{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article6472","name":"Finding Irrefutable Certificates for S_2^p via Arthur and Merlin","abstract":"We show that $S_2^psubseteq P^{prAM}$, where $S_2^p$ is the\r\n symmetric alternation class and $prAM$ refers to the promise\r\n version of the Arthur-Merlin class $AM$. This is derived as a\r\n consequence of our main result that presents an $FP^{prAM}$\r\n algorithm for finding a small set of ``collectively irrefutable\r\n certificates'' of a given $S_2$-type matrix. The main result also\r\n yields some new consequences of the hypothesis that $NP$ has\r\n polynomial size circuits. It is known that the above hypothesis\r\n implies a collapse of the polynomial time hierarchy ($PH$) to\r\n $S_2^psubseteq ZPP^{NP}$ (Cai 2007, K\"obler and Watanabe 1998).\r\n Under the same hypothesis, we show that $PH$ collapses to\r\n $P^{prMA}$. We also describe an $FP^{prMA}$ algorithm for learning\r\n polynomial size circuits for $SAT$, assuming such circuits exist.\r\n For the same problem, the previously best known result was a\r\n $ZPP^{NP}$ algorithm (Bshouty et al. 1996).","keywords":["Symmetric alternation","promise-AM","Karp--Lipton theorem","learning circuits"],"author":[{"@type":"Person","name":"Chakaravarthy, Venkatesan T.","givenName":"Venkatesan T.","familyName":"Chakaravarthy"},{"@type":"Person","name":"Roy, Sambuddha","givenName":"Sambuddha","familyName":"Roy"}],"position":15,"pageStart":157,"pageEnd":168,"dateCreated":"2008-02-06","datePublished":"2008-02-06","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by-nd\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Chakaravarthy, Venkatesan T.","givenName":"Venkatesan T.","familyName":"Chakaravarthy"},{"@type":"Person","name":"Roy, Sambuddha","givenName":"Sambuddha","familyName":"Roy"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.STACS.2008.1342","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6204","volumeNumber":1,"name":"25th International Symposium on Theoretical Aspects of Computer Science","dateCreated":"2008-02-05","datePublished":"2008-02-05","editor":[{"@type":"Person","name":"Albers, Susanne","givenName":"Susanne","familyName":"Albers"},{"@type":"Person","name":"Weil, Pascal","givenName":"Pascal","familyName":"Weil"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article6472","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6204"}}}