{"id":5481,"date":"2016-08-13T12:00:26","date_gmt":"2016-08-13T10:00:26","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=5481"},"modified":"2016-08-12T11:50:39","modified_gmt":"2016-08-12T09:50:39","slug":"resena-proving-divide-and-conquer-complexities-in-isabellehol","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/resena-proving-divide-and-conquer-complexities-in-isabellehol\/","title":{"rendered":"Rese\u00f1a: Proving divide and conquer complexities in Isabelle\/HOL"},"content":{"rendered":"<p>Se ha publicado un art\u00edculo de razonamiento formalizado en Isabelle\/HOL sobre algor\u00edtmica titulado <a href=\"http:\/\/home.in.tum.de\/~eberlm\/divide_and_conquer_isabelle.pdf\">Proving divide and conquer complexities in Isabelle\/HOL<\/a><\/p>\n<p>Su autor es <a href=\"http:\/\/home.in.tum.de\/~eberlm\">Manuel Eberl<\/a> (de la <em>Technische Universit\u00e4t M\u00fcnchen<\/em>, Alemania).<\/p>\n<p>Su resumen es<\/p>\n<blockquote><p>\n  The <a href=\"http:\/\/bioinfo.ict.ac.cn\/~dbu\/AlgorithmCourses\/Lectures\/LinearRecurrenceEquations.pdf\">Akra\u2013Bazzi method<\/a>, a generalisation of the well-known <a href=\"https:\/\/en.wikipedia.org\/wiki\/Master_theorem\">Master Theorem<\/a>, is a useful tool for analysing the complexity of Divide &amp; Conquer algorithms. This work describes a formalisation of the Akra\u2013Bazzi method (as generalised by <a href=\"http:\/\/courses.csail.mit.edu\/6.046\/spring04\/handouts\/akrabazzi.pdf\">Leighton<\/a>) in the interactive theorem prover Isabelle\/HOL and the derivation of a generalised version of the Master Theorem from it. We also provide some automated proof methods that facilitate the application of this Master Theorem and allow mostly automatic verification of \u0398-bounds for these <a href=\"http:\/\/bit.ly\/2aOhDMt\">Divide &amp; Conquer<\/a> recurrences. To our knowledge, this is the first formalisation of theorems for the analysis of such recurrences.\n<\/p><\/blockquote>\n<p>La versi\u00f3n final del trabajo se ha publicado en el <a href=\"http:\/\/link.springer.com\/article\/10.1007\/s10817-016-9378-0\">Journal of Automated Reasoning<\/a>.<\/p>\n<p>El c\u00f3digo de las correspondientes teor\u00edas en Isabelle\/HOL se encuentra <a href=\"http:\/\/www.isa-afp.org\/entries\/Akra_Bazzi.shtml\">aqu\u00ed<\/a>.<\/p>\n<p>Este art\u00edculo puede servir de lectura complementaria en los cursos de <a href=\"http:\/\/www.cs.us.es\/~jalonso\/cursos\/m-ra\">Razonamiento autom\u00e1tico<\/a>, <a href=\"http:\/\/www.cs.us.es\/cursos\/rac\/\">Razonamiento asistido por ordenador<\/a> y <a href=\"http:\/\/www.cs.us.es\/~mjoseh\/LCyTM-15\">L\u00f3gica computacional y teor\u00eda de modelos<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Se ha publicado un art\u00edculo de razonamiento formalizado en Isabelle\/HOL sobre algor\u00edtmica titulado Proving divide and conquer complexities in Isabelle\/HOL Su autor es Manuel Eberl (de la Technische Universit\u00e4t M\u00fcnchen, Alemania). Su resumen es The Akra\u2013Bazzi method, a generalisation of the well-known Master Theorem, is a useful tool for analysing the complexity of Divide &amp;&#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":[144,285],"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\/5481"}],"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=5481"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/5481\/revisions"}],"predecessor-version":[{"id":5482,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/5481\/revisions\/5482"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=5481"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=5481"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=5481"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}