Barto, Libor and Kozik, Marcin - Absorbing Subalgebras, Cyclic Terms, and the Constraint Satisfaction Problem

lmcs:673 - Logical Methods in Computer Science, February 20, 2012, Volume 8, Issue 1
Absorbing Subalgebras, Cyclic Terms, and the Constraint Satisfaction Problem

Authors: Barto, Libor and Kozik, Marcin

The Algebraic Dichotomy Conjecture states that the Constraint Satisfaction Problem over a fixed template is solvable in polynomial time if the algebra of polymorphisms associated to the template lies in a Taylor variety, and is NP-complete otherwise. This paper provides two new characterizations of finitely generated Taylor varieties. The first characterization is using absorbing subalgebras and the second one cyclic terms. These new conditions allow us to reprove the conjecture of Bang-Jensen and Hell (proved by the authors) and the characterization of locally finite Taylor varieties using weak near-unanimity terms (proved by McKenzie and Mar\'oti) in an elementary and self-contained way.


Source : oai:arXiv.org:1201.0557
DOI : 10.2168/LMCS-8(1:7)2012
Volume: Volume 8, Issue 1
Published on: February 20, 2012
Submitted on: December 30, 2010
Keywords: Computer Science - Logic in Computer Science,F.2.2, F.4.1


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