1. CJM 2011 (vol 65 pp. 3)
|Finitely Related Algebras in Congruence Distributive Varieties Have Near Unanimity Terms|
We show that every finite, finitely related algebra in a congruence distributive variety has a near unanimity term operation. As a consequence we solve the near unanimity problem for relational structures: it is decidable whether a given finite set of relations on a finite set admits a compatible near unanimity operation. This consequence also implies that it is decidable whether a given finite constraint language defines a constraint satisfaction problem of bounded strict width.
Keywords:congruence distributive variety, JÃ³nsson operations, near unanimity operation, finitely related algebra, constraint satisfaction problem
2. CJM 2009 (vol 61 pp. 451)
|A Subalgebra Intersection Property for Congruence Distributive Varieties |
We prove that if a finite algebra $\m a$ generates a congruence distributive variety, then the subalgebras of the powers of $\m a$ satisfy a certain kind of intersection property that fails for finite idempotent algebras that locally exhibit affine or unary behaviour. We demonstrate a connection between this property and the constraint satisfaction problem.
Keywords:congruence distributive, constraint satisfaction problem, tame congruence theory, \jon terms, Mal'cev condition
Categories:08B10, 68Q25, 08B05