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Many hard examples for resolution

Published:1988-10 Issue:4 Volume:35 Page:759-768
ISSN:0004-5411
Container-title:Journal of the ACM
language:en
Short-container-title:J. ACM

Author:

Chvátal Vašek¹,Szemerédi Endre²

Affiliation:

1. Rutgers Univ., New Brunswick, NJ

2. Rutgers Univ., New Brunswick, NJ and Hungarian Academy of Sciences, Budapest, Hungary

Abstract

For every choice of positive integers c and k such that k ≥ 3 and c 2 - k ≥ 0.7, there is a positive number ε such that, with probability tending to 1 as n tends to ∞, a randomly chosen family of cn clauses of size k over n variables is unsatisfiable, but every resolution proof of its unsatisfiability must generate at least (1 + ε) n clauses.

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Link

https://dl.acm.org/doi/pdf/10.1145/48014.48016

Reference17 articles.

1. Automated Theorem Proving

2. Probabilistic methods in graph theory;CHV TAL;Ann. Oper. Res.,1984

3. A Computing Procedure for Quantification Theory

4. On the complexity of regular resolution and the Davis-Putnam procedure;GALIL Z;Theoret. Comput. Sci.,1977

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