On the Use of Automata for Deciding Linear Arithmetic

This talk presents a survey of automata-based techniques for representing and manipulating linear arithmetic constraints. After introducing the basic concepts used in this approach, both representing integer constraints by finite-word automata and real constraints by infinite-word automata is discussed. Various results about the construction of automata from constraints and about the specific properties of automata representing arithmetic constraints are then presented. Finally, it is shown how this approach leads to simple and natural decision procedures that are in some ways related to tableaux.