Decomposition of Decidable First-Order Logics over Integers and Reals

We tackle the issue of representing infinite sets of real- valued vectors. This paper introduces an operator for combining integer and real sets. Using this operator, we decompose three well-known logics extending Presburger with reals. Our decomposition splits a logic into two parts : one integer, and one decimal (i.e. on the interval [0,1]). We also give a basis for an implementation of our representation

About Fast and TReX accelerations

Fast and TReX tools are designed to analyse systems with infinite state spaces. They both implement algorithms computing the set of reachable states of such systems. Since the state space may be infinite, acceleration techniques are used. In this paper, we study the differences between Fast and TReX acceleration techniques and show that although Fast remains in Presburger logics while accelerating, TReX can produce 1 st order arithmetical formulas even when accelerating functions from states belonging to a subset of Presburger