The state-explosion problem of formal verification has obstructed its application to large-scale software systems. In this article, we introduce a set of new condensation theories: IOT-failure equivalence, IOT-state equivalence, and firing-dependence theory to cope with this problem. Our condensation theories are much weaker than current theories used for the compositional verification of Petri nets. More significantly, our new condensation theories can eliminate the interleaved behaviors caused by asynchronously sending actions. Therefore, our technique provides a much more powerful means for the compositional verification of asynchronous processes. Our technique can efficiently analyze several state-based properties: boundedness, reachable markings, reachable submarkings, and deadlock states. Based on the notion of our new theories, we develop a set of condensation rules for efficient verification of large-scale software systems. The experimental results show a significant improvement in the analysis large-scale concurrent systems.
ACM Transactions on Programming Languages and Systems 20(5):917-979