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. 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.
Document type :
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
Liste complète des métadonnées


https://hal.inria.fr/inria-00455819
Contributor : Publications Loria <>
Submitted on : Thursday, February 11, 2010 - 12:05:36 PM
Last modification on : Monday, February 22, 2010 - 10:44:59 AM
Document(s) archivé(s) le : Friday, June 18, 2010 - 8:14:24 PM

File

hirsch.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00455819, version 1

Collections

Citation

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>

Share

Metrics

Record views

121

Document downloads

96