Abstract
Timed-arc Petri nets (TAPN’s) are not Turing powerful, because, in particular, they cannot simulate a counter with zero testing. Thus, we could think that this model does not increase significantly the expressiveness of untimed Petri nets. But this is not true; in a previous paper we have shown that the differences between them are big enough to make the reachability problem undecidable. On the other hand, coverability and boundedness are proved now to be decidable. This fact is a consequence of the close interrelationship between TAPN’s and transfer nets, for which similar results have been recently proved. Finally, we see that if dead tokens are defined as those that cannot be used for firing any transition in the future, we can detect these kind of tokens in an effective way.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
W.M.P. van der Aalst. Interval Timed Coloured Petri Nets and their Analysis. LNCS vol. 691, pp. 451–472. 1993.
P.A. Abdulla, K. Čerāns, B. Jonsson and T. Yih-Kuen. General Decidability Theorems for Infinite-State Systems. Proc. 11th IEEE Symp. Logic in Computer Science (LICS’96), New Brunswick, NJ, USA, July 1996, pages 313–321. 1996.
M. Ajmone Marsan, G. Balbo, A. Bobbio, G. Chiola, G. Conte and A. Cumani. On Petri Nets with Stochastic Timing. Proc. of the International Workshop on Timed Petri Nets, IEEE Computer Society Press, pp. 80–87. 1985.
A. Arnold and M. Latteux. Vector Addition Systems and Semi-Dyck Language. Research Report 78, Laboratoire de Calcul de l’Université des Sciences et Techniques de LILLE, December 1976.
T. Bolognesi and P. Cremonese. The Weakness of Some Timed Models for Concurrent Systems. Technical Report CNUCE C89-29. CNUCE-C.N.R. October 1989.
T. Bolognesi, F. Lucidi and S. Trigila. From Timed Petri Nets to Timed LOTOS. Proc. of the 10th International IFIP WG6.1 Symposium on Protocol Specification, Testing and Verification, North-Holland. 1990.
F.D.J. Bowden. Modelling Time in Petri Nets. Proc. Second Australia-Japan Workshop on Stochastic Models. 1996.
A. Cerone and A. Maggiolo-Schettini. Time-based Expressivity of Time Petri Nets for System Specification. Theoretical Computer Science (216)1–2, pp. 1–53. 1999.
C. Dufourd, A. Finkel and Ph. Schnoebelen. Reset Nets between Decidability and Undecidability. Proc. 25th. Int. Coll. Automata, Languages, and Programming (ICALP’98), Aalborg, Denmark, July 1998, LNCS vol. 1443, pp:103–115. Springer-Verlag, 1998.
C. Dufourd. Réseaux de Petri avec Reset/Transfert: Décidabilité et Indécidabilité. Thése de Docteur en Sciences de l’École Normale Supérieure de Cachan. October 1998.
C. Dufourd, P. Jančar and Ph. Schnoebelen. Boundedness of Reset P/T Nets. Proc. 26th. Int. Coll. Automata, Languages, and Programming (ICALP’99), Prague, Czech Rep., July 1999, LNCS vol. 1644, pp. 301–310. Springer-Verlag, 1999.
A. Finkel. Reduction and Covering of Infinite Reachability Trees. Information and Computation, 89(2):144–179, 1990.
A. Finkel and Ph. Schnoebelen. Fundamental Structures in Well-Structured Infinite Transition Systems. Proc. 3rd Latin American Theoretical Informatics Symposium (LATIN’98), Campinas, Brazil, Apr. 1998, LNCS vol. 1380, pp:102–118. Springer-Verlag, 1998.
H.-M. Hanisch. Analysis of Place/Transition Nets with Timed-Arcs and its Application to Batch Process Control. Application and Theory of Petri Nets, LNCS vol. 691, pp:282–299. Springer-Verlag, 1993.
R. Mayr. Lossy Counter Machines. Technical report TUM-I9827, TU-München, 1998.
P. Merlin. A Study of the Recoverability of Communication Protocols. PhD. Thesis, Univ. of California. 1974.
J. L. Peterson. Petri net Theory, and the Modeling of Systems. Prentice-Hall. 1981.
J. Quemada, A. Azcorra, and D. de Frutos. A Timed Calculus for LOTOS. Proc. FORTE’89, pp. 245–264. 1989.
C. Ramchandani. Performance Evaluation of Asynchronous Concurrent Systems by Timed Petri Nets. PhD. Thesis, Massachusetts Institute of Technology, Cambridge. 1973.
J. Sifakis. Use of Petri Nets for Performance Evaluation. Proc. of the Third International Symposium IFIP W.G.7.3., Measuring, Modelling and Evaluating Computer Systems. Elsevier Science Publishers, pp. 75–93. 1977.
V. Valero, D. de Frutos Escrig, and F. Cuartero. Decidability of the Strict Reachability Problem for TPN’s with Rational and Real Durations. Proc. 5th. International Workshop on Petri Nets and Performance Models, pp. 56–65. 1993.
V. Valero, D. de Frutos Escrig, and F. Cuartero. On Non-Decidability of Reachability for Timed-Arc Petri Nets. Proc. 8th. International Workshop on Petri Nets and Performance Models, pp. 188–196. 1999.
B. Walter. Timed Petri-Nets for Modelling and Analysing Protocols with Real-Time Characteristics. Proc. 3rd IFIP Workshop on Protocol Specification, Testing and Verification, North-Holland. 1983.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Escrig, D.d.F., Ruiz, V.V., Alonso, O.M. (2000). Decidability of Properties of Timed-Arc Petri Nets. In: Nielsen, M., Simpson, D. (eds) Application and Theory of Petri Nets 2000. ICATPN 2000. Lecture Notes in Computer Science, vol 1825. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44988-4_12
Download citation
DOI: https://doi.org/10.1007/3-540-44988-4_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67693-5
Online ISBN: 978-3-540-44988-1
eBook Packages: Springer Book Archive