{"id":16922,"date":"2017-08-16T17:00:12","date_gmt":"2017-08-16T22:00:12","guid":{"rendered":"http:\/\/bucktownbell.com\/?p=16922"},"modified":"2017-08-16T17:01:43","modified_gmt":"2017-08-16T22:01:43","slug":"a-solution-of-the-p-versus-np-problem","status":"publish","type":"post","link":"http:\/\/bucktownbell.com\/?p=16922","title":{"rendered":"A Solution of the P versus NP Problem"},"content":{"rendered":"<blockquote><p>Berg and Ulfberg and Amano and Maruoka have used CNF-DNF-approximators to prove exponential lower bounds for the monotone network complexity of the clique function and of Andreev&#8217;s function. We show that these approximators can be used to prove the same lower bound for their non-monotone network complexity. <strong>This implies P not equal NP.<\/strong><\/p><\/blockquote>\n<p>Source: <em><a href=\"https:\/\/arxiv.org\/abs\/1708.03486\">[1708.03486] A Solution of the P versus NP Problem<\/a><\/em><\/p>\n<p>More background at:\u00a0 <a href=\"http:\/\/www.win.tue.nl\/~gwoegi\/P-versus-NP.htm\">The P-versus-NP page<\/a><\/p>\n<blockquote><p>This page collects links around papers that try to settle the &#8220;P versus NP&#8221; question (in either way). Here are some links that explain\/discuss this question:<\/p><\/blockquote>\n<ul>\n<li>\n<blockquote><p>A clear <a href=\"http:\/\/www.claymath.org\/sites\/default\/files\/pvsnp.pdf\"> formulation<\/a> of the &#8220;P versus NP&#8221; question by <a href=\"http:\/\/www.cs.toronto.edu\/%7Esacook\/\"> Stephen Cook.<\/a><\/p><\/blockquote>\n<\/li>\n<li>&#8230;<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Berg and Ulfberg and Amano and Maruoka have used CNF-DNF-approximators to prove exponential lower bounds for the monotone network complexity of the clique function and of Andreev&#8217;s function. We show that these approximators can be used to prove the same &hellip; <a href=\"http:\/\/bucktownbell.com\/?p=16922\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1250],"tags":[338,180,1343,500],"class_list":["post-16922","post","type-post","status-publish","format-standard","hentry","category-white-paper","tag-encryption","tag-math","tag-np-problem","tag-study-says"],"_links":{"self":[{"href":"http:\/\/bucktownbell.com\/index.php?rest_route=\/wp\/v2\/posts\/16922","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/bucktownbell.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/bucktownbell.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/bucktownbell.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/bucktownbell.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=16922"}],"version-history":[{"count":2,"href":"http:\/\/bucktownbell.com\/index.php?rest_route=\/wp\/v2\/posts\/16922\/revisions"}],"predecessor-version":[{"id":16924,"href":"http:\/\/bucktownbell.com\/index.php?rest_route=\/wp\/v2\/posts\/16922\/revisions\/16924"}],"wp:attachment":[{"href":"http:\/\/bucktownbell.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=16922"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bucktownbell.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=16922"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bucktownbell.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=16922"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}