An Automata-Theoretic Approach to Presburger Arithmetic Constraints

This paper introduces a finite-automata based representation of Presburger arithmetic definable sets of integer vectors. The representation consists of concurrent automata operating on the binary encodings of the elements of the represented sets. This representation has several advantages. First, being automata-based it is operational in nature and hence leads directly to algorithms, for instance all usual operations on sets of integer vectors translate naturally to operations on automata. Second, the use of concurrent automata makes it compact. Third, it is insensitive to the representation size of integers. Our representation can be used whenever arithmetic constraints are needed. To illustrate its possibilities we show that it can handle integer programming optimally, and that it leads to a new original algorithm for the satisfiability of arithmetic inequalities

Constructing Automata from Temporal Logic Formulas: A Tutorial⋆

This paper presents a tutorial introduction to the construction of finite-automata on infinite words from linear-time temporal logic formulas. After defining the source and target formalisms, it describes a first construction whose correctness is quite direct to establish, but whose behavior is always equal to the worst-case upper bound. It then turns to the techniques that can be used to improve this algorithm in order to obtain the quite effective algorithms that are now in use