From Small Space to Small Width in Resolution

Yuval Filmus; Massimo Lauria; Mladen Mikša; Jakob Nordström; Marc Vinyals

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arXiv · 1409.2978

From Small Space to Small Width in Resolution

Yuval Filmus·Massimo Lauria·Mladen Mikša·Jakob Nordström·Marc Vinyals

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Abstract

In 2003, Atserias and Dalmau resolved a major open question about the resolution proof system by establishing that the space complexity of CNF 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.

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BibTeX RIS

Yuval Filmus, Massimo Lauria, Mladen Mikša, Jakob Nordström, Marc Vinyals. 2014-09-10. From Small Space to Small Width in Resolution. https://arxiv.org/abs/1409.2978

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