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Folk Theorems on the Determinization and Minimization of Timed Automata

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Formal Modeling and Analysis of Timed Systems (FORMATS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2791))

Abstract

Timed automata are known not to be complementable or determinizable. Natural questions are, then, could we check whether a given TA enjoys these properties? These problems are not algorithmically solvable, if we require not just a yes/no answer, but also a witness. Minimizing the “resources” of a TA (number of clocks or size of constants) are also unsolvable problems. Proofs are provided as simple reductions from the universality problem. These proofs are not applicable to the corresponding decision problems, the decidability of which remains open.

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References

  1. Alur, R., Courcoubetis, C., Halbwachs, N., Dill, D.L., Wong-Toi, H.: Minimization of timed transition systems. In: Cleaveland, W.R. (ed.) CONCUR 1992. LNCS, vol. 630, pp. 340–354. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  2. Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  3. Alur, R., Fix, L., Henzinger, T.: A determinizable class of timed automata. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, Springer, Heidelberg (1994)

    Google Scholar 

  4. Bouyer, P., D’Souza, D., Madhusudan, P., Petit, A.: Timed control with partial observability. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 180–192. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  5. Bouyer, P., Dufourd, C., Fleury, E., Petit, A.: Are timed automata updatable? In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  6. Bouyer, P., Dufourd, C., Fleury, E., Petit, A.: Expressiveness of updatable timed automata. In: Nielsen, M., Rovan, B. (eds.) MFCS 2000. LNCS, vol. 1893, p. 232. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  7. Courcoubetis, C., Yannakakis, M.: Minimum and maximum delay problems in real-time systems. In: Larsen, K.G., Skou, A. (eds.) CAV 1991. LNCS, vol. 575, Springer, Heidelberg (1992)

    Google Scholar 

  8. Daws, C., Yovine, S.: Reducing the number of clock variables of timed automata. In: Proc. 17th IEEE Real-Time Systems Symposium, RTSS 1996 (1996)

    Google Scholar 

  9. D’Souza, D., Madhusudan, P.: Controller synthesis for timed specifications. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, p. 571. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Nielsen, B., Skou, A.: Automated test generation from timed automata. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, p. 343. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  11. Springintveld, J., Vaandrager, F., D’Argenio, P.: Testing timed automata. Theoretical Computer Science 254 (2001)

    Google Scholar 

  12. Springintveld, J.G., Vaandrager, F.W.: Minimizable timed automata. In: Jonsson, B., Parrow, J. (eds.) FTRTFT 1996. LNCS, vol. 1135, pp. 130–147. Springer, Heidelberg (1996)

    Google Scholar 

  13. Tripakis, S.: Fault diagnosis for timed automata. In: Damm, W., Olderog, E.-R. (eds.) FTRTFT 2002. LNCS, vol. 2469, p. 205. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  14. Tripakis, S., Yovine, S.: Analysis of timed systems using time-abstracting bisimulations. Formal Methods in System Design 18(1), 25–68 (2001)

    Article  MATH  Google Scholar 

  15. Wilke, T.: Automaten und Logiken zur Beschreibung zeitabhängiger Systeme. PhD thesis, Institut Für Informatik und Praktische Mathematik, Christian- Albrechts Universität, Kiel (1994) ( in German)

    Google Scholar 

  16. Yannakakis, M., Lee, D.: An efficient algorithm for minimizing real-time transition systems. Formal Methods in System Design 11(2) (1997)

    Google Scholar 

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Authors and Affiliations

  1. VERIMAG Centre Equation, 2, avenue de Vignate, 38610, Gières, France

    Stavros Tripakis

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  1. Stavros Tripakis
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Editors and Affiliations

  1. Dept. of Computer Science, Aalborg University, Denmark

    Kim Guldstrand Larsen

  2. Laboratoire d’Informatique Fondamentale de Marseille, CMI, 39, rue Joliot Curie, 13453, Marseille Cedex 13, France

    Peter Niebert

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© 2004 Springer-Verlag Berlin Heidelberg

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Tripakis, S. (2004). Folk Theorems on the Determinization and Minimization of Timed Automata. In: Larsen, K.G., Niebert, P. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2003. Lecture Notes in Computer Science, vol 2791. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40903-8_15

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  • DOI: https://doi.org/10.1007/978-3-540-40903-8_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21671-1

  • Online ISBN: 978-3-540-40903-8

  • eBook Packages: Springer Book Archive

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