Depth Boundedness in Multiset Rewriting Systems with Name Binding

In this paper we consider ν-MSR, a formalism that combines the two main existing approaches for multiset rewriting, namely MSR and CMRS. In ν-MSR we rewrite multisets of atomic formulae, in which some names may be restricted. ν-MSR are Turing complete. In particular, a very straightforward encoding of π-calculus process can be done. Moreover, pν-PN, an extension of Petri nets in which tokens are tuples of pure names, are equivalent to ν-MSR. We know that the monadic subclass of ν-MSR is a Well Structured Transition System. Here we prove that depth-bounded ν-MSR, that is, ν-MSR systems for which the interdependance of names is bounded, are also Well Structured, by following the analogous steps to those followed by R. Meyer in the case of the π-calculus. As a corollary, also depth-bounded pν-PN are WSTS, so that coverability is decidable for them.