Results 1 
5 of
5
The complexity of propositional proofs
 Bulletin of Symbolic Logic
"... Abstract. Propositional proof complexity is the study of the sizes of propositional proofs, and more generally, the resources necessary to certify propositional tautologies. Questions about proof sizes have connections with computational complexity, theories of arithmetic, and satisfiability algorit ..."
Abstract

Cited by 21 (0 self)
 Add to MetaCart
Abstract. Propositional proof complexity is the study of the sizes of propositional proofs, and more generally, the resources necessary to certify propositional tautologies. Questions about proof sizes have connections with computational complexity, theories of arithmetic, and satisfiability algorithms. This is article includes a broad survey of the field, and a technical exposition of some recently developed techniques for proving lower bounds on proof sizes. Contents
Proof complexity of pigeonhole principles
 IN PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON DEVELOPMENTS IN LANGUAGE THEORY
, 2002
"... The pigeonhole principle asserts that there is no injective mapping from m pigeons to n holes as long as m> n. It is amazingly simple, expresses one of the most basic primitives in mathematics and Theoretical Computer Science (counting) and, for these reasons, is probably the most extensively studie ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
The pigeonhole principle asserts that there is no injective mapping from m pigeons to n holes as long as m> n. It is amazingly simple, expresses one of the most basic primitives in mathematics and Theoretical Computer Science (counting) and, for these reasons, is probably the most extensively studied combinatorial principle. In this survey we try to summarize what is known about its proof complexity, and what we would still like to prove. We also mention some applications of the pigeonhole principle to the study of efficient provability of major open problems in computational complexity, as well as some of its generalizations in the form of general matching principles.
Boundeddepth Frege lower bounds for weaker pigeonhole principles
 SIAM JOURNAL ON COMPUTING
, 2005
"... We prove a quasipolynomial lower bound on the size of boundeddepth Frege proofs of the pigeonhole principle PHP m n where m = (1 + 1/polylog n) n. This lower bound qualitatively matches the known quasipolynomialsize boundeddepth Frege proofs for these principles. Our technique, which uses a swit ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
We prove a quasipolynomial lower bound on the size of boundeddepth Frege proofs of the pigeonhole principle PHP m n where m = (1 + 1/polylog n) n. This lower bound qualitatively matches the known quasipolynomialsize boundeddepth Frege proofs for these principles. Our technique, which uses a switching lemma argument like other lower bounds for boundeddepth Frege proofs, is novel in that the tautology to which this switching lemma is applied remains random throughout the argument.
The Complexity of ResourceBounded Propositional Proofs
, 2001
"... Propositional Proof Complexity is an active area of research whose main focus is the study of the length of proofs in propositional logic. There are several motivations for such a study, the main of which is probably its connection to the P vs NP problem in Computational Complexity. The experience ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Propositional Proof Complexity is an active area of research whose main focus is the study of the length of proofs in propositional logic. There are several motivations for such a study, the main of which is probably its connection to the P vs NP problem in Computational Complexity. The experience
Barcelona Aarhus Barcelona
, 2002
"... This is the second annual progress report for the ALCOMFT project, supported by the European ..."
Abstract
 Add to MetaCart
This is the second annual progress report for the ALCOMFT project, supported by the European