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.2019.84
URN: urn:nbn:de:0030-drops-106605
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10660/
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Mertz, Ian ; Pitassi, Toniann ; Wei, Yuanhao

Short Proofs Are Hard to Find

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LIPIcs-ICALP-2019-84.pdf (0.5 MB)

Abstract

We obtain a streamlined proof of an important result by Alekhnovich and Razborov [Michael Alekhnovich and Alexander A. Razborov, 2008], showing that it is hard to automatize both tree-like and general Resolution. Under a different assumption than [Michael Alekhnovich and Alexander A. Razborov, 2008], our simplified proof gives improved bounds: we show under ETH that these proof systems are not automatizable in time n^f(n), whenever f(n) = o(log^{1/7 - epsilon} log n) for any epsilon > 0. Previously non-automatizability was only known for f(n) = O(1). Our proof also extends fairly straightforwardly to prove similar hardness results for PCR and Res(r).

BibTeX - Entry

@InProceedings{mertz_et_al:LIPIcs:2019:10660,
  author =	{Ian Mertz and Toniann Pitassi and Yuanhao Wei},
  title =	{{Short Proofs Are Hard to Find}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{84:1--84:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10660},
  URN =		{urn:nbn:de:0030-drops-106605},
  doi =		{10.4230/LIPIcs.ICALP.2019.84},
  annote =	{Keywords: automatizability, Resolution, SAT solvers, proof complexity}
}

Keywords: automatizability, Resolution, SAT solvers, proof complexity
Collection: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Issue Date: 2019
Date of publication: 04.07.2019

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