Towards scalable compositional analysis

Due to the state explosion problem, analysis of large concurrent programs will undoubtedly require compositional techniques. Existing compositional techniques are based on the idea of replacing complex subsystems with simpler processes with the same interfaces to their environments, and using the simpler processes to analyze the full system. Most algorithms for proving equivalence between two processes, however, require enumerating the states of both processes. When part of a concurrent system consists of many highly coupled processes, it may not be possible to decompose the system into components that are both small enough to enumerate and have simple interfaces with their enviornments. In such cases, analysis of the systems by standard methods will be infeasible.In this paper, we describe a technique for proving trace equivalence of deterministic and divergence-free systems without enumerating their states. (For deterministic systems, essentially all the standard notions of process equivalence collapse to trace equivalence, so this technique also establishes failures equivalence, observational equivalence, etc.) Our approach is to generate necessary conditions for the existence of a trace of one system that is not a trace of the other; if the necessary conditions cannot be satisfied the systems are equivalent. We have implemented the technique and used it to establish the equivalence of some systems with state spaces too large for enumeration to be practical.