Skip to Main content Skip to Navigation
Conference papers

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.
Complete list of metadata

Cited literature [15 references]  Display  Hide  Download
Contributor : Publications Loria Connect in order to contact the contributor
Submitted on : Thursday, February 11, 2010 - 12:05:36 PM
Last modification on : Monday, February 22, 2010 - 10:44:59 AM
Long-term archiving on: : Friday, June 18, 2010 - 8:14:24 PM


Files produced by the author(s)


  • HAL Id : inria-00455819, version 1



Edward A. Hirsch, Dmitry Itsykson. On optimal heuristic randomized semidecision procedures, with application to proof complexity. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Inria Nancy Grand Est & Loria, Mar 2010, Nancy, France. pp.453-464. ⟨inria-00455819⟩



Record views


Files downloads