scispace - formally typeset
Open AccessJournal ArticleDOI

The intractability of resolution

Armin Haken
- 01 Jan 1985 - 
- Vol. 39, pp 297-308
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

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, +1 more
- 01 Jul 1960 - 
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.