We develop an algebraic model for recognizing languages of words indexed by countable
linear orderings. This notion of recognizability is effectively equivalent to definability in …

Given a pseudoword over suitable pseudovarieties, we associate to it a labeled linear order
determined by the factorizations of the pseudoword. We show that, in the case of the …

We investigate the decidability of a family of logics mixing difference-logic constraints and
unary uninterpreted predicates. The focus is set on logics whose domain of interpretation is …

First-order logic fragments mixing quantifiers, arithmetic, and uninterpreted predicates are
often undecidable, as is, for instance, Presburger arithmetic extended with a single …

This paper is a survey on the equational descriptions of languages. The first part is devoted
to Birkhoff's and Reiterman's theorems on equational descriptions of varieties. Eilenberg's …

This paper expands the list of 0-1 problems that can be effectively modelled and solved as
Unconstrained Quadratic Binary Programs (UQPs). UQP has been presented as a general …

Deciding formulas mixing arithmetic and uninterpreted predicates is of practical interest,
notably for applications in verification. Some decision procedures consist in building by …

We develop an algebraic notion of recognizability for languages of words indexed by
countable linear orderings. We prove that this notion is effectively equivalent to definability in …

We define context-free grammars with Büchi acceptance condition generating languages of
countable words. We establish several closure properties and decidability results for the …

Any countable (infinite or not) linear (total) ordering can be represented by displaying all its
elements on an axis in increasing order. Such a representation can be generated using only …