Abstract
This paper presents new results concerned with liveness, liveness of a subset of transitions and deadlock in Petri nets. Liveness is seen as a particular case of what we call T-liveness: all transitions in the set T are live. The first results characterize the relation between supervisors enforcing liveness and T-liveness with supervisors preventing deadlock. Then we introduce a class of Petri net subnets allowing us to extendt wo well known results. Specifically we generalize the result relating deadlock to siphons and the extension to asymmetric choice Petri nets of the Commoner’s Theorem. We conclude by considering how the theoretical results of this paper can be used for deadlock prevention, least restrictive deadlock prevention and least restrictive T-liveness enforcement.
The authors gratefully acknowledge the partial support of the National Science Foundation (ECS-9912458) and of the Army Research Office (DAAG55-98-1-0199).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
K. Barkaoui and J. F. Pradat-Peyre. On liveness andcon trolledsiphons in Petri nets. In Lecture Notes in Computer Science: 17th International Conference in Application and Theory of Petri Nets (ICATPN’96), Osaka, Japan, volume 1091, pages 57–72. Springer-Verlag, June 1996.
J. Desel and J. Esparza. Free Choice Petri nets. Number 40 in Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1995.
J. Desel and W. Reisig. Place/transition petri nets. Lecture Notes in Computer Science: Lectures on Petri Nets I: Basic Models, 1491:122–173, 1998.
K. X. He and M. D. Lemmon. Liveness verification of discrete event systems modeled by n-safe ordinary Petri nets. In Nielsen, M. and Simpson, D., editors, Lecture Notes in Computer Science: 21st International Conference on Application and Theory of Petri Nets (ICATPN 2000), Aarhus, Denmark, June 2000, volume 1825, pages 227–243. Springer-Verlag, 2000.
M. V. Iordache, J. O. Moody, and P. J. Antsaklis. A method for deadlock prevention in discrete event systems using Petri nets. Technical report of the isis group, isis-99-006, University of Notre Dame, July 1999.
M. V. Iordache, J. O. Moody, and P. J. Antsaklis. Automated synthesis of deadlock prevention supervisors using Petri nets. Technical report of the isis group, isis-2000-003, University of Notre Dame, May 2000.
M. V. Iordache, J. O. Moody, and P. J. Antsaklis. Automated synthesis of liveness enforcement supervisors using Petri nets. Technical report of the isis group, isis-2000-004, University of Notre Dame, September 2000.
M. V. Iordache, J. O. Moody, and P. J. Antsaklis. A method for the synthesis of deadlock prevention controllers in systems modeled by Petri nets. In Proceedings of the 2000 American Control Conference, pages 3167–3171, June 2000.
K. Lautenbach and H. Ridder. The linear algebra of deadlock avoidance-a Petri net approach. Technical report, University of Koblenz, Institute for Computer Science, 1996.
T. Murata. Petri nets: Properties, analysis andapplications. In Proceedings of the IEEE, pages 541–580, April 1989.
W. Reisig. Petri Nets, volume 4 of EATCS Monographs on Theoretical Computer Science. Springer-Verlag, 1985.
S. R. Sreenivas. On a free-choice equivalent of a Petri net. In Proceedings of the 36th IEEE Conference on Decision and Control, pages 4092–4097, San Diego, California, December 1997.
S. R. Sreenivas. On the existence of supervisory policies that enforce liveness in discrete event dynamic systems modeled by controlled Petri nets. IEEE Transactions on Automatic Control, 42(7):928–945, July 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Iordache, M.V., Antsaklis, P.J. (2001). Generalized Conditions for Liveness Enforcement and Deadlock Prevention in Petri Nets. In: Colom, JM., Koutny, M. (eds) Applications and Theory of Petri Nets 2001. ICATPN 2001. Lecture Notes in Computer Science, vol 2075. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45740-2_12
Download citation
DOI: https://doi.org/10.1007/3-540-45740-2_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42252-5
Online ISBN: 978-3-540-45740-4
eBook Packages: Springer Book Archive