research-article

From Small Space to Small Width in Resolution

Authors:

Massimo Lauria,

Jakob Nordström,

Marc VinyalsAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 16, Issue 4

Article No.: 28, Pages 1 - 15

https://doi.org/10.1145/2746339

Published: 14 July 2015 Publication History

Abstract

In 2003, Atserias and Dalmau resolved a major open question about the resolution proof system by establishing that the space complexity of a Conjunctive Normal Form (CNF) formula is always an upper bound on the width needed to refute the formula. Their proof is beautiful but uses a nonconstructive argument based on Ehrenfeucht-Fraïssé games. We give an alternative, more explicit, proof that works by simple syntactic manipulations of resolution refutations. As a by-product, we develop a “black-box” technique for proving space lower bounds via a “static” complexity measure that works against any resolution refutation—previous techniques have been inherently adaptive. We conclude by showing that the related question for polynomial calculus (i.e., whether space is an upper bound on degree) seems unlikely to be resolvable by similar methods.

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Cited By

Papamakarios TRazborov A(2023)Space characterizations of complexity measures and size-space trade-offs in propositional proof systemsJournal of Computer and System Sciences10.1016/j.jcss.2023.04.006137(20-36)Online publication date: Dec-2023
https://doi.org/10.1016/j.jcss.2023.04.006
Galesi NKolodziejczyk LThapen N(2019)Polynomial Calculus Space and Resolution Width2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS.2019.00081(1325-1337)Online publication date: Dec-2019
https://doi.org/10.1109/FOCS.2019.00081
Krajíček J(2019)IndexProof Complexity10.1017/9781108242066.026(510-516)Online publication date: 25-Mar-2019
https://doi.org/10.1017/9781108242066.026
Show More Cited By

Index Terms

From Small Space to Small Width in Resolution
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
2. Theory of computation
  1. Design and analysis of algorithms

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Published In

cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 16, Issue 4

November 2015

273 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/2802139

Editor:
Orna Kupferman
School of Computer Science and Engineering, Hebrew University, Israel

Issue’s Table of Contents

Copyright © 2015 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 14 July 2015

Accepted: 01 March 2015

Revised: 01 March 2015

Received: 01 June 2014

Published in TOCL Volume 16, Issue 4

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the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC
Helge Ax:son Johnsons stiftelse
the European Union's Seventh Framework Programme (FP7/2007-2013)
the foundations Johan och Jakob Söderbergs stiftelse
National Science Foundation
Stiftelsen Längmanska kulturfonden
Swedish Research Council

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Cited By

Papamakarios TRazborov A(2023)Space characterizations of complexity measures and size-space trade-offs in propositional proof systemsJournal of Computer and System Sciences10.1016/j.jcss.2023.04.006137(20-36)Online publication date: Dec-2023
https://doi.org/10.1016/j.jcss.2023.04.006
Galesi NKolodziejczyk LThapen N(2019)Polynomial Calculus Space and Resolution Width2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS.2019.00081(1325-1337)Online publication date: Dec-2019
https://doi.org/10.1109/FOCS.2019.00081
Krajíček J(2019)IndexProof Complexity10.1017/9781108242066.026(510-516)Online publication date: 25-Mar-2019
https://doi.org/10.1017/9781108242066.026
Krajíček J(2019)BibliographyProof Complexity10.1017/9781108242066.025(481-505)Online publication date: 25-Mar-2019
https://doi.org/10.1017/9781108242066.025
Krajíček J(2019)The Nature of Proof ComplexityProof Complexity10.1017/9781108242066.024(472-480)Online publication date: 25-Mar-2019
https://doi.org/10.1017/9781108242066.024
Krajíček J(2019)OptimalityProof Complexity10.1017/9781108242066.023(456-471)Online publication date: 25-Mar-2019
https://doi.org/10.1017/9781108242066.023
Krajíček J(2019)Model Theory and Lower BoundsProof Complexity10.1017/9781108242066.022(442-455)Online publication date: 25-Mar-2019
https://doi.org/10.1017/9781108242066.022
Krajíček J(2019)Hard TautologiesProof Complexity10.1017/9781108242066.021(413-441)Online publication date: 25-Mar-2019
https://doi.org/10.1017/9781108242066.021
Krajíček J(2019)Feasible Interpolation: ApplicationsProof Complexity10.1017/9781108242066.020(384-410)Online publication date: 25-Mar-2019
https://doi.org/10.1017/9781108242066.020
Krajíček J(2019)Feasible Interpolation: A FrameworkProof Complexity10.1017/9781108242066.019(353-383)Online publication date: 25-Mar-2019
https://doi.org/10.1017/9781108242066.019
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