Group languages are regular languages recognized by finite groups, or equivalently by finite
automata in which each letter induces a permutation on the set of states. We investigate the …

The Boolean satisfiability problem plays a central role in computational complexity and is
often used as a starting point for showing NP lower bounds. Generalisations such as …

We show that it is decidable whether or not a relation on the reals definable in the structure
(R,+,<, Z) can be defined in the structure (R,+,<, 1). This result is achieved by obtaining a …

Given two subsets S 1, S 2 of N k, we say that S 1 is commutatively equivalent to S 2 if there
exists a bijection f: S 1⟶ S 2 from S 1 onto S 2 such that, for every v∈ S 1,| v|=| f (v)|, where …

We investigate the family of semi-linear sets of Nt and Zt. We study the growth function of
semi-linear sets and we prove that such a function is a piecewise quasi-polynomial on a …

Let $ G $ be a group acting acylindrically on a hyperbolic space and let $ E $ be an
exponential equation over $ G $. We show that $ E $ is equivalent to a finite disjunction of …

We study the problems of deciding whether a relation definable by a first-order formula in
linear rational or linear integer arithmetic with an order relation is definable in absence of the …

We show that it is decidable whether or not a relation on the reals definable in the structure
(R,+,<, Z) can be defined in the structure (R,+,<, 1). This result is achieved by obtaining a …

We show that it is decidable whether or not a relation on the reals definable in the structure
⟨ R,+,<, Z ⟩ can be defined in the structure ⟨ R,+,<, 1 ⟩. This result is achieved by obtaining …

We show that it is decidable whether or not a relation on the reals definable in the structure
can be defined in the structure. This result is achieved by obtaining a topological …