**Author details**

Samir Hamaci, Karim Labadi and A.Moumen Darcherif *EPMI, 13 Boulvard de l'Hautil, 95092, Cergy-Pontoise, France*

#### **8. References**


© 2012 Lee et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 Lee et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Reachability Criterion with** 

Gi Bum Lee, Han Zandong and Jin S. Lee

http://dx.doi.org/10.5772/50518

**1. Introduction** 

of a Petri net [14].

Additional information is available at the end of the chapter

**Sufficient Test Space for Ordinary Petri Net** 

Petri nets (PN) are widely recognized as a powerful tool for modelling and analyzing discrete event systems, especially systems are characterized by synchronization, concurrency, parallelism and resource sharing [1, 2]. One of the major advantages of using Petri net models is that the PN model can be used for the analysis of behaviour properties and performance evaluation, as well as for systematic construction of discrete-event simulators and controllers [3, 4]. The reachability from an initial marking to a destination marking is the most important issue for the analysis of Petri nets. Many other problems such

Two basic approaches are usually applied to solve the reachability problem. One is the construction of reachability tree [7, 8]. It can obtain all the reachable markings, but the computation complexity is exponentially increased with the size of a PN. The other is to solve the state equation [9]. The solution of the matrix equation provides a firing count vector that describes the relation between initial marking and reachable markings. Its major problem is

Many researchers have investigated the reachability problem [10, 11]. Iko Miyazawa *et al*. have utilized the state equation to solve the reachability problem of Petri nets with parallel structures [12]. Tadashi Matsumoto *et al*. have presented a formal necessary and sufficient condition on reachability of general Petri nets with known firing count vectors [13]. Tadao Murata's paper has concentrated on presenting and analyzing Petri nets as discrete time systems. Controllability and reachability are analyzed in terms of the matrix representation

In most cases, it is not necessary to find all reachable markings. One of the most important things is to know whether a given marking is reachable or not. If the destination marking

as liveness and coverability can be deduced from this reachability problem [5, 6].

the lack of information of firing sequences and the existence of spurious solutions.
