Computational Complexity of DECLARE Relation Problem for Sound non-Free-Choice Workflow Nets

Petri net is a mathematical tool for discrete event systems. Workflow analysis is one of successful application of Petri net. DECLARE relation template is one of important properties to check validity of workflows. This paper studies computational complexity to decide whether the DECLARE relation templates between transitions A and B. The problems are shown to verified in determinstic polynomial time for sound acyclic free choice workflow nets. They are shown to be co-NP hard for sound acyclic non-free choice workflow nets.