This paper explores the nature of the solution sets of systems of equations in virtually
abelian groups. We view this question from two angles. From a formal language perspective …

We investigate the connection between properties of formal languages and properties of
their generating series, with a focus on the class of\emph {holonomic} power series. We first …

We show that the geodesic growth function of any finitely generated virtually abelian group
is either polynomial or exponential; and that the geodesic growth series is holonomic, and …

We define a class of languages (RCM) obtained by considering Regular languages, linear
Constraints on the number of occurrences of symbols and Morphisms. The class RCM …

We study counting-regular languages—these are languages L for which there is a regular
language L′ such that the number of strings of length n in L and L′ are the same for all n …

We prove that the class of the languages recognized by one-way deterministic 1-reversal
bounded 1-counter machines is contained in RCM, a class of languages that has been …

We study counting-regular languages—these are languages L for which there is a regular
language L'such that the number of strings of length n in L and L'are the same for all n. Our …

This paper deals with the conversion of expressions denoting Hadamard series into
weighted rotating automata. We prove that any algorithm converting rational series into one …

We study the use of EDT0L languages to describe solutions to systems of equations in
various classes of groups. We show that solutions to systems of equations with rational …

We prove that the generating function of a language accepted by a one-way deterministic
one-reversal counter machine without negative cycles is holonomic. The result is achieved …