Free-Choice Petri Nets without Frozen Tokens, and Bipolar Synchronization Systems

Article type: Research Article

Authors: Wehler, Joachim

Affiliations: Ludwig-Maximilians-Universität, München Germany. E-mail: joachim.wehler@gmx.net

Abstract: Bipolar synchronization systems (BP-systems) constitute a class of coloured Petri nets, well suited for modelling the control flow of discrete dynamical systems. Every BP-system has an underlying ordinary Petri net, a T-system. It further has a second ordinary net attached, a free-choice system. We prove that a BP-system is safe and live if the T-system and the free-choice system are safe and live and the free-choice system in addition has no frozen tokens. This result is the converse of a theorem of Genrich and Thiagarajan and proves an old conjecture. As a consequence we obtain two results about the existence of safe and live BP-systems with prescribed ordinary Petri nets. For the proof of these theorems we introduce the concept of a morphism between Petri nets as a means of comparing different Petri nets. We then apply the classical theory of free-choice systems.

Keywords: Bipolar synchronization system, free-choice system, frozen token, Petri net morphism, structurally free of blocking

DOI: 10.3233/FI-2010-228

Journal: Fundamenta Informaticae, vol. 98, no. 2-3, pp. 283-320, 2010