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On the Complexity of Propositional Proof Systems
, 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 ..."
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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 ...
"... In this paper we introduce Gentzenstyle 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 Gentzenstyle 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
"... 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 ..."
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Cited by 4 (2 self)
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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
, 2003
"... Abstract A propositional proof system is automatizable if there is an algorithm that, given a formula, 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 formula, it produces a proof in time polynomial in the size of its smallest proof. This notion can
Finite Fields and Propositional Proof Systems
"... 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
"... 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
"... 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 Lsentence \Phi iff \Phi holds in all Lstructures definable in M. The combina ..."
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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 Lsentence \Phi iff \Phi holds in all Lstructures definable in M
Canonical Disjoint NPPairs of Propositional Proof Systems
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 106
, 2004
"... We prove that every disjoint NPpair is polynomialtime, manyone equivalent to the canonical disjoint NPpair of some propositional proof system. Therefore, the degree structure of the class of disjoint NPpairs and of all canonical pairs is identical. Secondly, we show that this degree structure i ..."
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Cited by 11 (3 self)
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We prove that every disjoint NPpair is polynomialtime, manyone equivalent to the canonical disjoint NPpair of some propositional proof system. Therefore, the degree structure of the class of disjoint NPpairs and of all canonical pairs is identical. Secondly, we show that this degree structure
A propositional proof system with quantification over permutations
, 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
Results 1  10
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1,368,836