Minimization of SM-Covers of Petri Net Specifications of Control Systems

Some methods of implementation of the concurrent systems require obtaining their cover with the sequential processes. There exists a range of algorithms generating such covers, which however may be redundant. The paper deals with this kind of redundancy in the context of Petri nets. The following task is considered: a Petri net is given, and a set of State Machine subnets covering the net is constructed; its minimum subset still covering the net has to be obtained. The task is solved using the hypergraph representation of the system. It is shown that in many cases the exact minimization can be obtained in polynomial time.