The complexity of soundness in workflow nets

TL;DR

This paper investigates the computational complexity of different variants of soundness in workflow nets, revealing that classical and structural soundness are EXPSPACE-complete, while generalized soundness is PSPACE-complete, which is unexpectedly simpler.

Contribution

It establishes the exact complexity classes for three variants of soundness in workflow nets, resolving a long-standing open problem.

Findings

Classical and structural soundness are EXPSPACE-complete.

Generalized soundness is PSPACE-complete.

Generalized soundness is computationally simpler than the other variants.

Abstract

Workflow nets are a popular variant of Petri nets that allow for algorithmic formal analysis of business processes. The central decision problems concerning workflow nets deal with soundness, where the initial and final configurations are specified. Intuitively, soundness states that from every reachable configuration one can reach the final configuration. We settle the widely open complexity of the three main variants of soundness: classical, structural and generalised soundness. The first two are EXPSPACE-complete, and, surprisingly, the latter is PSPACE-complete, thus computationally simpler.