From Small Space to Small Width in Resolution

Authors Yuval Filmus, Massimo Lauria, Mladen Miksa, Jakob Nordström, Marc Vinyals

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Yuval Filmus
Massimo Lauria
Mladen Miksa
Jakob Nordström
Marc Vinyals

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Yuval Filmus, Massimo Lauria, Mladen Miksa, Jakob Nordström, and Marc Vinyals. From Small Space to Small Width in Resolution. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 300-311, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


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.
  • proof complexity
  • resolution
  • width
  • space
  • polynomial calculus
  • PCR


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