Step coverability algorithms for communicating systems

Abstract

Coverability (of states) is an important, useful notion for the behavioural analysis of distributed dynamic systems. For systems like Petri nets, the classical Karp–Miller coverability tree construction is the basis for algorithms to decide questions related to the capacity of local states. We consider a modification of this construction which would allow one to deal with dynamic behaviour consisting of concurrent steps rather than single occurrences of transitions. This leads to an action-based extension of the notion of coverability, viewing bandwidth as a resource. However, when certain constraints are imposed on the steps, systems may exhibit non-monotonic behaviour. In those cases, new criteria for the termination of the step coverability tree construction are needed. We investigate a general class of Petri nets modelling systems that consist of components communicating through shared buffers and that operate under a maximally concurrent step semantics. Based on the description of their behaviour, we derive a correctly terminating step coverability tree construction for these Petri nets.