A Note on the Well-Foundedness of Adequate Orders Used for Truncating Unfoldings

Petri net unfolding prefixes are an important technique for formal verification and synthesis. In this paper we show that the requirement that the adequate order used for truncating a Petri net unfolding must be well-founded is superfluous in many important cases, i.e. it logically follows from other requirements. We give a complete analysis when this is the case. These results concern the very `core' of the unfolding theory. About the author Thomas Chatain received his PhD in computer science from University of Rennes 1 in 2006. He is currently doing a post-doc in the Department of Computer Science of the University of Aalborg, Denmark. He is interested in the use of formal models for the supervision, verification and control of distributed systems. In particular he studies true concurrency models (including timed models), partial order semantics, unfoldings and timed games. Victor Khomenko Obtained MSc with distinction in Computer Science, Applied Mathematics and Teaching of Mathematics and Computer Science in 1998 from Kiev Taras Shevchenko University, and PhD in Computing Science in 2003 from University of Newcastle upon Tyne. From September 2005 Victor is a Royal Academy of Engineering/EPSRC Post-Doctoral Research Fellow, working on the DAVAC project. His interests include model checking of Petri nets, Petri net unfolding techniques, self-timed (asynchronous) circuits. Suggested keywords ADEQUATE ORDER, WELL-FOUNDEDNESS, UNFOLDING PREFIX, PETRI NET A Note on the Well-Foundedness of Adequate Orders Used for Truncating Unfoldings Thomas Chatain and Victor Khomenko 1 Department of Computer Science, Aalborg University, Aalborg, Denmark E-mail: [email protected] 2 School of Computing Science, Newcastle University, Newcastle upon Tyne, United Kingdom E-mail: [email protected] Abstract. Petri net unfolding prefixes are an important technique for formal verification and synthesis. In this paper we show that the requirement that the adequate order used for truncating a Petri net unfolding must be well-founded is superfluous in many important cases, i.e., it logically follows from other requirements. We give a complete analysis when this is the case. These results concern the very ‘core’ of the unfolding theory. Petri net unfolding prefixes are an important technique for formal verification and synthesis. In this paper we show that the requirement that the adequate order used for truncating a Petri net unfolding must be well-founded is superfluous in many important cases, i.e., it logically follows from other requirements. We give a complete analysis when this is the case. These results concern the very ‘core’ of the unfolding theory.