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Revisiting Space in Proof Complexity: Treewidth and Pathwidth

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Mathematical Foundations of Computer Science 2013 (MFCS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8087))

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Abstract

So-called ordered variants of the classical notions of pathwidth and treewidth are introduced and proposed as proof theoretically meaningful complexity measures for the directed acyclic graphs underlying proofs. The ordered pathwidth of a proof is shown to be roughly the same as its formula space. Length-space lower bounds for R(k)-refutations are generalized to arbitrary infinity axioms and strengthened in that the space measure is relaxed to ordered treewidth.

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Author information

Authors and Affiliations

  1. Kurt Gödel Research Center, University of Vienna, Vienna, Austria

    Moritz Müller

  2. Institute of Information Systems, Vienna University of Technology, Vienna, Austria

    Stefan Szeider

Authors
  1. Moritz Müller
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  2. Stefan Szeider
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Editor information

Editors and Affiliations

  1. Institute for Science and Technology, 3400, Klosterneuburg, Austria

    Krishnendu Chatterjee

  2. Charles University, 11800, Prague, Czech Republic

    Jirí Sgall

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Müller, M., Szeider, S. (2013). Revisiting Space in Proof Complexity: Treewidth and Pathwidth. In: Chatterjee, K., Sgall, J. (eds) Mathematical Foundations of Computer Science 2013. MFCS 2013. Lecture Notes in Computer Science, vol 8087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40313-2_62

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  • DOI: https://doi.org/10.1007/978-3-642-40313-2_62

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40312-5

  • Online ISBN: 978-3-642-40313-2

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