## On an optimal quantified propositional proof system and a complete language for NP . . . (1997)

Venue: | In Proceedings of the 11th International Symposium on Fundamentals of Computing Theory, LNCS #1279 |

Citations: | 6 - 1 self |

### BibTeX

@INPROCEEDINGS{Sadowski97onan,

author = {Zenon Sadowski},

title = {On an optimal quantified propositional proof system and a complete language for NP . . .},

booktitle = {In Proceedings of the 11th International Symposium on Fundamentals of Computing Theory, LNCS #1279},

year = {1997},

pages = {423--428},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

. In this paper we prove that if there exists an optimal quantified propositional proof system then there exists a complete language for NP " co-NP. 1 Introduction There is a lot of activity around the complexity of propositional proof systems (see [7, 12]). Research into propositional proof systems is motivated by the open problem NP=co-NP? Research into quantified propositional proof systems is not so popular. The study of quantified propositional proof systems may be related to the problem NP=PSPACE? Some deep results about connections between quantified propositional proof systems and bounded arithmetic are contained in [8]. We propose to study the problem of the existence of an optimal quantified propositional proof system. The similar problem for propositional proof systems has been studied in [9]. It is not known whether complete languages exist for NP " co-NP and Sipser has shown in [10] that there are relativizations so that NP " co-NP has no complete languages (see also [4...

### Citations

4099 |
Introduction to Automata Theory, Languages and Computation, 2nd ed
- Hopcroft, Motwani, et al.
- 2000
(Show Context)
Citation Context ...antified propositional formula if every truth assignment makes ff true. The set of all tautological quantified propositional formulas we denote throughout the paper by the symbol QTAUT . Fact 1. (cf. =-=[1, 5, 11]-=-) QTAUT is PSPACE-complete. Definition2. (cf. [3, 8]) A quantified propositional proof system is a function F : \Sigma ? onto \Gamma! QTAUT computable by a deterministic Turing machine in time bounded... |

507 |
The complexity of theorem proving procedures
- Cook
- 1971
(Show Context)
Citation Context ...ed propositional formula if and only if the machine M k is n-strong nondeterministic. Fix n natural. Our construction of the formula SN n M;k is adapted from Cook's proof that SAT is NP-complete (cf. =-=[2]). The for-=-mula SN n M;k is of the form ffs:fi, where ff is a quantified propositional formula and fi is a propositional formula. The formula ff evaluates to "true" if and only if for any input w of le... |

344 | The relative efficiency of propositional proof systems
- Cook, Reckhow
- 1979
(Show Context)
Citation Context ... makes ff true. The set of all tautological quantified propositional formulas we denote throughout the paper by the symbol QTAUT . Fact 1. (cf. [1, 5, 11]) QTAUT is PSPACE-complete. Definition2. (cf. =-=[3, 8]-=-) A quantified propositional proof system is a function F : \Sigma ? onto \Gamma! QTAUT computable by a deterministic Turing machine in time bounded by a polynomial in the length of the input. A strin... |

227 |
Bounded Arithmetic, Propositional Logic, and Complexity Theory, Encyclopedia of Mathematics and its Applications 60, Cambridge Univ
- Kraj́ıček
- 1995
(Show Context)
Citation Context ...optimal quantified propositional proof system then there exists a complete language for NP " co-NP. 1 Introduction There is a lot of activity around the complexity of propositional proof systems =-=(see [7, 12]-=-). Research into propositional proof systems is motivated by the open problem NP=co-NP? Research into quantified propositional proof systems is not so popular. The study of quantified propositional pr... |

181 |
Structural Complexity I
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Citation Context ...antified propositional formula if every truth assignment makes ff true. The set of all tautological quantified propositional formulas we denote throughout the paper by the symbol QTAUT . Fact 1. (cf. =-=[1, 5, 11]-=-) QTAUT is PSPACE-complete. Definition2. (cf. [3, 8]) A quantified propositional proof system is a function F : \Sigma ? onto \Gamma! QTAUT computable by a deterministic Turing machine in time bounded... |

107 | The complexity of propositional proofs
- Urquhart
- 1995
(Show Context)
Citation Context ...optimal quantified propositional proof system then there exists a complete language for NP " co-NP. 1 Introduction There is a lot of activity around the complexity of propositional proof systems =-=(see [7, 12]-=-). Research into propositional proof systems is motivated by the open problem NP=co-NP? Research into quantified propositional proof systems is not so popular. The study of quantified propositional pr... |

94 |
Propositional proof systems, the consistency of first order theories and the complexity of computations
- Kraj́ıček, Pudlák
- 1989
(Show Context)
Citation Context ...tic are contained in [8]. We propose to study the problem of the existence of an optimal quantified propositional proof system. The similar problem for propositional proof systems has been studied in =-=[9]. It is no-=-t known whether complete languages exist for NP " co-NP and Sipser has shown in [10] that there are relativizations so that NP " co-NP has no complete languages (see also [4, 6]). The proble... |

29 |
On relativization and the existence of complete sets
- Sipser
- 1982
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Citation Context ...tified propositional proof system. The similar problem for propositional proof systems has been studied in [9]. It is not known whether complete languages exist for NP " co-NP and Sipser has show=-=n in [10] that ther-=-e are relativizations so that NP " co-NP has no complete languages (see also [4, 6]). The problem whether NP " co-NP has complete languages seems, at first glance, distant from the subject o... |

27 |
Quanti¯ed propositional calculi and fragments of bounded arithmetic. Zeitschrift fÄur Mathematische Logik und Grundlagen der Mathematik
- Kraj¶·cek, Pudl¶ak
- 1990
(Show Context)
Citation Context ...ntified propositional proof systems may be related to the problemsNP=PSPACE? Some deep results about connections between quantified propositional proof systems and bounded arithmetic are contained in =-=[8]-=-. We propose to study the problem of the existence of an optimal quantified propositional proof system. The similar problem for propositional proof systems has been studied in [9]. It is not known whe... |

10 |
The polynomial-time hierarchy, Theor
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Citation Context ...antified propositional formula if every truth assignment makes ff true. The set of all tautological quantified propositional formulas we denote throughout the paper by the symbol QTAUT . Fact 1. (cf. =-=[1, 5, 11]-=-) QTAUT is PSPACE-complete. Definition2. (cf. [3, 8]) A quantified propositional proof system is a function F : \Sigma ? onto \Gamma! QTAUT computable by a deterministic Turing machine in time bounded... |

5 |
Some connections between presentability of complexity classes and the power of formal systems of reasoning
- Kowalczyk
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Citation Context ...been studied in [9]. It is not known whether complete languages exist for NP " co-NP and Sipser has shown in [10] that there are relativizations so that NP " co-NP has no complete languages =-=(see also [4, 6]). Th-=-e problem whether NP " co-NP has complete languages seems, at first glance, distant from the subject of the optimal quantified propositional proof system. In our paper we bring together these two... |

4 |
On complete problems for NP " co-NP
- Hartmanis, Immerman
- 1985
(Show Context)
Citation Context ...been studied in [9]. It is not known whether complete languages exist for NP " co-NP and Sipser has shown in [10] that there are relativizations so that NP " co-NP has no complete languages =-=(see also [4, 6]). Th-=-e problem whether NP " co-NP has complete languages seems, at first glance, distant from the subject of the optimal quantified propositional proof system. In our paper we bring together these two... |