{"id":187086,"date":"2011-11-30T00:00:00","date_gmt":"2011-12-02T09:50:29","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/pcps-and-expander-graphs\/"},"modified":"2016-08-22T11:30:55","modified_gmt":"2016-08-22T18:30:55","slug":"pcps-and-expander-graphs","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/pcps-and-expander-graphs\/","title":{"rendered":"PCPs and Expander Graphs"},"content":{"rendered":"<div class=\"asset-content\">\n<p>A probabilistically checkable proof (PCP) is a special format for writing proofs that is very robust. In this format, a proof of a false theorem is guaranteed to have so many bugs that it can be checked by reading a constant number of random proof bits.<br \/>\nThe celebrated PCP theorem says that every NP language has a robust &#8220;PCP&#8221; proof.<br \/>\nIn the talk we will explain how to construct a PCP by taking any standard NP proof and then routing it through an expander graph (i.e., a graph that is very well-connected).<br \/>\nWe will also describe a complementary result that shows how in some restricted sense, every construction of a PCP must be based on an expander.<br \/>\nNo prior knowledge will be assumed.<br \/>\nBased in part on joint work with Tali Kaufman.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A probabilistically checkable proof (PCP) is a special format for writing proofs that is very robust. In this format, a proof of a false theorem is guaranteed to have so many bugs that it can be checked by reading a constant number of random proof bits. The celebrated PCP theorem says that every NP language [&hellip;]<\/p>\n","protected":false},"featured_media":196522,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"research-area":[13561],"msr-video-type":[],"msr-locale":[268875],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-187086","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/GG5PWH5avKE","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/187086"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/187086\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/196522"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=187086"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=187086"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=187086"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=187086"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=187086"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=187086"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}