Regular elements of the semigroup of all binary relations.
For an arbitrary permutation in the semigroup of full transformations on a set with elements, the regular elements of the centralizer of in are characterized and criteria are given for to be a regular semigroup, an inverse semigroup, and a completely regular semigroup.
In our main result, we establish a formal connection between Lindström quantifiers with respect to regular languages and the double semidirect product of finite monoids with a distinguished set of generators. We use this correspondence to characterize the expressive power of Lindström quantifiers associated with a class of regular languages.
In our main result, we establish a formal connection between Lindström quantifiers with respect to regular languages and the double semidirect product of finite monoids with a distinguished set of generators. We use this correspondence to characterize the expressive power of Lindström quantifiers associated with a class of regular languages.