A method to determine the number of firings by classification of petri net structure and addition of counter place.

In order t o solve the reachability problem of Petri nets, two approaches, reachability tree and matrix equation, are usually applied. Firing count vector which is a solution of matrix equation will give us available information when using the method of matrix equation. T h e major problem using matrix analysis is the lack of information of firing sequences and the existence of spurious solutions. I n ordinary cases, an incidence matrix does not have full rank t h a t is necessary condition to obtain the inverse matrix for the solutions of the matrix equation. Research must be done to determine which solutions should be tried as firing count vectors which number may be possibly infinite. This paper takes aim a t the classification of solutions of matrix equation related to parallel structure of a Petri net. A firing counter vector can be obtained as a solution of the matrix equation and a solution must be expressed by a form of one special solution and a n arbitrary linear combination of its fundamental solutions. Because the fundamental solutions are the transition invariant, the spurious solutions must be related t o the structure of the Petri net. T h e authors classify the solutions only related to parallel structure of a Petri net and show the number of these solutions must be finite. Certainly, we will also discuss the other solutions related to cycle structure and give a hint to solve those solutions.

show abstract

Classification of solutions of matrix equation related to parallel structure of a Petri net

Miyazawa

Tanaka

Sekiguchi

Proceedings 1996 IEEE Conference on Emerging Technologies and Factory Automation. ETFA '96

View full text Add to dashboard Cite

show abstract

A research on Petri net properties using transitive matrix

Liu

Itoh²,

Miyazawa³

et al.

IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028)

View full text Add to dashboard Cite

A method for adding counter-places to the incidence matrix of Petri net

Tanaka

Hikichi

Maruyama

et al.

Proceedings of the 1992 International Conference on Industrial Electronics, Control, Instrumentation, and Automation

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

A method to determine the number of firings by classification of petri net structure and addition of counter place.

Cited by 8 publications

References 1 publication

Classification of solutions of matrix equation related to parallel structure of a Petri net

Classification of solutions of matrix equation related to parallel structure of a Petri net

A research on Petri net properties using transitive matrix

A method for adding counter-places to the incidence matrix of Petri net

Contact Info

Product

Resources

About