{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article6695","name":"On Optimal Heuristic Randomized Semidecision Procedures, with Application to Proof Complexity","abstract":"The existence of a ($p$-)optimal propositional proof system is a major open question in (proof) complexity; many people conjecture that such systems do not exist. Kraj\\'{\\i}\\v{c}ek and Pudl\\'{a}k \\cite{KP} show that this question is equivalent to the existence of an algorithm that is optimal\\footnote{Recent papers \\cite{Monroe}\r\ncall such algorithms \\emph{$p$-optimal} while traditionally Levin's algorithm was called \\emph{optimal}. We follow the older tradition. Also there is some mess in terminology here, thus please see formal definitions in Sect.~\\ref{sec:prelim} below.} on all propositional tautologies. Monroe \\cite{Monroe} recently gave a conjecture implying that such algorithm does not exist.\r\n\r\nWe show that in the presence of errors such optimal algorithms \\emph{do} exist. The concept is motivated by the notion of heuristic algorithms. Namely, we allow the algorithm to claim a small number of false ``theorems'' (according to any polynomial-time samplable distribution on non-tautologies) and err with bounded probability on other inputs.\r\n\r\nOur result can also be viewed as the existence of an optimal proof system in a class of proof systems obtained by generalizing automatizable proof systems.","keywords":["Propositional proof complexity","optimal algorithm"],"author":[{"@type":"Person","name":"Hirsch, Edward A.","givenName":"Edward A.","familyName":"Hirsch"},{"@type":"Person","name":"Itsykson, Dmitry","givenName":"Dmitry","familyName":"Itsykson"}],"position":40,"pageStart":453,"pageEnd":464,"dateCreated":"2010-03-09","datePublished":"2010-03-09","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by-nd\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Hirsch, Edward A.","givenName":"Edward A.","familyName":"Hirsch"},{"@type":"Person","name":"Itsykson, Dmitry","givenName":"Dmitry","familyName":"Itsykson"}],"copyrightYear":"2010","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.STACS.2010.2475","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6208","volumeNumber":5,"name":"27th International Symposium on Theoretical Aspects of Computer Science","dateCreated":"2010-03-09","datePublished":"2010-03-09","editor":[{"@type":"Person","name":"Marion, Jean-Yves","givenName":"Jean-Yves","familyName":"Marion"},{"@type":"Person","name":"Schwentick, Thomas","givenName":"Thomas","familyName":"Schwentick"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article6695","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":"#volume6208"}}}