u8303\u5f0f\uff08DNF\uff09\u7684\u6982\u5ff5\u3002\u6b64\u5916\uff0c\u8fd8\u5c06\u8bc1\u660e\u8303\u5f0f\u5b9a\u7406\uff0c\u5373\u6240\u6709\u547d\u9898\u903b\u8f91\u8868\u8fbe\u5f0f\u90fd\u7b49\u4ef7\u4e8eCNF\u548cDNF\u8868\u8fbe\u5f0f\u3002\u8bc1\u660e\u5c06\u901a\u8fc7\u5bf9\u516c\u5f0f\u590d\u6742\u6027\u7684\u5f52\u7eb3\u8fdb\u884c\uff0c\u4ece\u800c\u8868\u660e\u6240\u6709\u547d\u9898\u903b\u8f91\u8868\u8fbe\u5f0f\u90fd\u53ef\u4ee5\u7528CNF\u548cDNF\u8868\u793a\u3002\u672c\u8bfe\u5c06\u5bf9\u7406\u89e3\u547d\u9898\u903b\u8f91\u7684\u57fa\u7840\u5e76\u5c06\u5176\u5e94\u7528\u4e8e\u5404\u4e2a\u77e5\u8bc6\u9886\u57df\u5927\u6709\u5e2e\u52a9\u3002 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