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Analysis and Synthesis of Weighted Marked Graph Petri Nets : Exact and Approximate Methods

Devillers Raymond, Hujsa Thomas

Fundamenta Informaticae

2019

Vol. 169, nr 1-2

1--30

Numerous real-world systems can be modeled with Petri nets, which allow a combination of concurrency with synchronizations and conflicts. To alleviate the difficulty of checking their behaviour, a common approach consists in studying specific subclasses. In the converse problem of Petri net synthesis, a Petri net of some subclass has to be constructed efficiently from a given specification, typically from a labelled transition system (lts) describing the behaviour of the desired net. In this paper, we focus on a notorious subclass of persistent Petri nets, the weighted marked graphs (WMGs), also called generalised (or weighted) event (or marked) graphs or weighted T-nets. In such nets, edges have multiplicities (weights) and each place has at most one ingoing and one outgoing transition. Although extensively studied in previous works and benefiting from strong results, both their analysis and synthesis can be further investigated. We provide new behavioural properties of WMGs expressed on their reachability graph, notably backward persistence and strong similarities between any two sequences sharing the same starting state and the same destination state. Besides, we design a general synthesis procedure aiming at the WMG class. Finally, when no solution to the synthesis problem exists, i.e., when the given lts is not WMG-solvable, we show how to construct a WMG whose reachability graph is a minimal over-approximation of the given lts.

Deadlock freeness supervisor for marked graph

Sioud H., Achour Z., Sava A., Rezg N.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2009

Vol. 57, nr 3

281-289

This note presents a control synthesis approach for discrete event systems modeled by marked graphs with uncontrollable transitions. The forbidden behavior is specified by General Mutual Exclusion Constraints (GMEC). We prove that, even if the system to be controlled .s live, the closed loop control may generate deadlock situations. Using the structural proprieties of marked graph we defined the causes of deadlock situations, and we defined a formal method to avoid them.