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An Effective Algorithm to Find Elementary Siphons in a Class of Petri Nets

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4 Author(s)
Anrong Wang ; Sch. of Electro-Mech. Eng., Xidian Univ., Xi''an ; Li, Z. ; Jianyuan Jia ; MengChu Zhou

As a structural object of Petri nets, siphons play a key role in the development of deadlock prevention policies for resource allocation systems. Elementary siphons are a novel concept in net theory. Based on graph theory, this paper proposes an effective algorithm with polynomial complexity to find a set of elementary siphons for a linear system of simple sequential processes with resources (LS3 PR), a subclass of Petri nets, which can model many flexible manufacturing systems. The algorithm is established through the use of a resource directed graph and complementary sets of strict minimal siphons (SMS) of the net. The upper bound of the number of SMS in such a net is identified. A running example is used to demonstrate the proposed method.

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Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on  (Volume:39 ,  Issue: 4 )