{"id":6102,"date":"2023-06-14T17:44:14","date_gmt":"2023-06-14T08:44:14","guid":{"rendered":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=6102"},"modified":"2023-06-14T17:44:14","modified_gmt":"2023-06-14T08:44:14","slug":"%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/","title":{"rendered":"\u30e9\u30f3\u30c0\u30e0 K-SAT \u306e\u76f8\u8ee2\u79fb\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0"},"content":{"rendered":"\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\" >\u6587\u732e\u60c5\u5831<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#%E6%A6%82%E8%A6%81\" >\u6982\u8981<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#%E8%83%8C%E6%99%AF\" >\u80cc\u666f<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#K-SAT_%E3%81%A8%E3%81%9D%E3%81%AE%E7%9B%B8%E8%BB%A2%E7%A7%BB\" >K-SAT \u3068\u305d\u306e\u76f8\u8ee2\u79fb<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#%E3%82%B9%E3%83%94%E3%83%B3%E3%82%B0%E3%83%A9%E3%82%B9%E7%90%86%E8%AB%96\" >\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u7406\u8ad6<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#%E6%89%8B%E6%B3%95\" >\u624b\u6cd5<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#%E3%82%B9%E3%83%94%E3%83%B3%E3%82%B0%E3%83%A9%E3%82%B9%E6%A8%A1%E5%9E%8B%E3%81%B8%E3%81%AE%E5%B8%B0%E7%9D%80\" >\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u3078\u306e\u5e30\u7740<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#Cavity_%E6%B3%95%E3%81%AE%E9%81%A9%E7%94%A8\" >Cavity \u6cd5\u306e\u9069\u7528<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#Cavity_bias_%E3%82%92%E9%87%8D%E3%81%AD%E5%90%88%E3%82%8F%E3%81%9B%E3%81%9F_%E2%80%9Csurvey%E2%80%9D_%E3%81%AE%E5%B0%8E%E5%85%A5\" >Cavity bias \u3092\u91cd\u306d\u5408\u308f\u305b\u305f &#8220;survey&#8221; \u306e\u5c0e\u5165<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#%E5%B9%B3%E5%9D%87%E3%82%A4%E3%83%B3%E3%82%B9%E3%82%BF%E3%83%B3%E3%82%B9%E3%81%AE%E6%8C%99%E5%8B%95%E3%81%AE%E8%A7%A3%E6%9E%90\" >\u5e73\u5747\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306e\u6319\u52d5\u306e\u89e3\u6790<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#%E6%96%B9%E6%B3%95\" >\u65b9\u6cd5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#%E7%B5%90%E6%9E%9C\" >\u7d50\u679c<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#%E7%89%B9%E5%AE%9A%E3%82%A4%E3%83%B3%E3%82%B9%E3%82%BF%E3%83%B3%E3%82%B9%E3%81%AB%E5%AF%BE%E3%81%99%E3%82%8B%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0\" >\u7279\u5b9a\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u5bfe\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#Survey_propagation_algorithm\" >Survey propagation algorithm<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#%E7%B5%90%E6%9E%9C-2\" >\u7d50\u679c<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#%E7%B5%90%E8%AB%96\" >\u7d50\u8ad6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\" >\u3042\u3068\u304c\u304d<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/06\/14\/%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0-k-sat-%e3%81%ae%e7%9b%b8%e8%bb%a2%e7%a7%bb%e3%81%a8%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/#%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\" >\u53c2\u8003\u6587\u732e<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\"><\/span>\u6587\u732e\u60c5\u5831<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u30bf\u30a4\u30c8\u30eb: Analytic and Algorithmic Solution of Random Satisfiability Problems<\/li>\n\n\n\n<li>\u8457\u8005: M. M\u00e9zard, G. Parisi, R. Zecchina<\/li>\n\n\n\n<li>\u66f8\u8a8c\u60c5\u5831: <a href=\"https:\/\/www.science.org\/doi\/10.1126\/science.1073287\">https:\/\/www.science.org\/doi\/10.1126\/science.1073287<\/a><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%A6%82%E8%A6%81\"><\/span>\u6982\u8981<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>K-SAT \u306f\u3001\u3044\u304f\u3064\u304b\u306e\u5909\u6570\u304b\u3089\u306a\u308b\u8ad6\u7406\u5f0f\u3092\u5145\u8db3\u3059\u308b\u3088\u3046\u306a\u771f\u507d\u5024\u306e\u5272\u5f53\u3092\u6c42\u3081\u308b\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u3067\u3059\u3002K-SAT \u306f $K \\ge 3$ \u306e\u3068\u304d\u306b NP \u5b8c\u5168\u554f\u984c\u3067\u3042\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u3066\u304a\u308a\u3001\u73fe\u5728\u306e\u3068\u3053\u308d\u3001\u5165\u529b\u30b5\u30a4\u30ba\u306b\u5bfe\u3057\u3066\u6700\u60aa\u591a\u9805\u5f0f\u6642\u9593\u3067\u89e3\u304f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b58\u5728\u306f\u77e5\u3089\u308c\u3066\u3044\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001K-SAT \u306b\u95a2\u3057\u3066\u4ee5\u4e0b\u306e 2 \u70b9\u306e\u7814\u7a76\u304c\u9032\u3081\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>K-SAT \u306e\u96e3\u3057\u3055\u306e\u539f\u56e0\u306e\u7406\u89e3 (\u8a08\u7b97\u8907\u96d1\u6027\u7406\u8ad6\u306e\u89b3\u70b9\u304b\u3089\u306e\u8208\u5473)<\/li>\n\n\n\n<li>K-SAT \u3092\u5e73\u5747\u7684\u306b\u9ad8\u901f\u306b\u89e3\u304f\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30c3\u30af\u306e\u958b\u767a<\/li>\n<\/ol>\n\n\n\n<p>\u672c\u8ad6\u6587\u3067\u306f\u3001\u7d71\u8a08\u529b\u5b66\u3001\u7279\u306b\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u7406\u8ad6\u306e\u624b\u6cd5\u3092\u7528\u3044\u3066 K-SAT \u3092\u89e3\u6790\u3057\u3001\u4e0a\u306e 2 \u3064\u306e\u554f\u3044\u306b\u5bfe\u3059\u308b\u6d1e\u5bdf\u3092\u4e0e\u3048\u307e\u3059\u3002\u3088\u308a\u5177\u4f53\u7684\u306b\u306f\u3001\u4ee5\u4e0b\u306e 2 \u3064\u306e\u4e8b\u9805\u306b\u3064\u3044\u3066\u8003\u5bdf\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>K-SAT \u306e\u89e3\u7a7a\u9593\u306e\u69cb\u9020\u3092\u8abf\u3079\u3001K-SAT \u306e\u76f8\u8ee2\u79fb\u3068\u305d\u306e\u539f\u56e0\u306b\u3064\u3044\u3066\u8003\u5bdf\u3059\u308b<\/li>\n\n\n\n<li>K-SAT \u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u306b\u3001\u305d\u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306e\u89e3\u306e\u5206\u5e03\u3092\u8abf\u3079\u308b\u3053\u3068\u3067\u3001\u52b9\u7387\u7684\u306b\u771f\u507d\u5024\u306e\u5272\u5f53\u3092\u6c7a\u5b9a\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u69cb\u6210\u3059\u308b<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E8%83%8C%E6%99%AF\"><\/span>\u80cc\u666f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"K-SAT_%E3%81%A8%E3%81%9D%E3%81%AE%E7%9B%B8%E8%BB%A2%E7%A7%BB\"><\/span>K-SAT \u3068\u305d\u306e\u76f8\u8ee2\u79fb<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>K-SAT \u306e\u8a73\u7d30\u306a\u554f\u984c\u8a2d\u5b9a\u3092\u8ff0\u3079\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8ad6\u7406\u5909\u6570 $x_1, x_2,\\dots,x_N$: $\\mathrm{true}$ \u304b $\\mathrm{false}$ \u306e2\u5024\u3092\u53d6\u308b\u5909\u6570<\/li>\n\n\n\n<li>\u30ea\u30c6\u30e9\u30eb: \u8ad6\u7406\u5909\u6570\u306e\u80af\u5b9a $x$ \u307e\u305f\u306f\u5426\u5b9a $\\lnot x$<\/li>\n\n\n\n<li>\u7bc0: $K$ \u500b\u306e\u30ea\u30c6\u30e9\u30eb\u306e\u8ad6\u7406\u548c<\/li>\n\n\n\n<li>\u8ad6\u7406\u5f0f: $M$ \u500b\u306e\u7bc0\u306e\u8ad6\u7406\u7a4d<\/li>\n<\/ul>\n\n\n\n<p>\u305f\u3068\u3048\u3070\u3001 $N=4$ \u5909\u6570\u3001 $M=3$ \u7bc0\u306e 3-SAT \u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9 (\u5177\u4f53\u7684\u306a\u554f\u984c) \u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5f62\u3092\u53d6\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ (x_1\\lor x_3 \\lor \\lnot x_4) \\land (\\lnot x_1\\lor \\lnot x_2 \\lor x_4) \\land (x_2 \\lor \\lnot x_3 \\lor x_4) $$<\/p>\n\n\n\n<p>\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u4e0e\u3048\u3089\u308c\u308b\u8ad6\u7406\u5f0f\u306b\u5bfe\u3057\u3066\u3001\u8ad6\u7406\u5f0f\u5168\u4f53\u306e\u5024\u3092 $\\mathrm{true}$ \u306b\u3059\u308b\u3088\u3046\u306a\u5404\u8ad6\u7406\u5909\u6570\u3078\u306e\u8ad6\u7406\u5024\u306e\u5272\u5f53\u3092\u898b\u3064\u3051\u308b\u304b\u3001\u307e\u305f\u306f\u305d\u306e\u3088\u3046\u306a\u5272\u5f53\u304c\u5b58\u5728\u3057\u306a\u3044\u3053\u3068\u3092\u5831\u544a\u3059\u308b\u554f\u984c\u304c K-SAT \u3067\u3059\u3002\u89e3\u304c\u5b58\u5728\u3059\u308b\u3068\u304d\u3001\u305d\u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306f\u5145\u8db3\u53ef\u80fd\u3001\u5b58\u5728\u3057\u306a\u3044\u3068\u304d\u306f\u5145\u8db3\u4e0d\u53ef\u80fd\u3067\u3042\u308b\u3068\u3044\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u4e0a\u306e\u4f8b\u306f\u5145\u8db3\u53ef\u80fd\u3067\u3042\u308a\u3001 $(x_1,x_2,x_3,x_4)=(\\mathrm{true}, \\mathrm{false},\\mathrm{false},\\mathrm{true})$ \u304c\u89e3\u306e\u4e00\u3064\u3067\u3059\u3002<\/p>\n\n\n\n<p>K-SAT \u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u89e3\u304c\u5b58\u5728\u3059\u308b\u304b\u5426\u304b\u306f\u3001\u8ad6\u7406\u5909\u6570\u306e\u500b\u6570 $N$ \u3068\u7bc0\u306e\u500b\u6570 $M$ \u306e\u6bd4 $\\alpha := M\/N$ \u306b\u3088\u3063\u3066\u5927\u307e\u304b\u306b\u6c7a\u5b9a\u3055\u308c\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u3059\u306a\u308f\u3061\u3001\u3042\u308b\u81e8\u754c\u5024 $\\alpha_c$ \u304c\u5b58\u5728\u3057\u3066\u3001 $\\alpha &lt; \\alpha_c$ \u3067\u306f\u307b\u3068\u3093\u3069\u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u304c\u5145\u8db3\u53ef\u80fd\u3001 $\\alpha &gt; \\alpha_c$ \u3067\u306f\u307b\u3068\u3093\u3069\u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u304c\u5145\u8db3\u4e0d\u53ef\u80fd\u3068\u306a\u308a\u307e\u3059\u3002\u307e\u305f\u3001 $\\alpha$ \u304c\u81e8\u754c\u5024 $\\alpha_c$ \u306b\u8fd1\u3044\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306f\u89e3\u304f\u3053\u3068\u304c\u96e3\u3057\u3044\u3053\u3068\u304c\u5b9f\u9a13\u7684\u306b\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3001\u3042\u308b\u81e8\u754c\u5024\u3092\u5883\u306b\u554f\u984c\u306e\u6027\u8cea\u304c\u6025\u6fc0\u306b\u5909\u5316\u3059\u308b\u73fe\u8c61\u306f<strong>\u76f8\u8ee2\u79fb<\/strong>\u3068\u547c\u3070\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u3088\u3046\u306a\u80cc\u666f\u304b\u3089\u3001K-SAT \u306b\u3064\u3044\u3066\u3001\u6b21\u306e\u554f\u984c\u306e\u89e3\u660e\u304c\u6c42\u3081\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$\\alpha \\approx \\alpha_c$ \u3067\u554f\u984c\u304c\u96e3\u3057\u304f\u306a\u308b\u306e\u306f\u306a\u305c\u304b\uff1f\u306a\u305c\u76f8\u8ee2\u79fb\u304c\u8d77\u3053\u308b\u306e\u304b\uff1f<\/li>\n\n\n\n<li>$\\alpha \\approx \\alpha_c$ \u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3092\u9ad8\u901f\u306b\u89e3\u304f\u3053\u3068\u306e\u3067\u304d\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f5c\u308b\u3053\u3068\u306f\u3067\u304d\u308b\u304b\uff1f<\/li>\n<\/ul>\n\n\n\n<p>\u672c\u8ad6\u6587\u3067\u306f\u3001\u4e21\u65b9\u306e\u554f\u306b\u3064\u3044\u3066\u8003\u5bdf\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%82%B9%E3%83%94%E3%83%B3%E3%82%B0%E3%83%A9%E3%82%B9%E7%90%86%E8%AB%96\"><\/span>\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u7406\u8ad6<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u307e\u305a\u3001\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u306e\u57fa\u790e\u3067\u3042\u308b Ising \u6a21\u578b\u306b\u3064\u3044\u3066\u8aac\u660e\u3092\u3057\u307e\u3059\u3002Ising \u6a21\u578b\u306f\u3001 $N$ \u500b\u306e\u30b9\u30d4\u30f3 $s_1, s_2, \\dots, s_N$ ($s_i$ \u306f $\\pm 1$ \u306e2\u5024\u3092\u53d6\u308b\u5909\u6570) \u304b\u3089\u306a\u308b\u7cfb\u3067\u3042\u308a\u3001\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306f\u6b21\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ E(\\{s_i\\}) = \\sum_{i,j} J_{i,j} s_i s_j $$<\/p>\n\n\n\n<p>$J_{i,j}$ \u306f\u7d50\u5408\u5b9a\u6570\u3068\u547c\u3070\u308c\u3001\u30b9\u30d4\u30f3 $s_i$ \u3068 $s_j$ \u306e\u9593\u306e\u76f8\u4e92\u4f5c\u7528\u3092\u8868\u3057\u307e\u3059\u3002 $J_{i,j}&lt;0$ \u306e\u3068\u304d\u306f $s_i,s_j$ \u304c\u540c\u3058\u5411\u304d\u3092\u5411\u304f\u306e\u304c\u3001 $J_{i,j}&gt;0$ \u306e\u3068\u304d\u306f $s_i,s_j$ \u304c\u7570\u306a\u308b\u5411\u304d\u3092\u5411\u304f\u306e\u304c\u305d\u308c\u305e\u308c\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u5c0f\u3055\u304f\u306a\u308a\u3001\u5b89\u5b9a\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>$J_{i,j} = (\\text{\u8ca0\u306e\u5b9a\u6570})$ \u3068\u3057\u305f\u6700\u3082\u57fa\u672c\u7684\u306a\u6a21\u578b\u306f\u3001\u78c1\u77f3\u306a\u3069\u306e\u5f37\u78c1\u6027\u4f53\u306e\u30e2\u30c7\u30eb\u3068\u3057\u3066\u7528\u3044\u3089\u308c\u307e\u3059\u3002\u3053\u306e\u30e2\u30c7\u30eb\u3067\u306f\u3001\u5404\u30b9\u30d4\u30f3\u306e\u5411\u304d\u304c\u63c3\u3046\u306e\u304c\u5b89\u5b9a\u306a\u72b6\u614b\u3067\u3042\u308a\u3001\u3053\u308c\u306f\u78c1\u77f3\u306e\u6027\u8cea\u3092\u6349\u3048\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u306f\u3001\u7d50\u5408\u5b9a\u6570 $J_{i,j}$ \u306e\u7b26\u53f7\u3084\u5927\u304d\u3055\u304c\u7d50\u5408\u306b\u3088\u3063\u3066\u30e9\u30f3\u30c0\u30e0\u306a\u5024\u3092\u53d6\u308b\u30e2\u30c7\u30eb\u3067\u3059\u3002\u3053\u306e\u30e2\u30c7\u30eb\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u30b9\u30d4\u30f3\u306e\u5024\u3092\u6c7a\u3081\u3066\u3082\u3001 $J_{i,j}s_is_j&gt;0$ \u3068\u306a\u308b\u4e0d\u5b89\u5b9a\u306a\u7d50\u5408\u304c\u751f\u3058\u307e\u3059\u3002\u3053\u306e\u4e0d\u5b89\u5b9a\u3055\u306f\u30d5\u30e9\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3\u3068\u547c\u3070\u308c\u3001\u3053\u308c\u306b\u3088\u308a\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u306f\u8907\u96d1\u306a\u6319\u52d5\u3092\u793a\u3057\u307e\u3059\u3002\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u3001\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u591a\u6570\u306e\u6975\u5c0f\u5024\u3092\u53d6\u308a\u307e\u3059\u3002\u305d\u308c\u305e\u308c\u306e\u8c37\u306f\u300c<strong>\u72b6\u614b (state)<\/strong>\u300d\u3068\u547c\u3070\u308c\u3001\u3053\u308c\u3089\u306f\u975e\u5e38\u306b\u5927\u304d\u306a\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u58c1\u3067\u906e\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/03\/Screen-Shot-2023-03-31-at-12.08.19.png\" alt=\"\" class=\"wp-image-6119\"\/><figcaption class=\"wp-element-caption\">&nbsp;\u56f31: \u72b6\u614b\u306e\u6a21\u5f0f\u56f3<\/figcaption><\/figure>\n\n\n\n<p>\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u3092\u5206\u6790\u3059\u308b\u624b\u6cd5\u306f\u7d71\u8a08\u7269\u7406\u5b66\u306b\u304a\u3044\u3066\u5927\u304d\u304f\u767a\u5c55\u3057\u3066\u3044\u307e\u3059\u3002\u307e\u305f\u3001\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3084\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u306a\u3069\u3001\u60c5\u5831\u79d1\u5b66\u306b\u304a\u3051\u308b\u8907\u96d1\u306a\u5bfe\u8c61\u3092\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u3067\u30e2\u30c7\u30eb\u5316\u3057\u3001\u89e3\u6790\u3059\u308b\u8a66\u307f\u304c\u591a\u304f\u884c\u308f\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u672c\u8ad6\u6587\u3067\u306f\u3001K-SAT \u3092\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u3067\u8868\u3057\u3001\u7269\u7406\u5b66\u306b\u304a\u3044\u3066\u767a\u5c55\u3057\u305f\u624b\u6cd5\u3067\u3042\u308b cavity \u6cd5\u3092\u7528\u3044\u3066 K-SAT \u306e\u6319\u52d5\u3092\u5206\u6790\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%89%8B%E6%B3%95\"><\/span>\u624b\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%82%B9%E3%83%94%E3%83%B3%E3%82%B0%E3%83%A9%E3%82%B9%E6%A8%A1%E5%9E%8B%E3%81%B8%E3%81%AE%E5%B8%B0%E7%9D%80\"><\/span>\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u3078\u306e\u5e30\u7740<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>K-SAT \u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u306b\u5bfe\u5fdc\u3055\u305b\u307e\u3059 (\u524d\u7bc0\u3067\u306e\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u306e\u8aac\u660e\u3067\u306f\u3001\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306f2\u3064\u306e\u30b9\u30d4\u30f3\u306e\u7a4d\u306e\u548c\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3057\u305f\u304c\u3001\u4ee5\u4e0b\u306e\u5bfe\u5fdc\u3067\u306f $K$ \u500b\u306e\u30b9\u30d4\u30f3\u306e\u7a4d\u306e\u548c\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044)\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5909\u6570 $x_i$ \u2192 \u30b9\u30d4\u30f3 $s_i$:\n<ul class=\"wp-block-list\">\n<li>$s_i=\\begin{cases}1 &amp; (x_i = \\mathrm{true})\\\\ -1 &amp; (x_i=\\mathrm{false})\\end{cases}$<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u30ea\u30c6\u30e9\u30eb \u2192 \u7d50\u5408\u5b9a\u6570 $J$:\n<ul class=\"wp-block-list\">\n<li>$J_a^r=\\begin{cases}1 &amp; (\\text{\u7bc0 $a$ \u306e $r$ \u756a\u76ee\u306e\u30ea\u30c6\u30e9\u30eb\u304c\u80af\u5b9a}) \\\\ -1 &amp; (\\text{\u7bc0 $a$ \u306e $r$ \u756a\u76ee\u306e\u30ea\u30c6\u30e9\u30eb\u304c\u5426\u5b9a})\\end{cases}$<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u7bc0\u306e\u30a8\u30cd\u30eb\u30ae\u30fc: $\\varepsilon_{J_a}(s_{i_1(a)},\\dots,s_{i_K(a)}) = \\begin{cases}0 &amp; (\\text{\u7bc0 $a$ \u304c $\\mathrm{true}$}) \\\\ 1 &amp; (\\text{\u7bc0 $a$ \u304c $\\mathrm{false}$})\\end{cases}=2^{-K}\\prod_{r=1}^K(1-J_a^r s_{i_r(a)})$<\/li>\n\n\n\n<li>\u5168\u30a8\u30cd\u30eb\u30ae\u30fc: $E = \\sum_a \\varepsilon_{J_a}$<\/li>\n<\/ul>\n\n\n\n<p>\u3059\u306a\u308f\u3061\u3001\u5168\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u5145\u8db3\u3055\u308c\u3066\u3044\u306a\u3044\u7bc0\u306e\u6570\u3067\u3059\u3002\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u304c\u5145\u8db3\u53ef\u80fd\u3067\u3042\u308b\u3053\u3068\u3068\u3001\u5168\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u6700\u5c0f\u5024 (\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc) \u304c $0$ \u3067\u3042\u308b\u3053\u3068\u306f\u540c\u5024\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u9006\u6e29\u5ea6 $\\beta \\to \\infty$ \u3068\u3057\u305f\u6975\u9650\u306b\u304a\u3044\u3066\u3001\u7cfb\u306f\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u6975\u5c0f\u5024\u3092\u53d6\u308b\u3053\u3068\u304c\u7d71\u8a08\u529b\u5b66\u304b\u3089\u5c0e\u51fa\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u3067\u306f\u3001\u6975\u5c0f\u5024\u304c\u975e\u5e38\u306b\u591a\u304f\u3042\u308b\u305f\u3081\u3001 $\\beta\\to\\infty$ \u306e\u6975\u9650\u3067\u3082\u7cfb\u306e\u72b6\u614b\u306f\u5b9a\u307e\u308a\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u300c\u6975\u5c0f\u5024\u305f\u3061\u304b\u3089\u306a\u308b\u7cfb\u300d\u306e\u7d71\u8a08\u529b\u5b66\u3067\u3042\u308b &#8220;zero-temperature thermodynamics&#8221; \u3092\u5c0e\u5165\u3057\u307e\u3059\u3002\u3053\u306e\u7cfb\u306f\u3001\u4ee5\u4e0b\u306e\u5f0f\u3067\u652f\u914d\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ \\exp(-Ny\\Phi(y))=\\int de \\exp(N(\\Sigma(e)-ye)) $$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$\\Phi(y)$: \u300c\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\u300d(\u901a\u5e38\u306e\u610f\u5473\u3067\u306e\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\u3067\u306f\u306a\u3044\u306e\u3067\u3001\u9264\u62ec\u5f27\u306b\u5165\u308c\u3066\u3044\u308b)<\/li>\n\n\n\n<li>$y$:\u300c\u9006\u6e29\u5ea6\u300d(\u540c\u4e0a)<\/li>\n\n\n\n<li>$e$: \u30a8\u30cd\u30eb\u30ae\u30fc<\/li>\n\n\n\n<li>$\\Sigma(e)$: &#8220;complexity&#8221;\u3001\u30a8\u30cd\u30eb\u30ae\u30fc $e$ \u3092\u6301\u3064\u72b6\u614b\u306e\u500b\u6570\u306e\u5bfe\u6570 (\u901a\u5e38\u306e\u7d71\u8a08\u529b\u5b66\u306b\u304a\u3051\u308b\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306b\u5bfe\u5fdc)<\/li>\n<\/ul>\n\n\n\n<p>\u901a\u5e38\u306e\u71b1\u529b\u5b66\u306b\u304a\u3044\u3066 $\\beta\\to\\infty$ \u306e\u6975\u9650\u3067\u7cfb\u304c\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u6975\u5c0f\u5024\u3092\u3068\u308b\u306e\u3068\u540c\u69d8\u306b\u3001$y\\to\\infty$ \u306e\u6975\u9650\u3067\u7cfb\u306e\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Cavity_%E6%B3%95%E3%81%AE%E9%81%A9%E7%94%A8\"><\/span>Cavity \u6cd5\u306e\u9069\u7528<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Cavity \u6cd5\u306f\u3001\u300c<strong>\u7cfb\u306e\u4e00\u90e8\u3092\u53d6\u308a\u51fa\u3057\u3001\u305d\u308c\u3068\u6b8b\u308a\u306e\u7cfb\u306e\u95a2\u4fc2\u3092\u8abf\u3079\u308b<\/strong>\u300d\u3068\u3044\u3046\u8003\u3048\u65b9\u306b\u57fa\u3065\u304f\u8a08\u7b97\u624b\u6cd5\u3067\u3059\u3002\u300c\u6b8b\u308a\u306e\u7cfb\u300d\u306e\u632f\u308b\u821e\u3044\u3092\u8a73\u7d30\u306b\u8a18\u8ff0\u3059\u308b\u306e\u306f\u96e3\u3057\u3044\u306e\u3067\u3001\u4ee3\u308f\u308a\u306b\u7cfb\u306e\u5e73\u5747\u5024\u3067\u7f6e\u304d\u63db\u3048\u308b\u3068\u3044\u3046\u8fd1\u4f3c\u3092\u884c\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001\u7bc0 $a$ \u3092\u53d6\u308a\u51fa\u3057\u3066\u3001\u305d\u308c\u306b\u542b\u307e\u308c\u308b\u30b9\u30d4\u30f3 $s_i$ \u3068\u3001\u6b8b\u308a\u306e\u7cfb\u306e\u95a2\u4fc2\u3092\u8abf\u3079\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u306b\u3001\u4ee5\u4e0b\u306e2\u3064\u306e\u91cf\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Cavity field<\/strong> $h_{i\\to a}$\n<ul class=\"wp-block-list\">\n<li>\u300c\u30b9\u30d4\u30f3 $s_i$ \u304c\u7bc0 $a$ \u3067\u3069\u3061\u3089\u306e\u5411\u304d\u3092\u5411\u304d\u305f\u3044\u304b\u300d\u3092\u8868\u3059\u91cf<\/li>\n\n\n\n<li>\u3059\u306a\u308f\u3061\u3001\u300c\u7bc0 $a$ \u3092\u53d6\u308a\u9664\u3044\u305f\u3068\u304d\u306b\u3001 $s_i$ \u304c\u3069\u3061\u3089\u306e\u5411\u304d\u3092\u5411\u304f\u50be\u5411\u304c\u3042\u308b\u304b\u300d\u3092\u8868\u3059\u91cf<\/li>\n\n\n\n<li>\u4f8b\u3048\u3070\u3001\u7bc0 $a$ \u3092\u53d6\u308a\u9664\u3044\u305f\u7cfb\u306b\u304a\u3044\u3066\u3001 $s_i = 1$ \u3068\u306a\u308b\u3053\u3068\u304c\u591a\u3044\u306a\u3089\u3001\u7bc0 $a$ \u3067\u3082 $s_i$ \u306f\u80af\u5b9a\u30ea\u30c6\u30e9\u30eb\u3067\u3042\u308b\u3053\u3068\u304c\u671b\u307e\u3057\u3044\u306e\u3067\u3001 $h_{i \\to a} &gt; 0$ \u3068\u306a\u308b\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Cavity bias<\/strong> $u_{a \\to i}$\n<ul class=\"wp-block-list\">\n<li>\u300c\u7bc0 $a$ \u304c $\\mathrm{true}$ \u3068\u306a\u308b\u305f\u3081\u306b\u3001\u30b9\u30d4\u30f3 $s_i$ \u306b\u3069\u3061\u3089\u306e\u5411\u304d\u3092\u5411\u3044\u3066\u307b\u3057\u3044\u304b\u300d\u3092\u8868\u3059\u91cf<\/li>\n\n\n\n<li>\u4f8b\u3048\u3070\u3001\u7bc0 $a$ \u306b\u304a\u3044\u3066 $s_i$ \u304c\u80af\u5b9a\u30ea\u30c6\u30e9\u30eb\u306a\u3089\u3001 $s_i=1$ \u3068\u306a\u308b\u3053\u3068\u304c\u671b\u307e\u3057\u3044\u306e\u3067\u3001 $u_{a \\to i}&gt;0$ \u3068\u306a\u308b\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>\u3053\u306e\u3088\u3046\u306b\u3001cavity \u6cd5\u306b\u304a\u3044\u3066\u3001\u7cfb\u306f\u95a2\u6570 (\u7bc0) \u3068\u5909\u6570 (\u30b9\u30d4\u30f3) \u306e\u9593\u306e\u300c\u30e1\u30c3\u30bb\u30fc\u30b8\u300d\u306e\u3084\u308a\u53d6\u308a\u3068\u3057\u3066\u6349\u3048\u3089\u308c\u307e\u3059\u3002cavity field \u304c\u30b9\u30d4\u30f3\u304b\u3089\u7bc0\u3078\u306e\u30e1\u30c3\u30bb\u30fc\u30b8\u3001cavity bias \u304c\u7bc0\u304b\u3089\u30b9\u30d4\u30f3\u3078\u306e\u30e1\u30c3\u30bb\u30fc\u30b8\u306b\u5f53\u305f\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u95a2\u6570\u3068\u5909\u6570\u306e\u95a2\u4fc2\u306f\u3001\u4ee5\u4e0b\u306b\u793a\u3059\u3088\u3046\u306a\u4e8c\u90e8\u30b0\u30e9\u30d5\u3067\u8868\u73fe\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4e0b\u56f3\u306b\u304a\u3044\u3066\u3001\u25a1 \u3067\u8868\u3055\u308c\u308b\u9802\u70b9\u306f\u95a2\u6570 (\u7bc0) \u3067\u3001\u25cb \u3067\u8868\u3055\u308c\u308b\u9802\u70b9\u306f\u5909\u6570 (\u30b9\u30d4\u30f3) \u3067\u3059\u3002\u3053\u306e\u30b0\u30e9\u30d5\u3092<strong>\u56e0\u5b50\u30b0\u30e9\u30d5<\/strong>\u3068\u547c\u3073\u307e\u3059\u30023-SAT \u306e\u56e0\u5b50\u30b0\u30e9\u30d5\u3067\u306f\u3001\u25a1 \u306f 3 \u3064\u306e \u25cb \u3068\u3064\u306a\u304c\u3063\u3066\u304a\u308a\u3001\u25cb \u306f\u5e73\u5747 $\\alpha=M\/N$ \u500b\u306e \u25a1 \u3068\u3064\u306a\u304c\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/03\/factorgraph.png\" alt=\"\" class=\"wp-image-6113\"\/><figcaption class=\"wp-element-caption\">\u56f32: 3-SAT \u306e\u56e0\u5b50\u30b0\u30e9\u30d5 (<a href=\"https:\/\/doi.org\/10.1126\/science.1073287\">https:\/\/doi.org\/10.1126\/science.1073287<\/a>)<\/figcaption><\/figure>\n\n\n\n<p>Cavity field \u3068 cavity bias \u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u307e\u305a\u3001cavity field $h_{i \\to a}$ \u306b\u3064\u3044\u3066\u306f\u3001\u7bc0 $a$ \u4ee5\u5916\u304b\u3089\u306e cavity bias \u306e\u7dcf\u548c\u3068\u3057\u3066\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ h_{i \\to a} = \\sum_{b \\neq a} u_{b\\to i} $$<\/p>\n\n\n\n<p>\u6b21\u306b\u3001cavity bias $u_{a \\to i}$ \u306b\u3064\u3044\u3066\u306f\u3001\u7bc0 $a$ \u306b\u3064\u3044\u3066 $s_i$ \u4ee5\u5916\u306e\u30b9\u30d4\u30f3\u3092\u52d5\u304b\u3057\u3066\u5168\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u6700\u5c0f\u5316\u3057\u305f\u3068\u304d\u306e $s_i$ \u306e\u4fc2\u6570\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001 $s_i$ \u4ee5\u5916\u306e\u5909\u6570\u306f\u3001\u6b8b\u308a\u306e\u7cfb\u304b\u3089\u306e\u5e73\u5747\u7684\u306a\u5f71\u97ff\u3092 cavity field \u3092\u901a\u3057\u3066\u53d7\u3051\u3066\u3044\u308b\u3068\u8003\u3048\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ \\min_{s_1,\\dots, s_{i-1},s_{i+1},\\dots, s_K} \\left( \\varepsilon_{J_a}(s_1,\\dots,s_K) &#8211; \\frac{1}{2} \\sum_{j \\neq i} h_{j \\to a} s_j \\right) = \\frac{1}{2} \\left( a_J( s_1,\\dots, s_{i-1},s_{i+1},\\dots, s_K) + s_i u_{a \\to i}(h_1,\\dots, h_{i-1},h_{i+1},\\dots, h_K) \\right) $$<\/p>\n\n\n\n<p>\u3059\u306a\u308f\u3061\u3001\u5de6\u8fba\u3092\u6700\u5c0f\u5316\u3057\u305f\u7d50\u679c\u304c\u53f3\u8fba\u306e\u5f62\u3067\u8868\u3055\u308c\u308b\u3088\u3046\u306b $a_J, u_{a \\to i}$ \u3092\u5b9a\u3081\u307e\u3059\u3002\u3053\u3053\u3067\u3001 $a_J$ \u306f\u7bc0 $a$ \u306e\u5e73\u5747\u30a8\u30cd\u30eb\u30ae\u30fc\u3067\u3059\u3002 $a_J, u_{a \\to i}$ \u306f\u3001 $\\varepsilon_{J_a}$ \u306e\u5b9a\u7fa9\u5f0f\u3092\u4ee3\u5165\u3059\u308b\u3053\u3068\u3067\u5177\u4f53\u7684\u306b\u66f8\u304d\u4e0b\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u304c\u3001\u3053\u3053\u3067\u306f\u7701\u7565\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0a\u306e\u3088\u3046\u306b\u3001 $h_{i \\to a}, u_{a \\to i}$ \u306f\u304a\u4e92\u3044\u306b\u5b9a\u7fa9\u3057\u5408\u3046\u5f62\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3092\u9023\u7acb\u65b9\u7a0b\u5f0f\u3068\u3057\u3066\u89e3\u304f\u3053\u3068\u3067\u3001 $h,u$ \u306e\u5024\u304c\u6c42\u3081\u3089\u308c\u307e\u3059\u3002\u3053\u306e\u9023\u7acb\u65b9\u7a0b\u5f0f\u3092\u89e3\u6790\u7684\u306b\u89e3\u304f\u306e\u306f\u56f0\u96e3\u3067\u3059\u304c\u3001\u78ba\u7387\u4f1d\u642c\u6cd5\u3092\u7528\u3044\u3066\u8fd1\u4f3c\u7684\u306b\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u56e0\u5b50\u30b0\u30e9\u30d5\u304c\u6728\u306a\u3089\u3070\u78ba\u7387\u4f1d\u642c\u6cd5\u306f\u53b3\u5bc6\u89e3\u306b\u53ce\u675f\u3059\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002K-SAT \u306e\u56e0\u5b50\u30b0\u30e9\u30d5\u306f\u6728\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u758e\u30b0\u30e9\u30d5\u306a\u306e\u3067\u5c40\u6240\u7684\u306b\u6728\u3068\u898b\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u3001\u5c40\u6240\u7684\u306b\u306f\u6b63\u3057\u3044\u5024\u304c\u6c42\u3081\u3089\u308c\u3066\u3044\u308b\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Cavity_bias_%E3%82%92%E9%87%8D%E3%81%AD%E5%90%88%E3%82%8F%E3%81%9B%E3%81%9F_%E2%80%9Csurvey%E2%80%9D_%E3%81%AE%E5%B0%8E%E5%85%A5\"><\/span>Cavity bias \u3092\u91cd\u306d\u5408\u308f\u305b\u305f &#8220;survey&#8221; \u306e\u5c0e\u5165<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Cavity bias \u3068 cavity field \u306f\u3001\u72b6\u614b (\u5c40\u6240\u6700\u9069\u89e3) \u3054\u3068\u306b\u5b9a\u7fa9\u3055\u308c\u308b\u91cf\u3067\u3059\u3002\u8907\u6570\u306e\u72b6\u614b\u306e\u6271\u3044\u65b9\u306b\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u8003\u3048\u65b9\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6700\u3082\u7c21\u5358\u306a\u65b9\u6cd5\u306f\u3001\u5358\u4e00\u306e\u72b6\u614b\u306e\u307f\u8003\u3048\u308b\u65b9\u6cd5\u3067\u3059\u3002\u3053\u308c\u306f RS (Replica Symmetry) \u4eee\u5b9a\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u8a08\u7b97\u306f\u7c21\u5358\u306b\u306a\u308a\u307e\u3059\u304c\u3001\u5b9f\u969b\u306b\u306f\u591a\u6570\u306e\u72b6\u614b\u304c\u3042\u308b\u7cfb\u3092\u5358\u4e00\u306e\u72b6\u614b\u306b\u3088\u3063\u3066\u4ee3\u8868\u3055\u305b\u308b\u8fd1\u4f3c\u306f\u7c97\u3059\u304e\u308b\u305f\u3081\u3001\u73fe\u5b9f\u3068\u6574\u5408\u3057\u306a\u3044\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002K-SAT \u306e\u554f\u984c\u306b\u304a\u3044\u3066\u306f\u3001RS \u4eee\u5b9a\u306b\u57fa\u3065\u304f\u8a08\u7b97\u306f\u554f\u984c\u306e\u6027\u8cea\u3092\u6349\u3048\u304d\u308c\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<p>\u3088\u308a\u6b63\u78ba\u306a\u8fd1\u4f3c\u65b9\u6cd5\u3068\u3057\u3066\u3001\u8907\u6570\u306e\u72b6\u614b\u3092\u8003\u3048\u3001\u305d\u308c\u3089\u3092\u5bfe\u7b49\u306b\u6271\u3046\u3068\u3044\u3046\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u306f 1 step RSB (Replica Symmetry Breaking) \u4eee\u5b9a\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u3001cavity bias \u306e\u4ee3\u308f\u308a\u306b\u3001 cavity bias \u306e\u5206\u5e03\u3092\u8003\u3048\u308b\u3053\u3068\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002Cavity bias \u306e\u5206\u5e03\u3092 survey $Q^{(y)}(u)$ \u3068\u547c\u3073\u3001\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ Q^{(y)}(u)=\\sum_\\omega \\delta (u-u^{(w)}) $$<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u3001 $u^{(\\omega)}$ \u306f\u72b6\u614b $\\omega$ \u306e cavity bias \u3067\u3059\u3002\u307e\u305f\u3001\u548c\u306f $y$ \u306b\u3088\u3063\u3066\u9078\u629e\u3055\u308c\u308b\u72b6\u614b $\\omega$ \u306b\u3064\u3044\u3066\u53d6\u308a\u307e\u3059\u3002\u3059\u306a\u308f\u3061\u3001zero-temperature thermodynamics \u306b\u304a\u3044\u3066\u3001\u300c\u9006\u6e29\u5ea6\u300d\u304c $y$ \u3067\u3042\u308b\u3068\u304d\u306b\u300c\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\u300d $\\Phi$ \u3092\u6700\u5c0f\u5316\u3059\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u3001\u3059\u306a\u308f\u3061 $\\Sigma(e)-ye$ \u3092\u6700\u5927\u5316\u3059\u308b\u30a8\u30cd\u30eb\u30ae\u30fc $e$ \u3092\u6301\u3064\u72b6\u614b $\\omega$ \u306b\u3064\u3044\u3066\u548c\u3092\u53d6\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>Cavity bias \u306e\u66f4\u65b0\u5f0f\u306b\u5023\u3063\u3066\u3001survey \u306e\u66f4\u65b0\u5f0f\u3092\u5c0e\u51fa\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ Q_{a\\to 1}^{(y)}(u)=C \\int \\prod_{r=1}^q dw_r Q_{b_r \\to 2}^{(y)}(w_r) \\int \\prod_{s=1}^{q&#8217;} dv_s Q_{c_s \\to 3}^{(y)}(v_s) \\delta(u-u_J(W,V)) \\exp(ya_J(W,V)) $$<\/p>\n\n\n\n<p>\u3053\u306e\u5f0f\u306f\u3001\u3053\u306e\u307e\u307e\u3067\u306f\u8a08\u7b97\u304c\u56f0\u96e3\u3067\u3059\u304c\u3001 $\\beta \\to \\infty$ \u306e\u6975\u9650\u306b\u304a\u3044\u3066\u5358\u7d14\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 $\\beta \\to \\infty$ \u3067\u3001cavity bias $u_{a\\to i}$ \u306f $0, \\pm 1$ \u306e 2 \u5024\u3092\u53d6\u308a\u307e\u3059 ($\\pm 1$ \u306e\u3069\u3061\u3089\u304b\u306f\u3001\u7bc0 $a$ \u306b\u304a\u3044\u3066\u5909\u6570 $i$ \u304c\u80af\u5b9a\u30ea\u30c6\u30e9\u30eb\u304b\u5426\u5b9a\u30ea\u30c6\u30e9\u30eb\u304b\u306b\u3088\u308a\u307e\u3059)\u3002\u3088\u3063\u3066\u3001survey \u306f\u300ccavity bias \u304c $0$ \u3068\u306a\u308b\u72b6\u614b\u306e\u5272\u5408\u300d\u3068\u3044\u3046\u4e00\u3064\u306e\u5b9f\u6570\u3067\u7279\u5fb4\u3065\u3051\u3089\u308c\u307e\u3059\u3002\u3053\u306e\u4e8b\u5b9f\u3092\u5229\u7528\u3059\u308b\u3068\u3001\u3088\u308a\u5358\u7d14\u306a survey \u306e\u66f4\u65b0\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u5177\u4f53\u7684\u306a\u5f0f\u306b\u3064\u3044\u3066\u306f\u6587\u732e [2] \u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%B9%B3%E5%9D%87%E3%82%A4%E3%83%B3%E3%82%B9%E3%82%BF%E3%83%B3%E3%82%B9%E3%81%AE%E6%8C%99%E5%8B%95%E3%81%AE%E8%A7%A3%E6%9E%90\"><\/span>\u5e73\u5747\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306e\u6319\u52d5\u306e\u89e3\u6790<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%96%B9%E6%B3%95\"><\/span>\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001\u524d\u7bc0\u3067\u8aac\u660e\u3057\u305f\u554f\u984c\u8a2d\u5b9a\u306e\u3082\u3068\u3001\u30e9\u30f3\u30c0\u30e0\u306a K-SAT \u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306e\u5e73\u5747\u7684\u306a\u6319\u52d5\u3092\u5206\u6790\u3057\u307e\u3059\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u70b9\u306b\u8208\u5473\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$\\alpha=M\/N$ \u306e\u5024\u3092\u5909\u5316\u3055\u305b\u305f\u3068\u304d\u306e\u3001\u5e73\u5747\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306e\u5145\u8db3\u53ef\u80fd\u6027<\/li>\n\n\n\n<li>\u5145\u8db3\u53ef\u80fd\u306a\u3089\u3001\u89e3\u306e\u767a\u898b\u306e\u96e3\u3057\u3055<\/li>\n\n\n\n<li>\u76f8\u8ee2\u79fb\u70b9 (\u554f\u984c\u306e\u6027\u8cea\u306b\u6025\u6fc0\u306a\u5909\u5316\u304c\u8d77\u3053\u308b $\\alpha$ \u306e\u5024)<\/li>\n<\/ul>\n\n\n\n<p>\u307e\u305a\u3001survey \u306e\u66f4\u65b0\u5f0f\u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u5e73\u5747\u3092\u53d6\u308a\u307e\u3059\u3002\u6b21\u306b\u3001\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u3067 survey \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u5f97\u3089\u308c\u305f survey \u304b\u3089\u3001\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc $\\Phi(y)$ \u3092 $y$ \u306e\u95a2\u6570\u3068\u3057\u3066\u6c42\u3081\u307e\u3059\u3002\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u3001complexity \u306f Legendre \u5909\u63db\u306b\u3088\u3063\u3066\u76f8\u4e92\u306b\u5909\u63db\u53ef\u80fd\u3067\u3042\u308b\u3053\u3068\u304c\u71b1\u529b\u5b66\u304b\u3089\u5c0e\u51fa\u3055\u308c\u308b\u305f\u3081\u3001\u6c42\u3081\u305f\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc $\\Phi(y)$ \u304b\u3089\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc\u3068 complexity \u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%B5%90%E6%9E%9C\"><\/span>\u7d50\u679c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>$\\alpha$ \u3092\u5909\u3048\u305f\u3068\u304d\u306e\u3001\u30a8\u30cd\u30eb\u30ae\u30fc $0$ \u306e\u72b6\u614b\u306e complexity $\\Sigma(0)$\u3001\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc $e_0$\u3001\u72b6\u614b\u6570\u304c\u6700\u5927\u3068\u306a\u308b\u30a8\u30cd\u30eb\u30ae\u30fc $e_{th}$ \u306e\u8a08\u7b97\u7d50\u679c\u3092\u30b0\u30e9\u30d5\u306b\u8868\u3057\u305f\u3082\u306e\u3092\u4e0b\u56f3\u306b\u793a\u3057\u307e\u3059\u3002\u4eca\u56de\u306f\u7269\u7406\u7684\u306a\u5bfe\u8c61\u3092\u6271\u3063\u3066\u3044\u308b\u308f\u3051\u3067\u306f\u306a\u3044\u306e\u3067\u3001\u7e26\u8ef8\u306b\u5358\u4f4d\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/03\/phase-1024x788.png\" alt=\"\" class=\"wp-image-6115\"\/><figcaption class=\"wp-element-caption\">\u56f33: 3-SAT \u306e\u76f8\u56f3 (<a href=\"https:\/\/doi.org\/10.1126\/science.1073287\">https:\/\/doi.org\/10.1126\/science.1073287<\/a>)<\/figcaption><\/figure>\n\n\n\n<p>\u3053\u306e\u56f3\u304b\u3089\u30013 \u3064\u306e\u76f8\u306e\u5b58\u5728\u304c\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002\u4ee5\u4e0b\u3001\u305d\u308c\u305e\u308c\u306e\u76f8\u306e\u7279\u5fb4\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>SAT \u76f8 $\\alpha < \\alpha_d \\approx 3.9$\n\n<ul class=\"wp-block-list\">\n\n<li>\u3053\u306e\u76f8\u3067\u306f\u3001 $e_0 = 0$ \u3067\u3042\u308a\u3001\u5e73\u5747\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306f\u5145\u8db3\u53ef\u80fd\u3067\u3059\u3002<\/li>\n\n\n<li>\u3053\u306e\u76f8\u3067\u306f\u3001\u3059\u3079\u3066\u306e survey \u304c $0$ \u3068\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u3059\u3079\u3066\u306e\u72b6\u614b\u3067 cavity bias \u304c $0$ \u3068\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u5404\u30b9\u30d4\u30f3\u306f\u7279\u5b9a\u306e\u5411\u304d\u3092\u5411\u3053\u3046\u3068\u3057\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u3001\u4e00\u90e8\u306e\u30b9\u30d4\u30f3\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u5411\u304d\u4ed8\u3051\u3066\u3082\u3001\u6b8b\u308a\u306e\u30b9\u30d4\u30f3\u3092\u9069\u5f53\u306b\u5411\u304d\u4ed8\u3051\u308b\u3053\u3068\u3067\u591a\u304f\u306e\u5834\u5408\u306b\u5145\u8db3\u53ef\u80fd\u3068\u306a\u308a\u307e\u3059\u3002<\/li>\n\n\n<li>\u3053\u306e\u76f8\u3067\u306f\u3001\u30b7\u30f3\u30d7\u30eb\u306a\u5c71\u767b\u308a\u6cd5\u3084 SA (Simulated Annealing) \u3092\u7528\u3044\u3066\u5bb9\u6613\u306b\u89e3\u304c\u6c42\u307e\u308a\u307e\u3059\u3002<\/li>\n\n<\/ul>\n\n<\/li>\n\n\n\n<li>Hard-SAT \u76f8 $\\alpha_d < \\alpha < \\alpha_c \\approx 4.3$\n\n<ul class=\"wp-block-list\">\n\n<li>\u3053\u306e\u76f8\u3067\u3082 $e_0 = 0$ \u3067\u3042\u308a\u3001\u5e73\u5747\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306f\u4f9d\u7136\u3068\u3057\u3066\u5145\u8db3\u53ef\u80fd\u3067\u3059\u3002<\/li>\n\n\n<li>\u3053\u306e\u76f8\u3067\u306f\u3001 survey \u306f $0$ \u4ee5\u5916\u306e\u5024\u3082\u53d6\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u307e\u305f\u3001 $\\Sigma(0)$ \u304c\u5c0f\u3055\u304f\u306a\u308a\u3001\u4ee3\u308f\u308a\u306b\u6b63\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u6301\u3064\u72b6\u614b\u304c\u591a\u304f\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u6b63\u306e\u5c40\u6240\u6700\u9069\u89e3\u304c\u3001\u30a8\u30cd\u30eb\u30ae\u30fc $0$ \u306e\u89e3\u306b\u6bd4\u3079\u3066\u591a\u6570\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001SA \u306a\u3069\u306e\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u5c40\u6240\u6700\u9069\u89e3\u306b\u9665\u308a\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u304c $0$ \u306e\u89e3\u306b\u5230\u9054\u3059\u308b\u3053\u3068\u304c\u96e3\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/li>\n\n<\/ul>\n\n<\/li>\n\n\n\n<li>UNSAT \u76f8 $\\alpha &gt; \\alpha_c$\n<ul class=\"wp-block-list\">\n<li>\u3053\u306e\u76f8\u3067\u306f\u3001 $e_0 &gt; 0$ \u3067\u3042\u308a\u3001\u5e73\u5747\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306f\u5145\u8db3\u4e0d\u53ef\u80fd\u3067\u3059\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>\u7d4c\u9a13\u7684\u306b\u77e5\u3089\u308c\u3066\u3044\u308b SAT-UNSAT \u5883\u754c\u3068\u4e00\u81f4\u3059\u308b $\\alpha_c$ \u304c\u5f97\u3089\u308c\u307e\u3057\u305f\u3002\u307e\u305f\u3001 $\\alpha \\approx \\alpha_c$ \u3067\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u96e3\u3057\u304f\u306a\u308b\u3068\u3044\u3046\u73fe\u8c61\u306b\u5bfe\u3057\u3066\u3001\u300c\u8ad6\u7406\u5f0f\u3092\u5145\u8db3\u3057\u306a\u3044\u5c40\u6240\u6700\u9069\u89e3\u304c\u975e\u5e38\u306b\u591a\u304f\u306a\u308b\u304b\u3089\u96e3\u3057\u304f\u306a\u308b\u300d\u3068\u3044\u3046\u8aac\u660e\u3092\u4e0e\u3048\u308b\u3053\u3068\u306b\u6210\u529f\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%89%B9%E5%AE%9A%E3%82%A4%E3%83%B3%E3%82%B9%E3%82%BF%E3%83%B3%E3%82%B9%E3%81%AB%E5%AF%BE%E3%81%99%E3%82%8B%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0\"><\/span>\u7279\u5b9a\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u5bfe\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Survey_propagation_algorithm\"><\/span>Survey propagation algorithm<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001\u7279\u5b9a\u306e K-SAT \u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u306b\u3001\u52b9\u7387\u7684\u306b\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3092\u89e3\u304f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n\n\n\n<p>Cavity \u6cd5\u3092\u7528\u3044\u3066\u5f97\u3089\u308c\u308b\u5404\u30b9\u30d4\u30f3\u306e\u5206\u5e03\u306e\u60c5\u5831\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u6b21\u306e\u3088\u3046\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u89e3\u3092\u69cb\u7bc9\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u306b\u3088\u308a survey \u3092\u8a08\u7b97\u3059\u308b<\/li>\n\n\n\n<li>Survey \u304b\u3089\u3001cavity field \u306e\u5206\u5e03\u3092\u8a08\u7b97\u3059\u308b<\/li>\n\n\n\n<li>Cavity field \u306e\u5206\u5e03\u304b\u3089\u3001\u30b9\u30d4\u30f3\u3092\u6c7a\u5b9a\u3059\u308b: $w_i^+, w_i^-$ \u3092\u305d\u308c\u305e\u308c\u3001\u30b9\u30d4\u30f3 $s_i$ \u306e cavity field \u304c\u6b63\/\u8ca0\u306b\u306a\u308b\u78ba\u7387\u3068\u3059\u308b\u3002 $|w_i^+-w_i^-|$ \u304c\u6700\u5927\u306e $i$ \u3092\u9078\u3093\u3067\u3001 $s_i$ \u3092 $w_i^+&gt;w_i^-$ \u306a\u3089 $1$\u3001 $w_i^+&lt;w_i^-$ \u306a\u3089 $-1$ \u306b\u3059\u308b\u3002<\/li>\n\n\n\n<li>\u30b9\u30d4\u30f3\u304c $1$ \u3064\u6e1b\u3063\u305f\u554f\u984c\u306b\u5bfe\u3057\u3066\u30011-3 \u3092\u7e70\u308a\u8fd4\u3059<\/li>\n\n\n\n<li>Survey \u304c\u3059\u3079\u3066 $0$ \u306b\u306a\u3063\u305f\u3089\u3001 SA \u3067\u6b8b\u308a\u306e\u554f\u984c\u3092\u89e3\u304f<\/li>\n<\/ol>\n\n\n\n<p>\u624b\u9806 5 \u3067\u306f\u3001survey \u304c\u3059\u3079\u3066 $0$ \u3067\u3042\u308b\u3088\u3046\u306a\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306f SAT \u76f8\u306b\u3042\u308b\u306f\u305a\u3060\u304b\u3089\u3001\u7c21\u5358\u306a SA \u3067\u89e3\u3051\u308b\u3068\u3044\u3046\u3001\u524d\u7bc0\u3067\u8aac\u660e\u3057\u305f\u7d50\u679c\u3092\u5229\u7528\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092 survey propagation algorithm \u3068\u547d\u540d\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%B5%90%E6%9E%9C-2\"><\/span>\u7d50\u679c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Survey propagation algorithm \u3092\u3001 3-SAT \u306e SAT-UNSAT \u5883\u754c\u306b\u8fd1\u3044\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u9069\u7528\u3057\u3066\u3001\u89e3\u3092\u898b\u3064\u3051\u308b\u307e\u3067\u306e\u5b9f\u884c\u6642\u9593\u3092\u8a08\u6e2c\u3057\u3001\u65e2\u5b58\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u6bd4\u8f03\u3059\u308b\u3053\u3068\u3067\u6027\u80fd\u306e\u8a55\u4fa1\u3092\u884c\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u307e\u305a\u3001\u65e2\u5b58\u306e\u30d9\u30f3\u30c1\u30de\u30fc\u30af $\\alpha \\approx 4.2, N \\approx 2000$ \u306b\u5bfe\u3057\u3066 survey propagation algorithm \u3092\u5b9f\u884c\u3057\u307e\u3057\u305f\u3002\u3059\u3079\u3066\u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u5bfe\u3057\u3066\u9ad8\u901f\u306b\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u6b21\u306b\u3001\u3088\u308a\u5927\u304d\u306a\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9 $\\alpha \\approx 4.2, N \\approx 10^5$ \u3092\u8907\u6570\u4f5c\u6210\u3057\u3001 survey propagation algorithm \u3092\u5b9f\u884c\u3057\u307e\u3057\u305f\u3002\u3053\u308c\u3082\u3059\u3079\u3066\u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3067\u3001\u5341\u5206\u9ad8\u901f\u306b\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002Survey propagation algorithm \u3068\u540c\u7a0b\u5ea6\u306e\u6027\u80fd\u3092\u6301\u3064\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u9ad8\u5ea6\u306b\u30c1\u30e5\u30fc\u30cb\u30f3\u30b0\u3057\u305f walksat \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u307f\u3067\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u6642\u9593\u8a08\u7b97\u91cf\u306f\u3001\u304a\u3088\u305d $O(N^2)$ \u306e\u30aa\u30fc\u30c0\u306b\u306a\u308b\u3053\u3068\u304c\u89b3\u5bdf\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%B5%90%E8%AB%96\"><\/span>\u7d50\u8ad6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u672c\u8ad6\u6587\u3067\u306f\u3001cavity \u6cd5\u3092\u7528\u3044\u3066 K-SAT \u554f\u984c\u3092\u89e3\u6790\u3057\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u7d50\u8ad6\u304c\u5f97\u3089\u308c\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u5e73\u5747\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306e\u6319\u52d5\u306e\u5206\u6790:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>SAT-UNSAT \u5883\u754c\u4ed8\u8fd1\u306b Hard-SAT \u76f8\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u304c\u78ba\u8a8d\u3055\u308c\u305f\u3002<\/li>\n\n\n\n<li>Hard-SAT \u76f8\u3067\u306f\u3001\u554f\u984c\u3092\u5145\u8db3\u3057\u306a\u3044\u5c40\u6240\u6700\u9069\u89e3\u304c\u975e\u5e38\u306b\u591a\u304f\u5b58\u5728\u3059\u308b\u305f\u3081\u3001\u5358\u7d14\u306a SA \u306a\u3069\u306e\u63a2\u7d22\u65b9\u6cd5\u3067\u306f\u89e3\u306b\u5230\u9054\u3059\u308b\u3053\u3068\u304c\u96e3\u3057\u3044\u3053\u3068\u304c\u5224\u660e\u3057\u305f\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u7279\u5b9a\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3092\u89e3\u304f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u69cb\u6210:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e0e\u3048\u3089\u308c\u305f\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u5bfe\u3057\u3066 cavity \u6cd5\u3092\u9069\u7528\u3057\u3066\u3001\u5404\u5909\u6570\u306e\u5024\u306e\u5206\u5e03\u304c\u5f97\u3089\u308c\u308b\u3002\u3053\u306e\u60c5\u5831\u3092\u5229\u7528\u3057\u3066\u5909\u6570\u306e\u5024\u3092\u9010\u6b21\u7684\u306b\u6c7a\u5b9a\u3059\u308b survey propagation algorithm \u3092\u8003\u6848\u3057\u305f\u3002<\/li>\n\n\n\n<li>Survey propagation algorithm \u306f\u3001SAT-UNSAT \u5883\u754c\u306b\u8fd1\u3044\u5927\u304d\u306a\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u5bfe\u3057\u3066\u3082\u52b9\u7387\u7684\u306b\u89e3\u3092\u767a\u898b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u305f\u3002\u3053\u308c\u306f\u3001\u65e2\u5b58\u306e\u307b\u3068\u3093\u3069\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 (\u5177\u4f53\u7684\u306b\u306f\u3001\u9ad8\u5ea6\u306b\u30c1\u30e5\u30fc\u30cb\u30f3\u30b0\u3057\u305f walksat \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u4ee5\u5916) \u3092\u4e0a\u56de\u308b\u6027\u80fd\u3067\u3042\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\"><\/span>\u3042\u3068\u304c\u304d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>NP \u5b8c\u5168\u554f\u984c\u306e\u3088\u3046\u306a\u975e\u5e38\u306b\u8907\u96d1\u306a\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u306b\u5bfe\u3057\u3066\u3082\u3001\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u7406\u8ad6\u306e\u77e5\u898b\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u3067\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u304d\u308b\u3053\u3068\u304c\u975e\u5e38\u306b\u8208\u5473\u6df1\u304b\u3063\u305f\u3067\u3059\u3002\u4ed6\u306e NP \u5b8c\u5168\u554f\u984c\u306b\u5bfe\u3057\u3066\u3082\u3001\u300c\u5c40\u6240\u6700\u9069\u89e3\u304c\u5897\u3048\u308b\u3053\u3068\u304c\u96e3\u3057\u3055\u306e\u539f\u56e0\u3067\u3042\u308b\u300d\u3068\u3044\u3046\u63cf\u50cf\u304c\u5f97\u3089\u308c\u308b\u306e\u304b\u3001\u9006\u306b P \u554f\u984c\u3092\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u306b\u5e30\u7740\u3055\u305b\u305f\u3068\u304d\u306b\u3069\u306e\u3088\u3046\u306a\u6319\u52d5\u3092\u793a\u3059\u306e\u304b\u306b\u8208\u5473\u3092\u6301\u3061\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\"><\/span>\u53c2\u8003\u6587\u732e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>[1] M. M\u00e9zard, G. Parisi, R. Zecchina, \u201cAnalytic and Algorithmic Solution of Random Satisfiability Ptroblems,\u201d Science, Vol 297, Issue 5582, pp. 812-815, 2002<\/p>\n\n\n\n<p>[2] M. M\u00e9zard and R. Zecchina, \u201cThe random K-satisfiability problem: from an analytic solution to an efficient algorithm,\u201d Phys. Rev. E 66 (2002) 056126<\/p>\n","protected":false},"excerpt":{"rendered":"<p>K-SAT \u306f\u3001\u3044\u304f\u3064\u304b\u306e\u5909\u6570\u304b\u3089\u306a\u308b\u8ad6\u7406\u5f0f\u3092\u5145\u8db3\u3059\u308b\u3088\u3046\u306a\u771f\u507d\u5024\u306e\u5272\u5f53\u3092\u6c42\u3081\u308b\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u3067\u3059\u3002K-SAT\u306fNP\u5b8c\u5168\u554f\u984c\u3067\u3042\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u3066\u304a\u308a\u3001\u73fe\u5728\u306e\u3068\u3053\u308d\u3001\u5165\u529b\u30b5\u30a4\u30ba\u306b\u5bfe\u3057\u3066\u6700\u60aa\u591a\u9805\u5f0f\u6642\u9593\u3067\u89e3\u304f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b58\u5728\u306f\u77e5\u3089\u308c\u3066\u3044\u307e\u305b\u3093\u3002K-SAT \u306e\u96e3\u3057\u3055\u306e\u539f\u56e0\u3092\u7406\u89e3\u3057\u3001K-SAT \u3092\u5e73\u5747\u7684\u306b\u9ad8\u901f\u306b\u89e3\u304f\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30c3\u30af\u3092\u958b\u767a\u3059\u308b\u305f\u3081\u306e\u7814\u7a76\u304c\u9032\u3081\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u672c\u8ad6\u6587\u3067\u306f\u3001\u7d71\u8a08\u529b\u5b66\u3001\u7279\u306b\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u7406\u8ad6\u306e\u624b\u6cd5\u3092\u7528\u3044\u3066 K-SAT \u3092\u89e3\u6790\u3057\u3001\u4e0a\u306e 2 \u3064\u306e\u554f\u3044\u306b\u5bfe\u3059\u308b\u6d1e\u5bdf\u3092\u4e0e\u3048\u307e\u3059\u3002<\/p>\n","protected":false},"author":16,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[110,112,115],"class_list":["post-6102","post","type-post","status-publish","format-standard","hentry","category-review","tag-110","tag-112","tag-115"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - 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