An algorithm to compute the minimal siphons in S4PR nets

Authors:
Elia Esther Cano;Carlos A. Rovetto;José-Manuel Colom
Affiliations:
Computer Systems Engineering Department, Technological University of Panama, Panama City, Panama;Computer Systems Engineering Department, Technological University of Panama, Panama City, Panama;Aragón Institute of Research Engineering (I3A), University of Zaragoza, Zaragoza, Spain
Venue:
Discrete Event Dynamic Systems
Year:
2012

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Abstract

Minimal siphons in the class of S 4 PR nets have become a conceptual and practical central tool for the study of the resource allocation related aspects in discrete event dynamic systems as, for example, the existence of deadlocks. Therefore the availability of efficient algorithms to compute the minimal siphons is essential. In this paper we try to take advantage of the particular properties of the siphons in S 4 PR to obtain an efficient algorithm. These properties allow us to express minimal siphons as the union of pruned minimal siphons containing only one resource. The pruning operation is built from the binary pruning relation defined on the set of minimal siphons containing only one resource. This pruning relation is represented by means of a directed graph. The computation of the minimal siphons is based on the maximal strongly connected components of this graph. The algorithm is highly economic in memory in all intermediate steps when compared to the classical algorithms.