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50
Resolution is Not Automatizable Unless W[P] is Tractable
 In 42nd Annual IEEE Symposium on Foundations of Computer Science
, 2001
"... We show that neither Resolution nor treelike Resolution is automatizable unless the class W[P] from the hierarchy of parameterized problems is xedparameter tractable by randomized algorithms with onesided error. ..."
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Cited by 50 (0 self)
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We show that neither Resolution nor treelike Resolution is automatizable unless the class W[P] from the hierarchy of parameterized problems is xedparameter tractable by randomized algorithms with onesided error.
Pseudorandom Generators Hard for kDNF Resolution and Polynomial Calculus Resolution
, 2003
"... A pseudorandom generator G n : f0; 1g is hard for a propositional proof system P if (roughly speaking) P can not ef ciently prove the statement G n (x 1 ; : : : ; x n ) 6= b for any string b 2 . We present a function (m 2 ) generator which is hard for Res( log n); here Res(k) is the ..."
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Cited by 42 (4 self)
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A pseudorandom generator G n : f0; 1g is hard for a propositional proof system P if (roughly speaking) P can not ef ciently prove the statement G n (x 1 ; : : : ; x n ) 6= b for any string b 2 . We present a function (m 2 ) generator which is hard for Res( log n); here Res(k) is the propositional proof system that extends Resolution by allowing kDNFs instead of clauses.
On the Automatizability of Resolution and Related Propositional Proof Systems
, 2002
"... We analyse the possibility that a system that simulates Resolution is automatizable. We call this notion "weak automatizability". We prove ..."
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Cited by 34 (6 self)
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We analyse the possibility that a system that simulates Resolution is automatizable. We call this notion "weak automatizability". We prove
On reducibility and symmetry of disjoint NPpairs
, 2001
"... . We consider some problems about pairs of disjoint NP sets. ..."
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Cited by 29 (0 self)
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. We consider some problems about pairs of disjoint NP sets.
Optimality of sizewidth tradeoffs for resolution
 Computational Complexity
, 2001
"... Abstract. This paper is concerned with the complexity of proofs and of searching for proofs in resolution. We show that the recently proposed algorithm of BenSasson & Wigderson for searching for proofs in resolution cannot give better than weakly exponential performance. This is a consequence o ..."
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Cited by 27 (10 self)
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Abstract. This paper is concerned with the complexity of proofs and of searching for proofs in resolution. We show that the recently proposed algorithm of BenSasson & Wigderson for searching for proofs in resolution cannot give better than weakly exponential performance. This is a consequence of our main result: we show the optimality of the general relationship called sizewidth tradeoff in BenSasson & Wigderson. Moreover we obtain the optimality of the sizewidth tradeoff for the widely used restrictions of resolution: regular, DavisPutnam, negative, positive.
On the Complexity of Resolution with Bounded Conjunctions
 IN 29TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING
, 2004
"... We analyze size and space complexity of Res(k), a family of propositional proof systems introduced by Kraj'icek in [21] which extends Resolution by allowing disjunctions of conjunctions of up to k 1 literals. We show that the treelike Res(k) proof systems form a strict hierarchy with respe ..."
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Cited by 27 (4 self)
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We analyze size and space complexity of Res(k), a family of propositional proof systems introduced by Kraj'icek in [21] which extends Resolution by allowing disjunctions of conjunctions of up to k 1 literals. We show that the treelike Res(k) proof systems form a strict hierarchy with respect to proof size and also with respect to space. Moreover
Satisfiability, Branchwidth and Tseitin Tautologies
, 2002
"... For a CNF , let w b () be the branchwidth of its underlying hypergraph. ..."
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Cited by 21 (2 self)
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For a CNF , let w b () be the branchwidth of its underlying hypergraph.
Constraint Propagation as a Proof System
 10th Int.Conf. on Principles and Practice of Constraint Programing, LN in Computer Science vol.3258
, 2004
"... Refutation proofs can be viewed as a special case of constraint propagation, which is a fundamental technique in solving constraintsatisfaction problems. ..."
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Cited by 19 (1 self)
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Refutation proofs can be viewed as a special case of constraint propagation, which is a fundamental technique in solving constraintsatisfaction problems.
The Proof Complexity of Linear Algebra
 IN SEVENTEENTH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE (LICS
, 2002
"... We introduce three formal theories of increasing strength for linear algebra in order to study the complexity of the concepts needed to prove the basic theorems of the subject. We give what is apparently the rst feasible proofs of the CayleyHamilton theorem and other properties of the determina ..."
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Cited by 17 (6 self)
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We introduce three formal theories of increasing strength for linear algebra in order to study the complexity of the concepts needed to prove the basic theorems of the subject. We give what is apparently the rst feasible proofs of the CayleyHamilton theorem and other properties of the determinant, and study the propositional proof complexity of matrix identities such as AB = I ! BA = I .
Polynomialsize Frege and Resolution Proofs of stConnectivity and Hex Tautologies
 Theorectical Computer Science
, 2003
"... A grid graph has rectangularly arranged vertices with edges permitted only between orthogonally adjacent vertices. The stconnectivity principle states that it is not possible to have a red path of edges and a green path of edges which connect diagonally opposite corners of the grid graph unless ..."
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Cited by 11 (0 self)
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A grid graph has rectangularly arranged vertices with edges permitted only between orthogonally adjacent vertices. The stconnectivity principle states that it is not possible to have a red path of edges and a green path of edges which connect diagonally opposite corners of the grid graph unless the paths cross somewhere.