Compositional Verification Using Petri Nets

Abstract

Petri Nets have been widely recognized as a suitable tool for modeling and analyzing concurrent systems [Murata, 1989, Silva, 1989, Yoeli, 1987]. However because of the complexity of state explosion [Lipton, 1987], efficient analysis by reachability graph is restricted to small system models. This section presents a Petri-net based methodology for the compositional verification of state-based properties. State-space reduction is based on three condensation theories, i.e., IOT-failure equivalence, IOT-state equivalence, and firing-dependence theory. To avoid the PSPACE problem, we use heuristic rule-based algorithms. The state space is reduced dynamically after one or more rules succeed. The process of reduction terminates once none of the rules become applicable. The time complexity of some rules is linear. The others are polynomial or can be adjusted to polynomial. Our condensation rules preserve the properties of boundedness, deadlock states, reachable markings, and/or reachable sub-markings.