Multiset Rewriting: A Semantic Framework for Concurrency with Name Binding

We revise multiset rewriting with name binding, by combining the two main existing approaches to the study of concurrency by means of multiset rewriting, multiset rewriting with existential quantification and constrained multiset rewriting. We obtain ν-MSRs, where we rewrite multisets of atomic formulae, in which some names may be restricted. We prove that ν-MSRs are equivalent to a class of Petri nets in which tokens are tuples of pure names, called pν-APNs. Then we encode π-calculus processes into ν-MSRs in a very direct way, that preserves the topology of bound names, by using the concept of derivatives of a πcalculus process. Finally, we discuss how the recent results on decidable subclasses of the π-calculus are independent of the particular reaction rule of the π-calculus, so that they can be obtained in the more general framework of ν-MSRs. Thus, those results carry over not only to the π-calculus, but to any other formalism that can be encoded within it, as pν-APNs.