Abstract
We extend discrete-timed Petri nets with a cost model that assigns token storage costs to places and firing costs to transitions, and study the minimal cost reachability/coverability problem. We show that the minimal costs are computable if all storage/transition costs are non-negative, while even the question of zero-cost coverability is undecidable in the case of general integer costs.
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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)
Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)
Alur, R., Torre, S.L., Pappas, G.J.: Optimal paths in weighted timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 49–62. Springer, Heidelberg (2001)
Berthomieu, B., Diaz, M.: Modeling and verification of time dependent systems using time Petri nets. IEEE Trans. on Software Engineering 17(3), 259–273 (1991)
Bouyer, P., Brihaye, T., Bruyère, V., Raskin, J.-F.: On the optimal reachability problem of weighted timed automata. Formal Methods in System Design 31(2), 135–175 (2007)
Bowden, F.D.J.: Modelling time in Petri nets. In: Proc. Second Australian-Japan Workshop on Stochastic Models (1996)
de Frutos Escrig, D., Ruiz, V.V., Alonso, O.M.: Decidability of Properties of Timed-Arc Petri Nets. In: Nielsen, M., Simpson, D. (eds.) ICATPN 2000. LNCS, vol. 1825, pp. 187–206. Springer, Heidelberg (2000)
Dickson, L.E.: Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors. Amer. J. Math. 35, 413–422 (1913)
Ghezzi, C., Mandrioli, D., Morasca, S., Pezzè, M.: A unified high-level Petri net formalism for time-critical systems. IEEE Trans. on Software Engineering 17(2), 160–172 (1991)
Jančar, P.: Decidability of a temporal logic problem for Petri nets. Theoretical Computer Science 74, 71–93 (1990)
Larsen, K.G., Behrmann, G., Brinksma, E., Fehnker, A., Hune, T., Pettersson, P., Romijn, J.: As cheap as possible: Efficient cost-optimal reachability for priced timed automata. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, p. 493. Springer, Heidelberg (2001)
Mayr, E.: An algorithm for the general Petri net reachability problem. SIAM Journal of Computing 13, 441–460 (1984)
Merlin, P., Farber, D.: Recoverability of communication protocols - implications of a theoretical study. IEEE Trans. on Computers, COM 24, 1036–1043 (1976)
Razouk, R., Phelps, C.: Performance analysis using timed Petri nets. In: Protocol Testing, Specification, and Verification, pp. 561–576 (1985)
Reinhardt, K.: Reachability in Petri nets with inhibitor arcs. In: Proc. RP 2008, 2 nd Workshop on Reachability Problems (2008)
Ruiz, V.V., Gomez, F.C., de Frutos Escrig, D.: On non-decidability of reachability for timed-arc Petri nets. In: Proc. 8th Int. Workshop on Petri Net and Performance Models (PNPM 1999), Zaragoza, Spain, 8-10 October 1999, pp. 188–196 (1999)
Valk, R., Jantzen, M.: The residue of vector sets with applications to decidability problems in Petri nets. Acta Inf., 21 (1985)
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Abdulla, P.A., Mayr, R. (2009). Minimal Cost Reachability/Coverability in Priced Timed Petri Nets. In: de Alfaro, L. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2009. Lecture Notes in Computer Science, vol 5504. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00596-1_25
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DOI: https://doi.org/10.1007/978-3-642-00596-1_25
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