On optimal heuristic randomized semidecision procedures, with application to proof complexity

Edward A. Hirsch, Dmitry Itsykson

Research output

8 Citations (Scopus)

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. Krajíček and Pudlák [KP89] show that this question is equivalent to the existence of an algorithm that is optimal1 on all propositional tautologies. Monroe [Mon09] recently gave a conjecture implying that such algorithm does not exist. We show that in the presence of errors such optimal algorithms 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. Our 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.

Original languageEnglish
Title of host publicationSTACS 2010 - 27th International Symposium on Theoretical Aspects of Computer Science
Pages453-464
Number of pages12
DOIs
Publication statusPublished - 1 Dec 2010
Event27th International Symposium on Theoretical Aspects of Computer Science, STACS 2010 - Nancy
Duration: 4 Mar 20106 Mar 2010

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume5
ISSN (Print)1868-8969

Conference

Conference27th International Symposium on Theoretical Aspects of Computer Science, STACS 2010
CountryFrance
CityNancy
Period4/03/106/03/10

Scopus subject areas

  • Software

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  • Cite this

    Hirsch, E. A., & Itsykson, D. (2010). On optimal heuristic randomized semidecision procedures, with application to proof complexity. In STACS 2010 - 27th International Symposium on Theoretical Aspects of Computer Science (pp. 453-464). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 5). https://doi.org/10.4230/LIPIcs.STACS.2010.2475