License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2016.94
URN: urn:nbn:de:0030-drops-62290
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6229/
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Chen, Hubie

Proof Complexity Modulo the Polynomial Hierarchy: Understanding Alternation as a Source of Hardness

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Abstract

We present and study a framework in which one can present alternation-based lower bounds on proof length in proof systems for quantified Boolean formulas. A key notion in this framework is that of proof system ensemble, which is (essentially) a sequence of proof systems where, for each, proof checking can be performed in the polynomial hierarchy. We introduce a proof system ensemble called relaxing QU-res which is based on the established proof system QU-resolution.

Our main results include an exponential separation of the tree-like and general versions of relaxing QU-res, and an exponential lower bound for relaxing QU-res; these are analogs of classical results in propositional proof complexity.

BibTeX - Entry

@InProceedings{chen:LIPIcs:2016:6229,
  author =	{Hubie Chen},
  title =	{{Proof Complexity Modulo the Polynomial Hierarchy: Understanding Alternation as a Source of Hardness}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{94:1--94:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6229},
  URN =		{urn:nbn:de:0030-drops-62290},
  doi =		{10.4230/LIPIcs.ICALP.2016.94},
  annote =	{Keywords: proof complexity, polynomial hierarchy, quantified propositional logic}
}

Keywords: proof complexity, polynomial hierarchy, quantified propositional logic
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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