Barnaby Martin ; Manuel Bodirsky ; Martin Hils - 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 - https://doi.org/10.2168/LMCS-8(3:13)2012
On the Scope of the Universal-Algebraic Approach to Constraint Satisfaction

Authors: Barnaby Martin ; Manuel Bodirsky ; Martin Hils

    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).


    Volume: Volume 8, Issue 3
    Published on: September 12, 2012
    Accepted on: June 25, 2015
    Submitted on: January 17, 2011
    Keywords: Computer Science - Logic in Computer Science,Computer Science - Artificial Intelligence,Computer Science - Computational Complexity

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    Source : ScholeXplorer IsReferencedBy DOI 10.1007/978-3-030-02149-8_1
    • 10.1007/978-3-030-02149-8_1
    • 10.1007/978-3-030-02149-8_1
    • 10.1007/978-3-030-02149-8_1
    Finite Relation Algebras with Normal Representations
    Bodirsky, Manuel ;

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