Functorial models for Petri nets

We show that although the algebraic semantics of place/transition Petri net s under the collective token philosophy can be fully explained in terms of strictly symmetric monoidal categories, the analogous construction under ti re individual token philosophy is not completely satisfactory, because it l acks universality and also functionality. We introduce the notion of pre-ne ts to overcome this, obtaining a fully satisfactory categorical treatment, where the operational semantics of nets yields an adjunction. This allows u s to present a uniform logical description of net behaviors under both the collective and the individual token philosophies in terms of theories and t heory morphisms in partial membership equational logic. Moreover, since the universal property of adjunctions guarantees that colimit constructions on nets are preserved in our algebraic models, the resulting semantic framewo rk has good compositional properties. (C) 2001 Academic Press.