コンプリメントなプレースと許可枝からなるペトリネットの到達可能性

Abstract

Complementary-places Petri Nets (CPNs) are proposed as modeling and analysis tools for discrete event systems. A CPN is composed of complementary pairs of places, transitions which have an incoming arc from one side of a pair and an outgoing arc to the other, and permissive arcs.In CPNs, deadlocks and traps are found as specific sub-structures of a net. A new method (FIMS-tree) for the reachability problem is developed for CPNs. The FIMS-tree can be created by repeating the process to detect these sub-structures. The FIMS-tree represents the backward reachability set, which is the set of markings reachable to a given goal marking.The advantages of the method over the reachability tree algorithm are:(1) The backward reachability set can be obtained as a logical expression;(2) A firing sequence from any initial marking to the goal marking can be found without a backtracking process;(3) And the firing count is, at most, the number of the levels of the FIMS-tree for any initial marking.The necessary and sufficient condition for the reachability to any goal marking from any initial marking is derived from the property of the FIMS-tree.As a practical example, a part of a power plant is modeled by CPNs. Then, using the FIMS-tree, it is proved that dangerous states are not reachable from an initial state, and that the initial state is reachable from any state.