Causality in extensions of Petri nets

Abstract

The causal semantics of standard net classes like Elementary Net Systems and Place/Transition Nets, is typically expressed in terms of partially ordered sets of transition occurrences. In each such partial order, causally related occurrences are ordered while concurrent transition occurrences remain unordered. Partial order semantics can, in particular, support model checking by efficient verification techniques based on net unfoldings. To enhance the modelling power of standard net classes, one can introduce different forms of 'testing' using, for example, inhibitor arcs. However, the causal semantics of such extended nets can often no longer be described solely in terms of partial orders. In this paper, we explain what modifications to the partial order semantics are needed in order to provide a satisfactory treatment for nets with activator, inhibitor and mutex arcs. On the technical side, the proposed solution is based on causal structures which enrich partial orders with additional order relations corresponding to other aspects of causality. With EN -systems as our starting point, we discuss how their extensions can be treated using these richer notions of causality. © Springer-Verlag 2013.