Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Hakoniemi, Tuomas https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-124707
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Feasible Interpolation for Polynomial Calculus and Sums-Of-Squares

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Abstract

We prove that both Polynomial Calculus and Sums-of-Squares proof systems admit a strong form of feasible interpolation property for sets of polynomial equality constraints. Precisely, given two sets P(x,z) and Q(y,z) of equality constraints, a refutation Π of P(x,z) ∪ Q(y,z), and any assignment a to the variables z, one can find a refutation of P(x,a) or a refutation of Q(y,a) in time polynomial in the length of the bit-string encoding the refutation Π. For Sums-of-Squares we rely on the use of Boolean axioms, but for Polynomial Calculus we do not assume their presence.

BibTeX - Entry

@InProceedings{hakoniemi:LIPIcs:2020:12470,
  author =	{Tuomas Hakoniemi},
  title =	{{Feasible Interpolation for Polynomial Calculus and Sums-Of-Squares}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{63:1--63:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12470},
  URN =		{urn:nbn:de:0030-drops-124707},
  doi =		{10.4230/LIPIcs.ICALP.2020.63},
  annote =	{Keywords: Proof Complexity, Feasible Interpolation, Sums-of-Squares, Polynomial Calculus}
}

Keywords: Proof Complexity, Feasible Interpolation, Sums-of-Squares, Polynomial Calculus
Seminar: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue date: 2020
Date of publication: 29.06.2020


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