文章基本信息

标题：From Small Space to Small Width in Resolution
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作者：Yuval Filmus ; Massimo Lauria ; Mladen Miksa 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2014
卷号：25
页码：300-311
DOI：10.4230/LIPIcs.STACS.2014.300
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：proof complexity; resolution; width; space; polynomial calculus; PCR