Download Augmented Marked Graphs by King Sing Cheung PDF

By King Sing Cheung

Petri nets are a proper and theoretically wealthy version for the modelling and research of structures. A subclass of Petri nets, augmented marked graphs own a constitution that's in particular fascinating for the modelling and research of structures with concurrent methods and shared resources.

This monograph comprises 3 elements: half I presents the conceptual heritage for readers who've no previous wisdom on Petri nets; half II elaborates the idea of augmented marked graphs; eventually, half III discusses the applying to approach integration. The e-book is acceptable as a primary self-contained quantity on augmented marked graphs, and may be priceless to either researchers and practitioners within the fields of Petri nets and procedure integration.

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7, S5 ¼ { p1, p3, p7 } is a NR-siphon. S5 itself is also a trap marked by M0. 3 Liveness and Reversibility of Augmented Marked Graphs In the literature, the liveness and reversibility of augmented marked graphs were mainly studied by Chu [1] and Cheung [2–4]. Siphon-based characterizations and cycle-based charcterizations are reported. This section investigates the liveness and reversibility of augmented marked graphs. It starts with the siphon-based characterizations. A cycle-inclusion property is then introduced, and the cycle-based characterizations would follow.

All of them are marked. 5 Let (N, M0; R) be an augmented marked graph. For every r ∈ R, there exists a minimal siphon which contains only one marked place r. Proof For each r ∈ R, let Dr ¼ { hts1, th1i, hts2, th2i, . , htsn, thni }, where r• ¼ { ts1, ts2, . , tsn } and •r ¼ { th1, th2, . , thn }. For each htsi, thii ∈ Dr, tsi connects to thi via an elementary path ρi which is not marked. Let S ¼ P1 [ P2 [ . . [ Pn [ { r }, where Pi is the set of places in ρi. For each p ∈ Pi, | •p | ¼ | p• | ¼ 1.

Step 3. 43 p3 p4 t4 p5 p6 t5 t6 Find all R-siphons based on ΩN[R]. Check if every R-siphon contains a marked trap. If yes, report (N, M0; R) is live and reversible. Otherwise, go to Step 3. For each R-siphon which does not contain any marked trap, check if it would never become empty. If yes, report (N, M0; R) is live and reversible. Otherwise, report (N, M0; R) is neither live nor reversible. In the following, we define another property, called cycle-inclusion property, for augmented marked graphs.

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