Discriminator or dual discriminator? (Q1771857)

A semidiscriminator on a set \(S\) is a ternary function \(f\) such that for every pair \((a,c)\) of elements of \(S\), \(f\) is either the discriminator for both pairs \((a,c)\) and \((c,a)\), or it is the dual discriminator for both of these pairs. The author characterizes semidiscriminator varieties. In the general case a continuum of non-finitely based semidiscriminator subvarieties is presented. A graph-theoretical picture leads to a variety of groupoids connecting the left-zero and the right-zero semigroups. For this variety some open problems are presented.