In: Theoretica Computer Science 308 (2003), pages 145-197. 2003/308.
Abstract: This work builds a bridge from * clustering techniques - merging neighbouring nodes which is a key feature for software engineering and the practical applications of Petri nets - to * folding techniques - merging only transitions with transitions and places with places, preserving behaviour and allowing theoretical connections to many models of concurrency. A new category of Petri nets is introduced. Morphisms support cluster-ing, offering attractive properties to software engineering and integrating smoothly with invariants. A computationally reasonable adjunction con-nects it to folding-based Petri nets, namely, to two new cocomplete and complete categories. The dichotomy of structure and behaviour of Petri nets is expressed as compatible adjunctions to behavioural categories. Finally reachability and process semantics are attached categorically and a new variant of occurrence nets is proposed as a purer image of causality and branching. This framework offers categorical support for practical applications of Petri nets.
Keywords: Petri nets; folding; clustering; structure; behaviour; semantics; category theory.