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.2020.63
URN: urn:nbn:de:0030-drops-124707
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12470/
Hakoniemi, Tuomas
Feasible Interpolation for Polynomial Calculus and Sums-Of-Squares
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}
}
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Keywords: |
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Proof Complexity, Feasible Interpolation, Sums-of-Squares, Polynomial Calculus |
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Collection: |
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47th International Colloquium on Automata, Languages, and Programming (ICALP 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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29.06.2020 |
