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.

Given a direct product of monoids M = A∗ ×N where A is finite and N is the additive monoid of nonnegative integers, the following problem is recursively decidable: given two rational subsests of M , does there exist a recognizable subset which includes one of the subsets and excludes the other.

A class of finite monoids M constructed from a groupG of Lie type is considered. We describe the irreducible complex representations and prove the complete reducibility of the representations of M . The sandwich matrix of M is decomposed into a product of matrices corresponding to maximal parabolic subgroups of G.

The topic of codes in the framework of trace monoids leads to interesting and challenging decision problems of combinatorial avour. We give an overview of the current state of some basic questions in this eld. Among these, we consider the existence problem for strong cod-ings, clique-preserving morphisms and the unique decipherability problem (code problem).

Divisibility monoids (resp. Garside monoids) are a natural algebraic generalization of Mazurkiewicz trace monoids (resp. spherical Artin monoids), namely monoids in which the distributivity of the underlying lattices (resp. the existence of common multiples) is kept as an hypothesis, but the relations between the generators are not supposed to necessarily be commutations (resp. be of Coxeter ty...

We prove a unique decomposition theorem for a class of ordered commutative monoids. Then, we use our theorem to establish that every weakly normed process definable in ACP with bounded communication can be expressed as the parallel composition of a multiset of weakly normed parallel prime processes in exactly one way.

We describe irreducible representations and character formulas of the Renner monoids for reductive monoids, which generalizes the Munn-Solomon representation theory of rook monoids to any Renner monoids. The type map and polytope associated with reductive monoids play a crucial role in our work. It turns out that the irreducible representations of certain parabolic subgroups of the Weyl groups ...

We demonstrate that categories of continuous actions topological monoids on discrete spaces are Grothendieck toposes. exhibit properties these toposes, giving a solution to the corresponding Morita-equivalence problem. characterize toposes in terms their canonical points. identify natural classes representatives with good properties, 'powder monoids' and then 'complete monoids', for monoids. Fi...

This paper is concerned with the many deep and far reaching consequences of Ash's positive solution of the type II conjecture for nite monoids. After rewieving the statement and history of the problem, we show how it can be used to decide if a nite monoid is in the variety generated by the Malcev product of a given variety and the variety of groups. Many interesting varieties of nite monoids ha...