This paper proposes monads as a framework for algebraic language theory. Examples of
monads include words and trees, finite and infinite. Each monad comes with a standard …

An important endeavor in computer science is to understand the expressive power of logical
formalisms over discrete structures, such as words. Naturally," understanding" is not a …

We introduce regular languages of morphisms in free monoidal categories, with their
associated grammars and automata. These subsume the classical theory of regular …

We characterize the strength, in terms of Weihrauch degrees, of certain problems related to
Ramsey-like theorems concerning colourings of the rationals and of the natural numbers …

L'objet de cette thèse est l'étude des fonctions régulières de coût. Il s' agit d'une extension
quantitative de la notion, classique, de langages réguliers, qui en préserve certaines …

MSO transductions are binary relations between structures which are defined using monadic
second-order logic. MSO transductions form a category, since they are closed under …

We apply Stone duality and model theory to study the structure theory of free pro-aperiodic
monoids. Stone duality implies that elements of the free pro-aperiodic monoid may be …

One of the main reasons for the correspondence of regular languages and monadic second-
order logic is that the class of regular languages is closed under images of surjective letter …

Already in the seventies, strong results illustrating the intimate relationship between
category theory and automata theory have been described and are still investigated. In this …

This chapter is devoted to the presentation of the factorisation forest theorem, a deep result
due to Simon, which provides advanced Ramsey-like arguments in the context of algebra …