Automata-based representations of arithmetic sets ------------------------------------------------- Bernard Boigelot University of Liège Using automata for representing sets of numbers is an old idea, orginally introduced as a tool for reasoning about decidable fragments of arithmetic. There is now a growing interest in using such automata-based representations as data structures for dealing with the sets of configurations that have to be handled during symbolic state-space exploration, especially when the analyzed systems rely on integers and real variables. In this survey, we will present automata-based representations of integer and real vectors, describe their main properties, and show how they can be used for exploring symbolically infinite state-spaces, as well as for manipulating systems of linear constraints.