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Horn versus Full First-order: Complexity Dichotomies in Algebraic Constraint Satisfaction
Ecole Polytechnique, Palaiseau, France.
Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, The Institute of Technology. (TCSLAB)
University of Virginia, USA.
2012 (English)In: Journal of logic and computation (Print), ISSN 0955-792X, E-ISSN 1465-363X, Vol. 22, no 3, 643-660 p.Article in journal (Refereed) Published
Abstract [en]

We study techniques for deciding the computational complexity of infinite-domain constraint satisfaction problems. For certain fundamental algebraic structures Delta, we prove definability dichotomy theorems of the following form: for every first-order expansion Gamma of Delta, either Gamma has a quantifier-free Horn definition in Delta, or there is an element d of Gamma such that all non-empty relations in Gamma contain a tuple of the form (d,...,d), or all relations with a first-order definition in Delta have a primitive positive definition in Gamma. The results imply that several families of constraint satisfaction problems exhibit a complexity dichotomy: the problems are in P or NP-hard, depending on the choice of the allowed relations. As concrete examples, we investigate fundamental algebraic constraint satisfaction problems. The first class consists of all first-order expansions of (Q;+). The second class is the affine variant of the first class. In both cases, we obtain full dichotomies by utilising our general methods.

Place, publisher, year, edition, pages
2012. Vol. 22, no 3, 643-660 p.
Keyword [en]
Constraint satisfaction problems, complexity dichotomy, primitive positive definability, linear program feasibility, linear programming
National Category
Computer Science
URN: urn:nbn:se:liu:diva-79513DOI: 10.1093/logcom/exr011OAI: diva2:543173
Available from: 2012-08-06 Created: 2012-08-06 Last updated: 2012-08-16

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