Martin, Barnaby and Bodirsky, Manuel and Hils, Martin - On the Scope of the Universal-Algebraic Approach to Constraint Satisfaction

lmcs:674 - Logical Methods in Computer Science, September 12, 2012, Volume 8, Issue 3
On the Scope of the Universal-Algebraic Approach to Constraint Satisfaction

Authors: Martin, Barnaby and Bodirsky, Manuel and Hils, Martin

The universal-algebraic approach has proved a powerful tool in the study of the complexity of CSPs. This approach has previously been applied to the study of CSPs with finite or (infinite) omega-categorical templates, and relies on two facts. The first is that in finite or omega-categorical structures A, a relation is primitive positive definable if and only if it is preserved by the polymorphisms of A. The second is that every finite or omega-categorical structure is homomorphically equivalent to a core structure. In this paper, we present generalizations of these facts to infinite structures that are not necessarily omega-categorical. (This abstract has been severely curtailed by the space constraints of arXiv -- please read the full abstract in the article.) Finally, we present applications of our general results to the description and analysis of the complexity of CSPs. In particular, we give general hardness criteria based on the absence of polymorphisms that depend on more than one argument, and we present a polymorphism-based description of those CSPs that are first-order definable (and therefore can be solved in polynomial time).


Source : oai:arXiv.org:0909.5097
DOI : 10.2168/LMCS-8(3:13)2012
Volume: Volume 8, Issue 3
Published on: September 12, 2012
Submitted on: January 17, 2011
Keywords: Computer Science - Logic in Computer Science,Computer Science - Artificial Intelligence,Computer Science - Computational Complexity


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