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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.
Keywords :
propositional proof complexity
optimal algorithm
Cited literature [15 references]
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
Long-term archiving on: : Friday, June 18, 2010 - 8:14:24 PM
Contributor : Publications Loria <>
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
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