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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2012.122
URN: urn:nbn:de:0030-drops-36689
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2012/3668/
Bodirsky, Manuel ;
Wrona, Michal
Equivalence Constraint Satisfaction Problems
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 = {10.4230/LIPIcs.CSL.2012.122},
annote = {Keywords: Constraint satisfaction problems, universal algebra, model theory, Ram- sey theory, temporal reasoning, computational complexity}
}
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Keywords: |
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Constraint satisfaction problems, universal algebra, model theory, Ram- sey theory, temporal reasoning, computational complexity |
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Collection: |
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Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL |
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Issue Date: |
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2012 |
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Date of publication: |
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03.09.2012 |
