On the computation of the minimal siphons of S4PR nets from a generating family of siphons

Minimal siphons in the class of S⁴PR nets have become a conceptual and practical central tool to deal with deadlocks caused by the sharing of resources in Flexible Manufacturing Systems. The availability of efficient algorithms to compute these structural objects is very important. In this paper we take advantage from the particular properties of the siphons in S⁴PR to obtain an efficient algorithm. These properties allow to compute the minimal siphons from a generating family of minimal siphons. This family is composed by the minimal siphons containing only one resource. The computation of the minimal siphons is based in the maximal strongly connected components of a graph representing the relations between the siphons of the generating family. The algorithm is very economic in memory in all intermediate steps with respect to the classical algorithms.