Towards Building the State Class Graph of the TSPN Model

Article type: Research Article

Authors: Abdelli, Abdelkrim | Badache, Nadjib

Affiliations: Department of Computer Science, LSI laboratory Algiers, USTHB University, Alger. {Abdelli, Badache}@lsi-usthb.dz

Note: [] Address for correspondence: Bp 32 El Alia Bab ezzouar Algiers Algeria 16111, Alger

Abstract: In this paper, we propose an enumerative approach to build the state class graph of the TSPN (Time Stream Petri Net) model. A TSPN model is a Petri net augmented with intervals on arcs and synchronization rules on transitions. It can be used to model complex systems, and it is proved to be more expressive than TPN (Time Petri Nets). In contrast with TPN where each class accessible in the graph is given as a pair (M,D) where M is a marking and D is a system of DBM inequalities, a TSPN class in this form is much complex to compute. To tackle this issue, we introduce a new formalism called the time distance function to define a TSPN class. This function makes it possible to determine an efficient algorithm to compute each class of the graph in a square complexity time. Finally, we show how to exploit the TSPN state class graph (when finite), to check over either linear properties of the model, or to compute minimal and maximal time distances of any firing sequence.

Keywords: Time Stream Petri Net, Time Petri Net, State class graph, Time distance function, Difference bound Matrix, Multimedia

Journal: Fundamenta Informaticae, vol. 86, no. 4, pp. 371-409, 2008