Space complexity in propositional calculus

Michael Alekhnovich, Eli Ben-Sasson, Alexander A. Razborov, Avi Wigderson

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

9 Scopus citations

Abstract

We study space complexity in the framework of propositional proofs. We consider a natural model analogous to space bounded Turing machines with a read-only input tape, and such popular propositional proof systems as Resolution, Polynomial Calculus and Frege systems. We study two different space measures. The first, introduced by [5] for Resolution and extended here to other systems, is the structured measure which counts the number of clauses/monomials kept is memory simultaneously. The other is an unstructured measure related to the number of bits describing the memory content. We develop lower bound techniques that enable proving tight linear lower bounds for the first measure, and tight quadratic lower bounds for the second, for large classes of tautologies (including familiar ones like the pigeonhole principle) in both Resolution and (extensions of) Polynomial Calculus. We also prove some structural results concerning the clause space for Resolution and Frege Systems.

Original languageEnglish
Title of host publicationProceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000
Pages358-367
Number of pages10
DOIs
StatePublished - 2000
Event32nd Annual ACM Symposium on Theory of Computing, STOC 2000 - Portland, OR, United States
Duration: 21 May 200023 May 2000

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference32nd Annual ACM Symposium on Theory of Computing, STOC 2000
Country/TerritoryUnited States
CityPortland, OR
Period21/05/0023/05/00

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