An algorithm for the minimum initial marking problem of a structurally live Petri net with inhibitor arcs

Abstract

Inhibitor arcs increase the expressive power of Petri nets. However, they also make Petri net analysis more complex. Some properties of an ordinary Petri net are not always inherited in its extended version with inhibitor arcs. This paper reports a necessary and sufficient condition for deciding the structurally live property in an original Petri net and its extended one with inhibitor arcs. In addition, supposing that a net is structurally live, a natural problem is how to distribute the minimal number of tokens into the structurally live net to ensure that the marked net is live. A method is developed to find an optimal token allocation solution by putting tokens only in some key places. The algorithm can be completed within polynomial time, which overcomes the drawback of exhaustive solutions from all possible markings. Examples are given to illustrate the proposed approach. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.