In: Information and Computation, Vol. 122, No. 2, pages 268-285. 1995.
Abstract: This paper presents a framework for giving a compositional theory of Petri nets using category theory. An integral part of our approach is the use of linear logic in specifying and reasoning about Petri nets. We construct categories of nets based on V.C.V. de Paiva's dialectica category models of linear logic [in `Proc. Category Theory and Computer Science, Manchester' (D.H. Pitt, D.E. Rydeheard, P. Dybjer, A.M. Pitts, and A. Poigne, Eds.), Lecture Notes in Computer Science, Vol. 389, Springer-Verlag, Berlin/New York, 1989] and exploit the structure of de Paiva's models to give constructions on nets. We compare our categories of nets with others in the literature, and show how some of the most widely-studied categories can be expressed within our framework. Taking a category of elementary nets as an example we show how this approach yields both existing and novel constructions on nets and discuss their computational interpretation.
Keywords: Petri nets, category theory, compositional theory, linear logic.