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The relative efficiency of propositional proof systems

by Stephen A. Cook, Robert A. Reckhow - JOURNAL OF SYMBOLIC LOGIC , 1979
"... ..."
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On the Complexity of Propositional Proof Systems

by Nicola Galesi , 2000
"... In the thesis we have investigated the complexity of proofs in several propositional proof systems. Our main motivation has been to contribute to the line of research started by Cook and Reckhow to obtain how much knowledge as possible about the complexity of different proof systems to show that the ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
In the thesis we have investigated the complexity of proofs in several propositional proof systems. Our main motivation has been to contribute to the line of research started by Cook and Reckhow to obtain how much knowledge as possible about the complexity of different proof systems to show

A Propositional Proof System for ...

by Chris Pollett
"... In this paper we introduce Gentzen-style quantified propositional proof systems L i for the theories R i 2 . We formalize the systems L i within the bounded arithmetic theory R 1 2 and we show that for i 1, R i 2 can prove the validity of a sequent derived by an L i -proof. This stateme ..."
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In this paper we introduce Gentzen-style quantified propositional proof systems L i for the theories R i 2 . We formalize the systems L i within the bounded arithmetic theory R 1 2 and we show that for i 1, R i 2 can prove the validity of a sequent derived by an L i -proof

ON THE CORRESPONDENCE BETWEEN ARITHMETIC THEORIES AND PROPOSITIONAL PROOF SYSTEMS

by OLAF BEYERSDORFF
"... Bounded arithmetic is closely related to propositional proof systems, and this relation has found many fruitful applications. The aim of this paper is to explain and develop the general correspondence between propositional proof systems and arithmetic theories, as introduced by Krajíček and Pudlák ..."
Abstract - Cited by 4 (2 self) - Add to MetaCart
Bounded arithmetic is closely related to propositional proof systems, and this relation has found many fruitful applications. The aim of this paper is to explain and develop the general correspondence between propositional proof systems and arithmetic theories, as introduced by Krajíček and Pudlák

On the Automatizability of Resolutionand Related Propositional Proof Systems \Lambda

by Albert Atserias, Bonetdepartament Llenguatges , 2003
"... Abstract A propositional proof system is automatizable if there is an algorithm that, given a for-mula, it produces a proof in time polynomial in the size of its smallest proof. This notion can ..."
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Abstract A propositional proof system is automatizable if there is an algorithm that, given a for-mula, it produces a proof in time polynomial in the size of its smallest proof. This notion can

Finite Fields and Propositional Proof Systems

by Michael Soltys
"... Propositional proof complexity is a well established area of theoretical computer science; it is an area of research intimately connected with complexity theory and automated reasoning. In this paper we introduce a proof system, which we call A (a fragment of the theory LA), for formalizing algebrai ..."
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Propositional proof complexity is a well established area of theoretical computer science; it is an area of research intimately connected with complexity theory and automated reasoning. In this paper we introduce a proof system, which we call A (a fragment of the theory LA), for formalizing

Logical Closure Properties of Propositional Proof Systems

by Olaf Beyersdorff
"... Abstract. In this paper we define and investigate basic logical closure properties of propositional proof systems such as closure of arbitrary proof systems under modus ponens or substitutions. As our main result we obtain a purely logical characterization of the degrees of schematic extensions of E ..."
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Abstract. In this paper we define and investigate basic logical closure properties of propositional proof systems such as closure of arbitrary proof systems under modus ponens or substitutions. As our main result we obtain a purely logical characterization of the degrees of schematic extensions

Combinatorics of first order structures and propositional proof systems

by Jan Krajícek
"... We define the notion of a combinatorics of a first order structure, and a relation of covering between first order structures and propositional proof systems. Namely, a first order structure M combinatorially satisfies an L-sentence \Phi iff \Phi holds in all L-structures definable in M. The combina ..."
Abstract - Cited by 6 (0 self) - Add to MetaCart
We define the notion of a combinatorics of a first order structure, and a relation of covering between first order structures and propositional proof systems. Namely, a first order structure M combinatorially satisfies an L-sentence \Phi iff \Phi holds in all L-structures definable in M

Canonical Disjoint NP-Pairs of Propositional Proof Systems

by Christian Glaßer, Alan L. Selman, Liyu Zhang - ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 106 , 2004
"... We prove that every disjoint NP-pair is polynomial-time, many-one equivalent to the canonical disjoint NP-pair of some propositional proof system. Therefore, the degree structure of the class of disjoint NP-pairs and of all canonical pairs is identical. Secondly, we show that this degree structure i ..."
Abstract - Cited by 11 (3 self) - Add to MetaCart
We prove that every disjoint NP-pair is polynomial-time, many-one equivalent to the canonical disjoint NP-pair of some propositional proof system. Therefore, the degree structure of the class of disjoint NP-pairs and of all canonical pairs is identical. Secondly, we show that this degree structure

A propositional proof system with quantification over permutations

by Grzegorz Herman, Tim Paterson, Michael Soltys , 2007
"... We introduce a new propositional proof system, which we call H, that allows quantification over permutations. In H we may write (∃ab)α and (∀ab)α, which is semantically equivalent to α(a, b) ∨ α(b, a) and α(a, b) ∧ α(b, a), respectively. We show that H with cuts restricted to Σ1 formulas (we deno ..."
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We introduce a new propositional proof system, which we call H, that allows quantification over permutations. In H we may write (∃ab)α and (∀ab)α, which is semantically equivalent to α(a, b) ∨ α(b, a) and α(a, b) ∧ α(b, a), respectively. We show that H with cuts restricted to Σ1 formulas (we
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