On Generating *-Sound Nets with Substitution

TL;DR

This paper introduces a hierarchical method for generating sound workflow nets through substitution, ensuring correctness and generalizing previous approaches, with a new soundness notion suited for this method.

Contribution

It presents a novel hierarchical net generation technique with a new soundness concept that is preserved under generalized substitution, improving upon existing soundness notions.

Findings

The method is correct and generalizes existing approaches.

The new soundness notion is better suited for the substitution technique.

The proposed soundness notion is optimal for this context.

Abstract

We present a method for hierarchically generating sound workflow nets by substitution of nets with multiple inputs and outputs. We show that this method is correct and generalizes the class of nets generated by other hierarchical approaches. The method involves a new notion of soundness which is preserved by the generalized type of substitution that is presented in this paper. We show that this notion is better suited than *-soundness for use with the presented type of generalized substitution, since {*}-soundness is not preserved by it. It is moreover shown that it is in some sense the optimal notion of soundness for the purpose of generating sound nets by the presented type of substitution.