Decidability of Zenoness, Syntactic Boundedness and Token-Liveness for Dense-Timed Petri Nets

  • Parosh Abdulla
  • Pritha Mahata
  • Richard Mayr
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3328)


We consider Timed Petri Nets (TPNs) : extensions of Petri nets in which each token is equipped with a real-valued clock. We consider the following three verification problems for TPNs.

(i) Zenoness: whether there is an infinite computation from a given marking which takes only a finite amount of time. We show decidability of zenoness for TPNs, thus solving an open problem from [dFERA00].

(ii) Token Liveness: whether a token is alive in a marking, i.e., whether there is a computation from the marking which eventually consumes the token.We show decidability of the problem by reducing it to the coverability problem,which is decidable for TPNs.

(iii)Boundedness: whether the size of the reachable markings is bounded. We consider two versions of the problem; namely semantic boundedness where only live tokens are taken into consideration in the markings,and syntactic boundedness where also dead tokens are considered. We show undecidability of semantic boundedness, while we prove that syntactic boundedness is decidable through an extension of the Karp-Miller algorithm.


Minimal Element Coverability Problem Input Place Output Place Discrete Time Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AD90]
    Alur, R., Dill, D.: Automata for modelling real-time systems. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 322–335. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  2. [ADM04]
    Abdulla, P.A., Deneux, J., Mahata, P.: Multi-clock timed networks. In: Proc. LICS 2004, pp. 345–354. IEEE Computer Society Press, Los Alamitos (2004)Google Scholar
  3. [AJ03]
    Abdulla, P.A., Jonsson, B.: Model checking of systems with many identical timed processes. Theoretical Computer Science 290(1), 241–264 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  4. [Alu91]
    Alur, R.: Techniques for Automatic Verification of Real-Time Systems. PhD thesis, Dept. of Computer Sciences, Stanford University (1991)Google Scholar
  5. [AN01]
    Abdulla, P.A., Nylén, A.: Timed Petri nets and BQOs. In: Colom, J.-M., Koutny, M. (eds.) ICATPN 2001. LNCS, vol. 2075, pp. 53–70. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. [AN02]
    Abdulla, P.A., Nylén, A.: Undecidability of ltl for timed petri nets. In: INFINITY 2002, 4th International Workshop on Verification of Infinite-State Systems (2002)Google Scholar
  7. [Bow96]
    Bowden, F.D.J.: Modelling time in Petri nets. In: Proc. Second Australian-Japan Workshop on Stochastic Models (1996)Google Scholar
  8. [dFERA00]
    D. de Frutos Escrig, V. Valero Ruiz, and O. Marroquín Alonso. Decidability of properties of timed-arc Petri nets. In ICATPN 2000, number 1825 in Lecture Notes in Computer Science, pages 187–206, 2000.CrossRefGoogle Scholar
  9. [DJS99]
    Dufourd, C., Jančar, P.: Boundedness of Reset P/T Nets. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, p. 301. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  10. [God94]
    Godskesen, J.C.: Timed Modal Specifications. PhD thesis, Aalborg University (1994)Google Scholar
  11. [Hig52]
    Higman, G.: Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 2, 326–336 (1952)zbMATHCrossRefMathSciNetGoogle Scholar
  12. [KM69]
    Karp, R.M., Miller, R.E.: Parallel program schemata. Journal of Computer and Systems Sciences 3(2), 147–195 (1969)zbMATHMathSciNetCrossRefGoogle Scholar
  13. [May03]
    Mayr, R.: Undecidable problems in unreliable computations. TCS 297(1-3), 337–354 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  14. [RGdFE99]
    Valero Ruiz, V., Cuartero Gomez, F., de Frutos Escrig, D.: On non-decidability of reachability for timed-arc Petri nets. In: Proc. 8th International Workshop on Petri Nets and Performance Models, pp. 88–196 (1999)Google Scholar
  15. [Tri99]
    Tripakis, S.: Verifying progress in times systems. In: Katoen, J.-P. (ed.) AMAST-ARTS 1999, ARTS 1999, and AMAST-WS 1999. LNCS, vol. 1601, pp. 299–314. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  16. [VJ85]
    Valk, R., Jantzen, M.: The Residue of Vector Sets with Applications to Decidability Problems in Petri Nets. Acta Informatica 21, 643–674 (1985)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Parosh Abdulla
    • 1
  • Pritha Mahata
    • 1
  • Richard Mayr
    • 2
  1. 1.Uppsala UniversitySweden
  2. 2.North Carolina State UniversityRaleighUSA

Personalised recommendations