抄録
This paper deals with determination of a firing sequence of transitions in reachability problem of a Petri net. In general, the reachability problem can be solved by checking whether there exists a non-negative integer solution such that the matrix equation of Petri net holds true. Even if the solution exists, however, there exists a problem for finding a firing sequence which makes it possible to reach the given final marking on the places set of Petri net. The determination problem of a firing sequence is very important from the point of practical view, especially in the control of event-driven systems, in the failure diagnosis of sequence control systems modelled by means of Petri net.
In the paper, the method of determining a firing sequence of transitions is proposed. First, the determination problem discussed in this paper is defined. Second, the two kind of notions, that is, the reverse graph of primal Petri net and the transition matrix representing the paths of firing transitions, are newly introduced in order to determine the firing order of transitions. Third, an algorithm to determine the firing sequence by tracing reversely from the final marking to the initial one on the places set is presented. Finally, the method proposed in this paper is applied to the failure diagnosis of a simple type of sequence control system modelled by Petri net.
