The intractability of resolution
Reads0
Chats0
TLDR
It is proved that, for infinitely many disjunctive normal form propositional calculus tautologies ξ, the length of the shortest resolution proof of ξ cannot be bounded by any polynomial of the lengthof ξ.About:
This article is published in Theoretical Computer Science.The article was published on 1985-01-01 and is currently open access. It has received 870 citations till now. The article focuses on the topics: Propositional proof system & Proof complexity.read more
Citations
More filters
Proceedings Article
Hard and easy distributions of SAT problems
TL;DR: It is shown that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which satisfiability testing is quite difficult.
Book
Knowledge Representation and Reasoning
TL;DR: This landmark text takes the central concepts of knowledge representation developed over the last 50 years and illustrates them in a lucid and compelling way, and offers the first true synthesis of the field in over a decade.
Book
Handbook of Knowledge Representation
TL;DR: The Handbook of Knowledge Representation is an up-to-date review of twenty-five key topics in knowledge representation written by the leaders of each field, an essential resource for students, researchers and practitioners in all areas of Artificial Intelligence.
Book
Handbook of Satisfiability
TL;DR: A collection of papers on all theoretical and practical aspects of SAT solving will be extremely useful to both students and researchers and will lead to many further advances in the field.
Journal ArticleDOI
Short proofs are narrow—resolution made simple
Eli Ben-Sasson,Avi Wigderson +1 more
TL;DR: This paper relates proof width to proof length (=size), in both general Resolution, and its tree-like variant, and presents a family of tautologies on which it is exponentially faster.
References
More filters
Journal ArticleDOI
A Machine-Oriented Logic Based on the Resolution Principle
TL;DR: The paper concludes with a discussion of several principles which are applicable to the design of efficient proof-procedures employing resolution as the basle logical process.
Journal ArticleDOI
A Computing Procedure for Quantification Theory
Martin Davis,Hilary Putnam +1 more
TL;DR: In the present paper, a uniform proof procedure for quantification theory is given which is feasible for use with some rather complicated formulas and which does not ordinarily lead to exponentiation.
Journal ArticleDOI
The relative efficiency of propositional proof systems
TL;DR: All standard Hilbert type systems and natural deduction systems are equivalent, up to application of a polynomial, as far as minimum proof length goes, and extended Frege systems are introduced, which allow introduction of abbreviations for formulas.
Proceedings ArticleDOI
On the lengths of proofs in the propositional calculus (Preliminary Version)
TL;DR: This paper studies the complexity of decision procedures for the propositional calculus, and the fundamental issue here is whether there exists any proof system, and a polynomial p( n) such that every valid formula has a proof of length not exceeding p(n), where n is the length of the formula.