An Axiomatisation of Duplication Equivalence in the Petri Box Calculus

The Petri Box Calculus (PBC) consists of an algebra of box expressions, and a corresponding algebra of boxes (a class of labelled Petri nets). A compositional semantics provides a translation from box expressions to boxes. There are several alternative ways of defining an equivalence notion for boxes, the strongest one being net isomorphism. In this paper we consider slightly weaker notion of equivalence, called duplication equivalence, which still can be argued to capture a very close structural similarity of concurrent systems represented by boxes. We transfer the notion of duplication equivalence to the domain of box expressions and investigate the relationship between duplication equivalent boxes and box expressions. The main result of this investigation is a sound and complete axiomatisation of duplication equivalence for a fragment of recursion-free PBC.