Verification of Protocols Using Presburger Array Theory

One of the verification methods of programs is to show certain predicates about program variables to be invariant. In general, it is undecidable whether or not a given predicate is invariant. In this paper, a class of concurrent program systems which include array variables is introduced, and a class of predicates about program variables is defined. The invariance problem for a predicate in the class is still undecidable. But it is shown that it is decidable whether or not a given predicate in the class satisfies a certain condition which is a sufficient one for the predicate to be,invariant. An abstract protocol which is an example of the concurrent program systems is described, and it is formally shown that some predicates which assert properties of the abstract protocol are invariant.