The central issue of this paper is to find a class of Petri nets that a necessary and sufficient condition for reachability is obtainable. For this purpose, several new classes of Petri nets are defined by structural conditions related to directed circuits. A necessary and sufficient condition for reachability is obtained for trap circuit Petri nets (TC nets), where a Petri net is called a TC net if the set of places on any directed circuit forms a trap, and for deadlock circuit Petri nets (DC nets), where a Petri net is called a DC net if the set of places on any directed circuit forms a deadlock. The class of TC nets is a subclass of normal Petri nets. For normal Petri nets, a sufficient condition for reachability is obtained. Reachability for any conflict-free Petri net can be decided by finding a legal firing sequence for a finite number of minimal solutions of the state equation. This property also holds for larger classes of Petri nets. These are a class of non-decreasing circuit Petri nets (NDC nets), where a Petri net is called an NDC net if the number of tokens on any directed circuit is not decreased by any firing of transitions, and a class of non-increasing circuit Petri nets (NIC nets), where a Petri net is called an NIC net if the number of tokens on any directed circuit is non increased by any firing of transitions. The class of NDC nets and the class of NIC nets are subclasses of TC nets and DC nets, respectively.
In these subclasses a necessary and sufficient condition for reachability is available (see REF ).
A Class of Petri Nets That a Necessary and Sufficient Condition for Reachability is Obtainable
Journal of the Society of Instrument and Control Engineers
Computer Science