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

Edward A. Hirsch 1 Dmitry Itsykson 1, *
* Corresponding author
1 Steklov Institute of Mathematics at St. Petersburg
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. Krajicek and Pudlak (1989) show that this question is equivalent to the existence of an algorithm that is optimal on all propositional tautologies. Monroe (2009) 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 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.
Keywords : propositional proof complexity optimal algorithm
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Conference papers
Jean-Yves Marion and Thomas Schwentick. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Mar 2010, Nancy, France. pp.453-464, 2010, Proceedings of the 27th Annual Symposium on the Theoretical Aspects of Computer Science
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Edward A. Hirsch, Dmitry Itsykson. On optimal heuristic randomized semidecision procedures, with application to proof complexity. Jean-Yves Marion and Thomas Schwentick. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Mar 2010, Nancy, France. pp.453-464, 2010, Proceedings of the 27th Annual Symposium on the Theoretical Aspects of Computer Science. 〈inria-00455819〉

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