An algorithm for an optimal set of elementary siphons in Petri nets for deadlock control

Elementary siphons are important concepts in Petri net theory. Based on them, effective deadlock control can be developed for a net system. The research shows that different sets of elementary siphons have different effects in terms of reachable states using a same control synthesis method. This work illustrates an algorithm, which can find an optimal set of elementary siphons in polynomial time given all siphons. Its use produces more reachable states of the controlled net than other ones do when a same deadlock control policy is applied. Our research starts with theoretical results and ends with experimental ones.