COMPUTATIONAL COMPLEXITY OF VARIOUS MAL'CEV CONDITIONS

Abstract

This paper examines the computational complexity of determining whether or not an algebra satisfies a certain Mal'Cev condition. First, we define a class of Mal'Cev conditions whose satisfaction can be determined in polynomial time (special cube term satisfying the DCP) when the algebra in question is idempotent and provide an algorithm through which this determination may be made. The aforementioned class notably includes near unanimity terms and edge terms of fixed arity. Second, we define a different class of Mal'Cev conditions whose satisfaction, in general, requires exponential time to determine (Mal'Cev conditions satisfiable by CPB0 operations).