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Assigning the cover of Petri nets with subnets of the automatic type

Dylewski R.

Przegląd Elektrotechniczny

2013

R. 89, nr 11

285-289

In the article the problem of the decomposition of a concurrent digital automaton for its state machine components is considered. A new method of cover is proposed with safe, live and reversible Petri nets. In order to determine basic and correct P-invariants which generate strongly connected subnets of the state machine type the suitable linear programming problem based on the matrix of marking corresponding to the global states of the net is used. The operating of the method for the example Petri nets is illustrated and benefits in relation to other methods are presented.

W artykule rozważa się problem dekompozycji współbieżnego automatu cyfrowego na jego sekwencyjne składowe automatowe. Zaproponowano nową metodę pokrycia bezpiecznych, żywych i powracanych sieci Petriego. Do wyznaczania p-inwariantów podstawowych i poprawnych, generujących mocno spójne podsieci typu maszyna stanów używa się odpowiedniego zadania programowania liniowego, bazującego na macierzy znakowań odpowiadającej stanom globalnym sieci. Zilustrowano działanie metody dla przykładowych sieci Petriego i przedstawiono zalety w stosunku do innych metod.

Diagnosis-time assessment in discrete event systems using timed Petri nets

Tabakow I.

Systems Science

2008

Vol. 34, no 3

17-23

This paper describes a method of diagnosis-time assessment in discrete event systems. Any such system is modelled by a live, bounded, and reversible place-transition Petri net N. There are assumed some deterministically given delays associated with the transitions of N, and hence, N is assumed to be deterministic timed. Without loss of generality, the single place fault model is considered below and the corresponding diagnosis process is assumed to be sequential. The notions of D-partition of the set of places P of a given place-transition net N and net k-distinguishability are first introduced. Then, the corresponding net place invariants are computed. The system k-distinguishability measure is obtained in a unique way from the place-invariant matrix. For a large value of k, the system model is extended by using some set of additional places called test points and at the same time preserving the original net properties. In accordance with the above assumption of sequential fault diagnosis, the process of fault isolation is carried out step by step, where each step depends on the result of the diagnostic experiment at the previous step. Hence, the diagnosis-time assessment is realised by computing the absolute value of the time difference between the minimum cycle time of N and the worst-case fault-isolation time according to the diagnostic tree obtained. The complexity of the method proposed depends on the effectivity of the existing algorithms for computation of the P-cover, i.e., the set of P-invariants covering N. The approach proposed can be extended to higher level Petri nets, e.g., such as coloured ones. Several examples are given.