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.STACS.2016.35
URN: urn:nbn:de:0030-drops-57367
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5736/
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Filmus, Yuval ; Hrubeš, Pavel ; Lauria, Massimo

Semantic Versus Syntactic Cutting Planes

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Abstract

In this paper, we compare the strength of the semantic and syntactic version of the cutting planes proof system.

First, we show that the lower bound technique of Pudlák applies also to semantic cutting planes: the proof system has feasible interpolation via monotone real circuits, which gives an exponential lower bound on lengths of semantic cutting planes refutations.

Second, we show that semantic refutations are stronger than syntactic ones. In particular, we give a formula for which any refutation in syntactic cutting planes requires exponential length, while there is a polynomial length refutation in semantic cutting planes. In other words, syntactic cutting planes does not p-simulate semantic cutting planes. We also give two incompatible integer inequalities which require exponential length refutation in syntactic cutting planes.

Finally, we pose the following problem, which arises in connection with semantic inference of arity larger than two: can every multivariate non-decreasing real function be expressed as a composition of non-decreasing real functions in two variables?

BibTeX - Entry

@InProceedings{filmus_et_al:LIPIcs:2016:5736,
  author =	{Yuval Filmus and Pavel Hrube{\v{s}} and Massimo Lauria},
  title =	{{Semantic Versus Syntactic Cutting Planes}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{35:1--35:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Nicolas Ollinger and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5736},
  URN =		{urn:nbn:de:0030-drops-57367},
  doi =		{10.4230/LIPIcs.STACS.2016.35},
  annote =	{Keywords: proof complexity, cutting planes, lower bounds}
}

Keywords: proof complexity, cutting planes, lower bounds
Collection: 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Issue Date: 2016
Date of publication: 16.02.2016

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