Introduction In the theory of groups, the important concepts of Abelian group, solvable group, nilpotent group, the center of a group and centraliz-ers, are all defined from the binary operation [x,â€¦ (More)

The Constraint Satisfaction Problem Dichotomy Conjecture of Feder and Vardi (1999) has in the last 10 years been profitably reformulated as a conjecture about the set SPfin(A) of subalgebras ofâ€¦ (More)

22nd Annual IEEE Symposium on Logic in Computerâ€¦

2007

A k-edge operation phi on a finite set A is a k + 1-ary operation that satisfies the identities phi (x,x,y,...,y) ap phi(x,y,x,y,...,y) ap y, phi(y,y,y,x,y,...,y) ap phi(y,y,y,y,x,y,...,y) ap ... apâ€¦ (More)

We develop the theories of the strong commutator, the rectangular commutator, the strong rectangular commutator, as well as a solvability theory for the nonmodular TC commutator. These theories areâ€¦ (More)

We show that the class of locally finite varieties omitting type 1 has the following properties. This class (1) is definable by an idempotent, linear, strong Malâ€™cev condition in a language with oneâ€¦ (More)

We show that a number of natural membership problems for classes associated with finite semigroups are computationally difficult. In particular, we construct a 55-element semigroup S such that theâ€¦ (More)

Aichinger et al. (2011) have proved that every finite algebra with a cubeterm (equivalently, with a parallelogram-term; equivalently, having few subpowers) is finitely related. Thus finite algebrasâ€¦ (More)

We prove that every clone of operations on a finite set A, if it contains a Malcev operation, is finitely related â€“ i.e., identical with the clone of all operations respecting R for some finitaryâ€¦ (More)