Abstract
Time dependant models have been intensively studied for many reasons, among others because of their applications in software verification and due to the development of embedded platforms where reliability and safety depend to a large extent on the time features. Many of the time dependant models were suggested as real-time extensions of several well-known untimed models. The most studied formalisms include Networks of Timed Automata which extend the model of communicating finite-state machines with a finite number of real-valued clocks, and timed extensions of Petri nets where the added time constructs include e.g. time intervals that are assigned to the transitions (Time Petri Nets) or to the arcs (Timed-Arc Petri Nets). In this paper, we shall semi-formally introduce these models, discuss their strengths and weaknesses, and provide an overview of the known results about the relationships among the models.
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
Abdulla, P.A., Mahata, P., Mayr, R.: Dense-timed Petri nets: Checking zenoness, token liveness and boundedness. Logical Methods in Computer Science 3(1), 1–61 (2007)
Abdulla, P.A., Nylén, A.: Better is better than well: On efficient verification of infinite-state systems. In: Proceedings of 15th Annual IEEE Symposium on Logic in Computer Science (LICS 2000), pp. 132–140 (2000)
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., Deneux, J., Mahata, P., Nylén, A.: Forward reachability analysis of timed Petri nets. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS 2004 and FTRTFT 2004. LNCS, vol. 3253, pp. 343–362. Springer, Heidelberg (2004)
Aceto, L., Laroussinie, F.: Is your model checker on time? On the complexity of model checking for timed modal logics. Journal of Logic and Algebraic Programming, 52–53, 7–51 (2002)
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)
Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)
Alur, R., La Torre, S., Pappas, G.J.: Optimal paths in weighted timed automata. Theoretical Computer Science 318(3), 297–322 (2004)
Amnell, T., Behrmann, G., Bengtsson, J., D’Argenio, P.R., David, A., Fehnker, A., Hune, T., Jeannet, B., Larsen, K.G., Möller, M.O., Pettersson, P., Weise, C., Yi, W.: UPPAAL: Now, next, and future. In: Cassez, F., Jard, C., Rozoy, B., Dermot, M. (eds.) MOVEP 2001. LNCS, vol. 2067, pp. 99–124. Springer, Heidelberg (2001)
Arnold, A.: Finite Transition Systems. Prentice-Hall, Englewood Cliffs (1994)
Barreto, R., Cavalcante, S., Maciel, P.: A time Petri net approach for finding pre-runtime schedules in embedded hard real-time systems. In: Proceedings of the 24th International Conference on Distributed Computing Systems Workshops - W7: EC (ICDCSW 2004), pp. 846–851. IEEE Computer Society, Los Alamitos (2004)
Behrmann, G., Cougnard, A., David, A., Fleury, E., Larsen, K.G., Lime, D.: UPPAAL-Tiga: Timed games for everyone. In: Aceto, L., Ingolfdottir, A. (eds.) Proceedings of the 18th Nordic Workshop on Programming Theory (NWPT 2006). Reykjavik University, Reykjavik (2006)
Behrmann, G., Cougnard, A., David, A., Fleury, E., Larsen, K.G., Lime, D.: Uppaal-tiga: Time for playing games. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 121–125. Springer, Heidelberg (2007)
Behrmann, G., David, A., Larsen, K.G.: A tutorial on uppaal. In: Bernardo, M., Corradini, F. (eds.) SFM-RT 2004. LNCS, vol. 3185, pp. 200–236. Springer, Heidelberg (2004)
Bender, D.F., Combemale, B., Crégut, X., Farines, J.-M., Berthomieu, B., Vernadat, F.: Ladder metamodeling and PLC program validation through time Petri nets. In: Schieferdecker, I., Hartman, A. (eds.) ECMDA-FA 2008. LNCS, vol. 5095, pp. 121–136. Springer, Heidelberg (2008)
Bengtsson, J., Yi, W.: Timed automata: Semantics, algorithms and tools. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) Lectures on Concurrency and Petri Nets. LNCS, vol. 3098, pp. 87–124. Springer, Heidelberg (2004)
Bérard, B., Cassez, F., Haddad, S., Lime, D., Roux, O.H.: Comparison of different semantics for time Petri nets. In: Peled, D.A., Tsay, Y.-K. (eds.) ATVA 2005. LNCS, vol. 3707, pp. 293–307. Springer, Heidelberg (2005)
Bérard, B., Cassez, F., Haddad, S., Lime, D., Roux, O.H.: Comparison of the expressiveness of timed automata and time Petri nets. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 211–225. Springer, Heidelberg (2005)
Bérard, B., Cassez, F., Haddad, S., Lime, D., Roux, O.H.: When are timed automata weakly timed bisimilar to time Petri nets? In: Ramanujam, R., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 273–284. Springer, Heidelberg (2005)
Bérard, B., Cassez, F., Haddad, S., Lime, D., Roux, O.H.: When are timed automata weakly timed bisimilar to time Petri nets? Theoretical Computer Science (forthcoming, 2008)
Berthomieu, B., Peres, F., Vernadat, F.: Bridging the gap between timed automata and bounded time Petri nets. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 82–97. Springer, Heidelberg (2006)
Berthomieu, B., Ribet, P.-O., Vernadat, F.: The tool TINA — construction of abstract state spaces for Petri nets and time Petri nets. International Journal of Production Research 42(14), 2741–2756 (2004)
Berthomieu, B., Diaz, M.: Modeling and verification of time dependent systems using time Petri nets. IEEE Trans. Software Eng. 17(3), 259–273 (1991)
Berthomieu, B., Menasche, M.: An enumerative approach for analyzing time Petri nets. In: Proceedings of IFIP Congress 1983 on Information Processing, vol. 9, pp. 41–46. Elsevier Science Publishers, Amsterdam (1983)
Bolognesi, T., Cremonese, P.: The weakness of some timed models for concurrent systems. Technical Report CNUCE C89-29, CNUCE–C.N.R (1989)
Bolognesi, T., Lucidi, F., Trigila, S.: From timed Petri nets to timed LOTOS. In: Proceedings of the IFIP WG 6.1 Tenth International Symposium on Protocol Specification, Testing and Verification (Ottawa 1990), pp. 1–14. North-Holland, Amsterdam (1990)
Boucheneb, H., Gardey, G., Roux, O.H.: TCTL model checking of time Petri nets. Technical Report IRCCyN number RI2006-14, Nantes Cedex, 2006, updated in (2008)
Bouyer, P., Brinksma, E., Larsen, K.G.: Staying alive as cheaply as possible. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 203–218. Springer, Heidelberg (2004)
Bouyer, P., Chevalier, F.: On conciseness of extensions of timed automata. Journal of Automata, Languages and Combinatorics 10(4), 393–405 (2005)
Bouyer, P., Haddad, S., Reynier, P.-A.: Timed Petri nets and timed automata: On the discriminating power of zeno sequences. Information and Computation 206(1), 73–107 (2008)
Bouyer, P., Reynier, P.-A., Haddad, S.: Extended timed automata and time Petri nets. In: Proceedings of the 6th International Conference on Application of Concurrency to System Design (ACSD 2006), pp. 91–100. IEEE Computer Society, Los Alamitos (2006)
Bowden, F.D.J.: Modelling time in Petri nets. In: Proceedings of the Second Australia-Japan Workshop on Stochastic Models (1996)
Boyer, M., Diaz, M.: Non equivalence between time Petri nets and time stream Petri nets. In: Proceedings of the 8th International Workshop on Petri Nets and Performance Models (PNPM 1999), pp. 198–207. IEEE Computer Society, Los Alamitos (1999)
Boyer, M., Roux, O.H.: Comparison of the expressiveness of arc, place and transition time Petri nets. In: Kleijn, J., Yakovlev, A. (eds.) ICATPN 2007. LNCS, vol. 4546, pp. 63–82. Springer, Heidelberg (2007)
Boyer, M., Vernadat, F.: Language and bisimulation relations between subclasses of timed Petri nets with strong timing semantic. Technical Report No. 146, LAAS (2000)
Boyer, M., Diaz, M.: Multiple enabledness of transitions in Petri nets with time. In: Proceedings of the 9th international Workshop on Petri Nets and Performance Models (PNPM 2001), pp. 219–228. IEEE Computer Society, Los Alamitos (2001)
Bozga, M., Daws, C., Maler, O., Olivero, A., Tripakis, S., Yovine, S.: Kronos: A model-checking tool for real-time systems. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 546–550. Springer, Heidelberg (1998)
Bozga, M., Graf, S., Ober, I., Ober, I., Sifakis, J.: The IF toolset. In: Bernardo, M., Corradini, F. (eds.) SFM-RT 2004. LNCS, vol. 3185, pp. 237–267. Springer, Heidelberg (2004)
Cassez, F., David, A., Fleury, E., Larsen, K.G., Lime, D.: Efficient on-the-fly algorithms for the analysis of timed games. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 66–80. Springer, Heidelberg (2005)
Cassez, F., Roux, O.H.: Structural translation from time Petri nets to timed automata. Journal of Systems and Software 79(10), 1456–1468 (2006)
Čerāns, K.: Decidability of bisimulation equivalences for parallel timer processes. In: Probst, D.K., von Bochmann, G. (eds.) CAV 1992. LNCS, vol. 663, pp. 302–315. Springer, Heidelberg (1993)
Cerone, A., Maggiolio-Schettini, A.: Time-based expressivity of timed Petri nets for system specification. Theoretical Computer Science 216(1-2), 1–53 (1999)
Cortés, L.A., Eles, P., Peng, Z.: Verification of real-time embedded systems using Petri net models and timed automata. In: Proceedings of the 8th International Conference on Real-Time Computing Systems and Applications (RTCSA 2002), pp. 191–199 (2002)
D’Aprile, D., Donatelli, S., Sangnier, A., Sproston, J.: From time Petri nets to timed automata: An untimed approach. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 216–230. Springer, Heidelberg (2007)
Dong, J.S., Hao, P., Qin, S.C., Sun, J., Yi., W.: Timed patterns: TCOZ to timed automata. In: Davies, J., Schulte, W., Barnett, M. (eds.) ICFEM 2004. LNCS, vol. 3308, pp. 483–498. Springer, Heidelberg (2004)
Esparza, J.: Decidability and complexity of Petri net problems — an introduction. In: Reisig, W., Rozenberg, G. (eds.) APN 1998. LNCS, vol. 1491, pp. 374–428. Springer, Heidelberg (1998)
Esparza, J., Nielsen, M.: Decidability issues for Petri nets — a survey. Bulletin of the European Association for Theoretical Computer Science 52, 245–262 (1994)
Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theoretical Computer Science 256(1–2), 63–92 (2001)
Haar, S., Kaiser, L., Simonot-Lion, F., Toussaint, J.: Equivalence of timed state machines and safe TPN. In: Proceedings of the 6th International Workshop on Discrete Event Systems (WODES 2002), pp. 119–126. IEEE Computer Society, Los Alamitos (2002)
Hanisch, H.M.: Analysis of place/transition nets with timed-arcs and its application to batch process control. In: Ajmone Marsan, M. (ed.) ICATPN 1993. LNCS, vol. 691, pp. 282–299. Springer, Heidelberg (1993)
Heitmann, F., Moldt, D., Mortensen, K.H., Rölke, H.: Petri nets tools database quick overview (Accessed: 11.6.2008), http://www.informatik.uni-hamburg.de/TGI/PetriNets/tools/quick.html
Heitmann, F., Moldt, D., Mortensen, K.H., Rölke, H.: Applications of Petri nets (Accessed: 15.6.2008), http://www.informatik.uni-hamburg.de/TGI/PetriNets/applications
Henzinger, T.A., Sifakis, J.: The discipline of embedded systems design. Computer 40(10), 32–40 (2007)
Jančar, P.: Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science 148(2), 281–301 (1995)
Jones, N.D., Landweber, L.H., Lien, Y.E.: Complexity of some problems in Petri nets. Theoretical Computer Science 4(3), 277–299 (1977)
Krichen, M., Tripakis, S.: Black-box conformance testing for real-time systems. In: Graf, S., Mounier, L. (eds.) SPIN 2004. LNCS, vol. 2989, pp. 109–126. Springer, Heidelberg (2004)
Laroussinie, F., Larsen, K.G.: CMC: A tool for compositional model-checking of real-time systems. In: Proceedings of the FIP TC6 WG6.1 Joint International Conference on Formal Description Techniques for Distributed Systems and Communication Protocols (FORTE XI) and Protocol Specification, Testing and Verification (PSTV XVIII), pp. 439–456. Kluwer, B.V (1998)
Larsen, K.G., Pettersson, P., Yi, W.: Uppaal in a Nutshell. International Journal on Software Tools for Technology Transfer 1(1–2), 134–152 (1997)
Larsen, K.G., Yi, W.: Time-abstracted bisimulation: Implicit specifications and decidability. Information and Computation 134(2), 75–101 (1997)
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, pp. 493–505. Springer, Heidelberg (2001)
Larsen, K.G., Mikucionis, M., Nielsen, B.: Online testing of real-time systems using Uppaal. In: Grabowski, J., Nielsen, B. (eds.) FATES 2004. LNCS, vol. 3395, pp. 79–94. Springer, Heidelberg (2005)
Lime, D., Roux, O.H.: State class timed automaton of a time Petri net. In: Proceedings of the 10th International Workshop on Petri Net and Performance Models (PNPM 2003), pp. 124–133 (2003)
Lime, D., Roux, O.H.: Model checking of time Petri nets using the state class timed automaton. Journal of Discrete Events Dynamic Systems — Theory and Applications (DEDS) 16(2), 179–205 (2006)
Maler, O., Pnueli, A., Sifakis, J.: On the synthesis of discrete controllers for timed systems (an extended abstract). In: STACS 1995. LNCS, vol. 900, pp. 229–242. Springer, Heidelberg (1995)
Mayr, E.W.: An algorithm for the general Petri net reachability problem (preliminary version). In: Proceedings of the 13th Ann. ACM Symposium on Theory of Computing, pp. 238–246. Assoc. for Computing Machinery (1981)
Merlin, P.M.: A Study of the Recoverability of Computing Systems. PhD thesis, University of California, Irvine, CA, USA (1974)
Merlin, P.M., Faber, D.J.: Recoverability of communication protocols: Implications of a theoretical study. IEEE Transactions on Communications 24(9), 1036–1043 (1976)
Montano, L., Peñalvo, F.J.G., Villarroel, J.L.: Using the time Petri net formalism for specification, validation, and code generation in robot-control applications. International Journal of Robotic Research 19(1), 59–76 (2000)
Nielsen, M., Sassone, V., Srba, J.: Properties of distributed timed-arc Petri nets. In: Hariharan, R., Mukund, M., Vinay, V. (eds.) FSTTCS 2001. LNCS, vol. 2245, pp. 280–291. Springer, Heidelberg (2001)
Pelayo, F.L., Cuartero, F., Valero, V., Macia, H., Pelayo, M.L.: Applying timed-arc Petri nets to improve the performance of the MPEG-2 encoding algorithm. In: Proceedings of the 10th International Multimedia Modelling Conference (MMM 2004), pp. 49–56. IEEE Computer Society, Los Alamitos (2004)
Pelayo, F.L., Cuartero, F., Valero, V., Pelayo, M.L., Merayo, M.G.: How does the memory work? by timed-arc Petri nets. In: Proceedings of the 4th IEEE International Conference on Cognitive Informatics (ICCI 2005), pp. 128–135 (2005)
Penczek, W., Pólrola, A.: Advances in Verification of Time Petri Nets and Timed Automata: A Temporal Logic Approach. Springer, Heidelberg (2006)
Petri, C.A.: Kommunikation mit Automaten. PhD thesis, Darmstadt (1962)
Popova-Zeugmann, L.: On time Petri nets. Elektronische Informationsverarbeitung und Kybernetik 27(4), 227–244 (1991)
Popova-Zeugmann, L., Heiner, M., Koch, I.: Time Petri nets for modelling and analysis of biochemical networks. Fundamenta Informatica 67(1-3), 149–162 (2005)
Ramchandani, C.: Performance Evaluation of Asynchronous Concurrent Systems by Timed Petri Nets. PhD thesis, Massachusetts Institute of Technology, Cambridge (1973)
Valero Ruiz, V., de Frutos Escrig, D., Marroquin Alonso, O.: 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)
Valero Ruiz, V., Cuartero Gomez, F., de Frutos Escrig, D.: On non-decidability of reachability for timed-arc Petri nets. In: Proceedings of the 8th International Workshop on Petri Net and Performance Models (PNPM 1999), pp. 188–196 (1999)
Ruiz, V.V., Pardo, J.J., Cuartero, F.: Translating TPAL specifications into timed-arc Petri nets. In: Esparza, J., Lakos, C.A. (eds.) ICATPN 2002. LNCS, vol. 2360, pp. 414–433. Springer, Heidelberg (2002)
Ruiz, V.V., Pelayo, F.L., Cuartero, F., Cazorla, D.: Specification and analysis of the MPEG-2 video encoder with timed-arc Petri nets. Electronic Notes Theoretial Computer Science 66(2) (2002)
Seidner, Ch., Gardey, G., Lime, D., Magnin, M., Roux, O.: Romeo: A tool for time Petri net analysis (Accessed: 11.6.2008), http://romeo.rts-software.org/
Sifakis, J.: Use of Petri nets for performance evaluation. In: Proceedings of the Third International Symposium IFIP W.G. 7.3., Measuring, Modelling and Evaluating Computer Systems, Bonn-Bad Godesberg, pp. 75–93. Elsevier Science Publishers, Amsterdam (1977)
Sifakis, J., Yovine, S.: Compositional specification of timed systems. In: Puech, C., Reischuk, R. (eds.) STACS 1996. LNCS, vol. 1046, pp. 347–359. Springer, Heidelberg (1996)
Srba, J.: Timed-arc Petri nets vs. networks of timed automata. In: Ciardo, G., Darondeau, P. (eds.) ICATPN 2005. LNCS, vol. 3536, pp. 385–402. Springer, Heidelberg (2005)
UPPAAL-Cora (Accessed: 18.6.2008), http://www.cs.aau.dk/~behrmann/cora/
UPPAAL-Tiga (Accessed: 18.6.2008), http://www.cs.aau.dk/~adavid/tiga/
UPPAAL-Tron (Accessed: 23.6.2008), http://www.cs.aau.dk/~marius/tron/
Wang, J.: Timed Petri Nets, Theory and Application. Kluwer Academic Publishers, Dordrecht (1998)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Srba, J. (2008). Comparing the Expressiveness of Timed Automata and Timed Extensions of Petri Nets. In: Cassez, F., Jard, C. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2008. Lecture Notes in Computer Science, vol 5215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85778-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-85778-5_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85777-8
Online ISBN: 978-3-540-85778-5
eBook Packages: Computer ScienceComputer Science (R0)