A modification of the CSP algorithm for infinite languages

Constraint Satisfaction Problem on finite sets is known to be NP-complete in general but certain restrictions on the constraint language can ensure tractability. It was proved that if a constraint language has a weak near unanimity polymorphism then the corresponding constraint satisfaction problem is tractable, otherwise it is NP-complete. In the paper we present a modification of the algorithm that works in polynomial time even for infinite constraint languages.

[1]  C. Bergman,et al.  Universal Algebra: Fundamentals and Selected Topics , 2011 .

[2]  Marc Gyssens,et al.  Closure properties of constraints , 1997, JACM.

[3]  Alan K. Mackworth Consistency in Networks of Relations , 1977, Artif. Intell..

[4]  Emil L. Post The two-valued iterative systems of mathematical logic , 1942 .

[5]  Libor Barto,et al.  Absorbing Subalgebras, Cyclic Terms, and the Constraint Satisfaction Problem , 2012, Log. Methods Comput. Sci..

[6]  Tomás Feder,et al.  The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory , 1999, SIAM J. Comput..

[7]  M. Maróti,et al.  Existence theorems for weakly symmetric operations , 2008 .

[8]  Andrei A. Bulatov,et al.  Recent Results on the Algebraic Approach to the CSP , 2008, Complexity of Constraints.

[9]  Lefteris M. Kirousis,et al.  Fast Parallel Constraint Satisfaction , 1993, Artif. Intell..

[10]  Peter Jeavons,et al.  Classifying the Complexity of Constraints Using Finite Algebras , 2005, SIAM J. Comput..

[11]  Martin C. Cooper,et al.  Tractable Constraints on Ordered Domains , 1995, Artif. Intell..

[12]  Dmitriy Zhuk The Lattice of the Clones of Self-Dual Functions in Three-Valued Logic , 2011, 2011 41st IEEE International Symposium on Multiple-Valued Logic.

[13]  Dmitriy Zhuk The predicate method to construct the Post lattice , 2011 .

[14]  Dmitriy Zhuk,et al.  A Proof of CSP Dichotomy Conjecture , 2017, 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS).

[15]  Ugo Montanari,et al.  Networks of constraints: Fundamental properties and applications to picture processing , 1974, Inf. Sci..

[16]  Andrei A. Bulatov,et al.  A Dichotomy Theorem for Nonuniform CSPs , 2017, 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS).

[17]  Dmitriy Zhuk The cardinality of the set of all clones containing a given minimal clone on three elements , 2012 .

[18]  Martin C. Cooper,et al.  Characterising Tractable Constraints , 1994, Artif. Intell..