Decidability Results for Soundness Criteria of Resource-Constrained Workflow Nets

This paper focuses on the decidability status of various forms of behavioral correctness criteria for resource-constrained workflow (RCWF) nets (Petri net models of RCWF systems). These behavioral correctness criteria, usually called soundness criteria, are natural extensions of similar correctness criteria for workflow nets (Petri net models of workflow systems). While all forms of soundness are known to be decidable for workflow nets, only soundness for RCWF nets with just one resource type is known to be decidable. In this paper, we show that if we limit the number of cases, then soundness for RCWF nets with arbitrarily many resource types is decidable. Moreover, we show that some “intermediate” forms of soundness, as well as a restrictive form of structural soundness for RCWF nets, are decidable too. The proof technique is based on instantiation nets as a general tool for dealing with arbitrarily many cases and arbitrarily large resources in workflow nets and RCWF nets. It is also shown why this technique cannot be extended to the most general form of soundness.