ABSORBING SUBALGEBRAS, CYCLIC TERMS, AND THE CONSTRAINT SATISFACTION PROBLEM

作者：Barto Libor^*; Kozik Marcin

来源：Logical Methods in Computer Science, 2012, 8(1): 07.

DOI：10.2168/LMCS-8(1:07)2012

• Constraint Satisfaction Problem
• Taylor variety
• cyclic term
• absorbing subalgebra

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 Maroti) in an elementary and self-contained way.

• 出版日期2012