Abstract
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.
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References
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)
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)
Abdulla, P.A., Jonsson, B.: Model checking of systems with many identical timed processes. Theoretical Computer Science 290(1), 241–264 (2003)
Alur, R.: Techniques for Automatic Verification of Real-Time Systems. PhD thesis, Dept. of Computer Sciences, Stanford University (1991)
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)
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)
Bowden, F.D.J.: Modelling time in Petri nets. In: Proc. Second Australian-Japan Workshop on Stochastic Models (1996)
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.
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)
Godskesen, J.C.: Timed Modal Specifications. PhD thesis, Aalborg University (1994)
Higman, G.: Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 2, 326–336 (1952)
Karp, R.M., Miller, R.E.: Parallel program schemata. Journal of Computer and Systems Sciences 3(2), 147–195 (1969)
Mayr, R.: Undecidable problems in unreliable computations. TCS 297(1-3), 337–354 (2003)
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)
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)
Valk, R., Jantzen, M.: The Residue of Vector Sets with Applications to Decidability Problems in Petri Nets. Acta Informatica 21, 643–674 (1985)
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Abdulla, P., Mahata, P., Mayr, R. (2004). Decidability of Zenoness, Syntactic Boundedness and Token-Liveness for Dense-Timed Petri Nets. In: Lodaya, K., Mahajan, M. (eds) FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2004. Lecture Notes in Computer Science, vol 3328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30538-5_6
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DOI: https://doi.org/10.1007/978-3-540-30538-5_6
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