### 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 optimal^{1} 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 language | English |
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Title of host publication | STACS 2010 - 27th International Symposium on Theoretical Aspects of Computer Science |

Pages | 453-464 |

Number of pages | 12 |

DOIs | |

Publication status | Published - 1 Dec 2010 |

Event | 27th International Symposium on Theoretical Aspects of Computer Science, STACS 2010 - Nancy Duration: 4 Mar 2010 → 6 Mar 2010 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 5 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 27th International Symposium on Theoretical Aspects of Computer Science, STACS 2010 |
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Country | France |

City | Nancy |

Period | 4/03/10 → 6/03/10 |

### Scopus subject areas

- Software

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## Cite this

*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