We survey the properties of sets of integers recognizable by automata when they are written in p-ary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different… (More)

This paper is driven by a general motto: bisimulate an hybrid system by a finite symbolic dynamical system. In the case of ominimal hybrid systems, the continuous and discrete components can be… (More)

We first propose a “geometrical” axiomatization for the theory of closed ordered differential fields (denoted CODF) introduced by M.Singer in 1978 (see [Si]). This axiomatization is the analogue of… (More)

Let N he the set of nonnegative integers. We show the two following facts about Presburger’s arithmetic: 1. Let LEN, If L is not definable in (N, A-} then there is an L’S N definable in (N, +, L),… (More)

This paper is driven by a general motto: bisimulate a hybrid system by a finite symbolic dynamical system. In the case of o-minimal hybrid systems, the continuous and discrete components can be… (More)

This paper describes a very simple (high school level) algorithm of quantifier elimination for real closed fields and algebraically closed fields following an idea of A. Muchnik. The algorithm… (More)

The main result of this paper lies in the framework of BSS computabil-ity : it shows roughly that any recursively enumerable set S in R N , N 6 1, where R is a real closed eld, is isomorphic to R dim… (More)

Definition 1.2. Let (M, ) be an o-minimal dynamical system, let T be the associated transition system on M2 , and let P be a finite definable partition of M2 . Let us recall that is the finite… (More)