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DOI: 10.4230/LIPIcs.CSL.2012.122
URN: urn:nbn:de:0030-drops-36689
URL: http://drops.dagstuhl.de/opus/volltexte/2012/3668/
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Bodirsky, Manuel ; Wrona, Michal

Equivalence Constraint Satisfaction Problems

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Abstract

The following result for finite structures Gamma has been conjectured to hold for all countably infinite omega-categorical structures Gamma: either the model-complete core Delta of Gamma has an expansion by finitely many constants such that the pseudovariety generated by its polymorphism algebra contains a two-element algebra all of whose operations are projections, or there is a homomorphism f from Delta^k to Delta, for some finite k, and an automorphism alpha of Delta satisfying f(x1,...,xk) = alpha(f(x2,...,xk,x1)). This conjecture has been confirmed for all infinite structures Gamma that have a first-order definition over (Q;<), and for all structures that are definable over the random graph. In this paper, we verify the conjecture for all structures that are definable over an equivalence relation with a countably infinite number of countably infinite classes. Our result implies a complexity dichotomy (into NP-complete and P) for a family of constraint satisfaction problems (CSPs) which we call equivalence constraint satisfaction problems. The classification for equivalence CSPs can also be seen as a first step towards a classification of the CSPs for all relational structures that are first-order definable over Allen's interval algebra, a well-known constraint calculus in temporal reasoning.

BibTeX - Entry

@InProceedings{bodirsky_et_al:LIPIcs:2012:3668,
  author =	{Manuel Bodirsky and Michal Wrona},
  title =	{{Equivalence Constraint Satisfaction Problems}},
  booktitle =	{Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL},
  pages =	{122--136},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-42-2},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{16},
  editor =	{Patrick C{\'e}gielski and Arnaud Durand},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3668},
  URN =		{urn:nbn:de:0030-drops-36689},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.CSL.2012.122},
  annote =	{Keywords: Constraint satisfaction problems, universal algebra, model theory, Ram- sey theory, temporal reasoning, computational complexity}
}

Keywords: Constraint satisfaction problems, universal algebra, model theory, Ram- sey theory, temporal reasoning, computational complexity
Seminar: Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL
Issue Date: 2012
Date of publication: 27.08.2012


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