Synchronized Products of Transition Systems and Their Analysis

Abstract

Petri Nets and the synchronized products of transition systems introduced by Arnold and Nivat are two closely related models of concurrent systems. The second one is used to model finite state systems whose analysis is made on a “behavioural” basis: evaluation of state properties expressed in some temporal logic on the state graph of the system. On the other hand, Petri Nets model infinite state systems, and their analysis is often made on a “structural” basis. But, as soon as the number of states of a finite-state system is so large that it cannot be encoded in the memory of the machine, it is indeed infinite. A way of dealing with such a situation could be to proceed to structural analysis, borrowing concepts from Petri Nets Theory.