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Computation of elementary siphons proposed by Li et al. is essential for deadlock control and expensive since complete siphon enumeration of the Petri net is needed, and the number of strict minimal siphons (SMS) grows quickly and exponentially with the size of the net. They assumed that the siphon constructed from each resource circuit is an elementary one and proposed a polynomial algorithm to compute elementary siphons. However, the author demonstrates a counter example where there may be an exponential number of resource circuits. Hence, constructing elementary siphons from resource circuits will result in an exponential number of elementary siphons, which is wrong. The author then develops a polynomial algorithm to find elementary siphons, which also constructs all SMS on the way. This is because, in the method proposed by Li et al., a linear algebraic expression must be established for each dependent siphon, which implies, all SMS must be located. However, all elementary siphons with polynomial complexity can be located.
Inspec keywords: linear algebra; Petri nets; computational complexity; flexible manufacturing systems
Other keywords: Petri net; incremental approach; linear algebraic expression; elementary siphon; polynomial algorithm; flexible manufacturing system; polynomial complexity; deadlock control; strict minimal siphon
Subjects: Combinatorial mathematics; Algebra; Control technology and theory; Algebra; Manufacturing systems; Computational complexity; Combinatorial mathematics; Control applications in manufacturing processes