Model Checking of Systems Employing Commutative Functions

The paper presents methods for model checking a class of possibly infinite state concurrent programs using various types of bi-simulation reductions. The proposed methods work for the class of programs in which the functions that update the variables are mutually commutative. A number of bi-simulation relations are presented for such systems. Explicit state model checking methods that employ on-the-fly reductions with respect to these bi-simulations are given. Some of these methods have been implemented and have been used to verify some well known protocols that employ integer variables. Various applications of the methods and optimization techniques for special cases are also given in appendix.