{"id":2172,"date":"2012-09-10T05:30:27","date_gmt":"2012-09-10T05:30:27","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=2172"},"modified":"2013-03-08T05:48:12","modified_gmt":"2013-03-08T05:48:12","slug":"formalizing-frankls-conjecture-fc-families","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formalizing-frankls-conjecture-fc-families\/","title":{"rendered":"Rese\u00f1a: Formalizing Frankl&#8217;s conjecture: FC-families"},"content":{"rendered":"<p>En las <a href=\"http:\/\/www.informatik.uni-bremen.de\/cicm2012\/cicm.php\">CICM 2012<\/a> (Conferences on Intelligent Computer Mathematics) se ha presentado un trabajo de razonamiento formalizado en <a href=\"http:\/\/www.cl.cam.ac.uk\/research\/hvg\/isabelle\/index.html\">Isabelle\/HOL<\/a> titulado <a href=\"http:\/\/argo.matf.bg.ac.rs\/publications\/2012\/frankl.pdf\">Formalizing Frankl&#8217;s conjecture: FC-families<\/a>.<\/p>\n<p>Sus autores son <a href=\"http:\/\/poincare.matf.bg.ac.rs\/~filip\">Filip Mari\u0107<\/a>, Miodrag \u017divkovi\u0107 y Bojan Vu\u010dkovi\u0107 (del grupo <a href=\"http:\/\/argo.matf.bg.ac.rs\">ARGO<\/a> (Automated Reasoning GrOup) de la Universidad de Belgrado).<\/p>\n<p>Su resumen es<\/p>\n<blockquote><p>\nThe <a href=\"http:\/\/en.wikipedia.org\/wiki\/Union-closed_sets_conjecture\">Frankl\u2019s conjecture<\/a>, formulated in 1979. and still open, states that in every family of sets closed for unions there is an element contained in at least half of the sets. FC-families are families for which it is proved that every union-closed family containing them satisfies the Frankl\u2019s condition (e.g., in every union-closed family that contains a one- element set a, the element a is contained in at least half of the sets, so families of the form a are the simplest FC-families). FC-families play an important role in attacking the Frankl\u2019s conjecture, since they enable significant search space pruning. We present a formalization of the computer assisted approach for proving that a family is an FC-family. Proof-by-computation paradigm is used and the proof assistant Isabelle\/HOL is used both to check mathematical content, and to perform (verified) combinatorial searches on which the proofs rely. FC-families known in the literature are confirmed, and a new FC-family is discovered.\n<\/p><\/blockquote>\n<p>El c\u00f3digo con la formalizaci\u00f3n en Isabelle\/HOL se encuentra <a href=\"http:\/\/argo.matf.bg.ac.rs\/downloads\/formalizations\/frankl.zip\">aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>En las CICM 2012 (Conferences on Intelligent Computer Mathematics) se ha presentado un trabajo de razonamiento formalizado en Isabelle\/HOL titulado Formalizing Frankl&#8217;s conjecture: FC-families. Sus autores son Filip Mari\u0107, Miodrag \u017divkovi\u0107 y Bojan Vu\u010dkovi\u0107 (del grupo ARGO (Automated Reasoning GrOup) de la Universidad de Belgrado). Su resumen es The Frankl\u2019s conjecture, formulated in 1979. and&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[100],"tags":[144,273,285],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_likes_enabled":false,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/2172"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/comments?post=2172"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/2172\/revisions"}],"predecessor-version":[{"id":2780,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/2172\/revisions\/2780"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=2172"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=2172"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=2172"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}