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Supercritical Space-Width Trade-Offs for Resolution

Authors Christoph Berkholz, Jakob Nordström

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Keywords
  • Proof complexity
  • resolution
  • space
  • width
  • trade-offs
  • supercritical

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Abstract

We show that there are CNF formulas which can be refuted in resolution in both small space and small width, but for which any small-width resolution proof must have space exceeding by far the linear worst-case upper bound. This significantly strengthens the space-width trade-offs in [Ben-Sasson 2009], and provides one more example of trade-offs in the "supercritical" regime above worst case recently identified by [Razborov 2016]. We obtain our results by using Razborov’s new hardness condensation technique and combining it with the space lower bounds in [Ben-Sasson and Nordström 2008].

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Christoph Berkholz and Jakob Nordström. Supercritical Space-Width Trade-Offs for Resolution. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 57:1-57:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.ICALP.2016.57

Author Details

Christoph Berkholz
Jakob Nordström

References

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