Abstract
In 2003, Atserias and Dalmau resolved a major open question about the resolution proof system by establishing that the space complexity of formulas is always an upper bound on the width needed to refute them. Their proof is beautiful but somewhat mysterious in that it relies heavily on tools from finite model theory. We give an alternative, completely elementary, 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.
Original language | English |
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Title of host publication | 31st International Symposium on Theoretical Aspects of Computer Science, STACS 2014 |
Editors | Ernst W. Mayr, Natacha Portier |
Pages | 300-311 |
Number of pages | 12 |
Volume | 25 |
ISBN (Electronic) | 9783939897651 |
DOIs | |
State | Published - 1 Mar 2014 |
Externally published | Yes |
Event | 31st International Symposium on Theoretical Aspects of Computer Science, STACS 2014 - Lyon, France Duration: 5 Mar 2014 → 8 Mar 2014 |
Conference
Conference | 31st International Symposium on Theoretical Aspects of Computer Science, STACS 2014 |
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Country/Territory | France |
City | Lyon |
Period | 5/03/14 → 8/03/14 |
Keywords
- PCR
- Polynomial calculus
- Proof complexity
- Resolution
- Space
- Width
ASJC Scopus subject areas
- Software