McMillan’s Complete Prefix for Contextual Nets

Abstract

In a seminal paper, McMillan proposed a technique for constructing a finite complete prefix of the unfolding of bounded (i.e., finite-state) Petri nets, which can be used for verification purposes. Contextual nets are a generalisation of Petri nets suited to model systems with read-only access to resources. When working with contextual nets, a finite complete prefix can be obtained by applying McMillan's construction to a suitable encoding of the contextual net into an ordinary net. However, it has been observed that if the unfolding is itself a contextual net, then the complete prefix can be significantly smaller than the one obtained with the above technique. A construction for generating such a contextual complete prefix has been proposed for a special class of nets, called read-persistent. In this paper, we propose an algorithm that works for arbitrary semi-weighted, bounded contextual nets. The construction explicitly takes into account the fact that, unlike in ordinary or read-persistent nets, an event can have several different histories in general contextual net computations.