On Some Compositional Petri

This paper continues a research on universal contexts and Petri net semantics started in NPS95]. We regard generalized, labelled Petri nets, N, where some transitions and places are distinguished as`public'. They form the interface of N that may communicate with a Petri net context. An elementary calculus, E, is introduced that allows to construct any Petri net with an interface from trivial constants (single places, single transitions) by drawing arcs, adding tokens, and hiding public places and transitions. We prove the existence of a universal context U such that two Petri nets behave the same in any context ii their behaviour is equal in the universal context. Let B(UN]) be the behaviour of N embedded in its universal context, where B may be the interleaving language, step{language, or true{concurrent pomset{language. In any of these cases, B(UN]) (in contrast to B(N)) turns out to be a fully{abstract semantics of N with respect to the algebra E.