Abstract. Workflow Petri nets (wf-nets) are an important formalism for the modeling of business processes. For them we are typically interested in the soundness problem, that intuitively consists in deciding whether several concurrent executions can always terminate properly. ResourceConstrained Workflow Nets (rcfw-nets) are wf-nets enriched with static places, that model global resources. In this paper we prove the undecidability of soundness for rcwf-nets when there may be several static places and in which instances are allowed to terminate having created or consumed resources. In order to have a clearer presentation of the proof, we define an asynchronous version of a class of Petri nets with dynamic name creation. Then, we prove that reachability is undecidable for them, and reduce it to dynamic soundness in rcwf-nets. Finally, we prove that if we restrict our class of rcwf-nets, assuming in particular that a single instance is sound when it is given infinitely many global resources, then dynamic soundness is decidable by reducing it to the home space problem in P/T nets for a linear set of markings.

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We combine the two existing approaches to the study of concurrency by means of multiset rewriting: multiset rewriting with existential quantification (MSR) and constrained multiset rewriting. We obtain ν-MSR, where we rewrite multisets of atomic formulae, in which terms can only be pure names, where some names can be restricted. We consider the subclass of depth-bounded ν-MSR, for which the interdependence of names is bounded. We prove that they are strictly Well Structured Transition Systems, so that coverability, termination and boundedness are all decidable for depth-bounded ν-MSR. This allows us to obtain new verification results for several formalisms with name binding that can be encoded within ν-MSR, namely polyadic ν-PN (Petri nets with tuples of names as tokens), the π-calculus, MSR or Mobile Ambients.

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