Deciding presburger arithmetic by model checking and comparisons with other methods

Abstract

We present a new way of using Binary Decision Diagrams in automata based algorithms for solving the satisfiability problem of quantifier-free Presburger arithmetic. Unlike in previous approaches [5,2,19], we translate the satisfiability problem into a model checking problem and use the existing BDD-based model checker SMV [13] as our primary engine. We also compare the performance of various Presburger tools, based on both automata and ILP approaches, on a large suite of parameterized randomly generated test cases. The strengths and weaknesses of each approach as a function of these parameters are reported, and the reasons for the same are discussed. The results show that no single tool performs better than the others for all the parameters. On the theoretical side, we provide tighter bounds on the number of states of the automata.