Efficient verification of determinate processes

Abstract

Determinacy, or predictability, is often demanded from engineered concurrent systems. In this paper we use labeled transition systems to express the specifications and implementations of concurrent systems, and present three efficient algorithms (1) to determine if a process P has determinacy property as defined by Robin Milner; (2) to verify whether an implementation process P is observationally equivalent to a determinate specification process S; and (3) to compute the equivalence classes of determinate process P under observational equivalence. We deal only with finite state processes in this paper.

Suppose P has n states and m transitions, and S has n ₁ states and m ₁ transitions. The first algorithm has time complexity O(m+n log n) and space complexity O(m+n); the second algorithm has time complexity O(m+n+m ₁+n ₁ log n ₁) and space complexity O(m+n+m ₁+n ₁); and the third algorithm has time complexity O(m+n log n) and space complexity O(m+n). Empirical results are presented comparing the algorithms in practice with similar algorithms implemented in other tools.