Application of comparability graphs in decomposition of Petri nets

Abstract

In the article we present a new algorithm of Petri net decomposition into State Machine Components (SMCs). The idea bases on the application of the comparability graph theory. The comparability graphs are classified as a subclass of the perfect graphs and have unique properties. If a graph belongs to the comparability class, many problems (like graph coloring, maximal clique problem) can be solved in polynomial time. Therefore, if the sequentiality graph of a Petri net belongs to comparability class, the whole decomposition process turns to be polynomial. The preliminary experiments have demonstrated the effectiveness of the proposed idea. Over 90% of concurrency and sequentiality graphs of tested benchmarks belong to the comparability class. The efficiency is even higher if the Petri net class is reduced to the EFC (Extended Free-Choice).