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Controller Synthesis and Ordinal Automata

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Automated Technology for Verification and Analysis (ATVA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 4218))

Abstract

Ordinal automata are used to model physical systems with Zeno behavior. Using automata and games techniques we solve a control problem formulated and left open by Demri and Nowak in 2005. It involves partial observability and a new synchronization between the controller and the environment.

The author acknowledges partial support by the ACI “Sécurité et Informatique” CORTOS. http://www.lsv.ens-cachan.fr/aci-cortos/

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References

  1. de Alfaro, L., Faëlla, M., Henzinger, T.A., Majumdar, R., Stoelinga, M.: The element of surprise in timed games. In: Amadio, R.M., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 142–156. Springer, Heidelberg (2003)

    Google Scholar 

  2. Asarin, E., Maler, O.: Achilles and the tortoise climbing up the arithmetical hierarchy. JCSS 57(3), 389–398 (1998)

    MATH  MathSciNet  Google Scholar 

  3. Bès, A., Carton, O.: A Kleene theorem for languages of words indexed by linear orderings. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 158–167. Springer, Heidelberg (2005)

    Chapter  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. Bedon, N.: Langages reconnaissables de mots indexés par des ordinaux. PhD thesis, Université de Marne-la-Vallée (1998)

    Google Scholar 

  6. Bournez, O.: Achilles and the tortoise climbing up the hyper-arithmetical hierarchy. TCS 210(1), 21–71 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bérard, B., Picaronny, C.: Accepting Zeno words: A way toward timed refinements. Acta Informatica 37(1), 45–81 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Buchi, J.R., Siefkes, D.: The monadic second order theory of all countable ordinals. Lect. Notes in Math., vol. 328. Springer, Heidelberg (1973)

    Google Scholar 

  9. Carton, O.: Accessibility in automata on scattered linear orderings. In: Diks, K., Rytter, W. (eds.) MFCS 2002. LNCS, vol. 2420, pp. 155–164. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Durand-Lose, J.: Abstract geometrical computation for black hole computation (extended abstract). In: Margenstern, M. (ed.) MCU 2004. LNCS, vol. 3354, pp. 176–187. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. Demri, S., Nowak, D.: Reasoning about transfinite sequences (extended abstract). In: Peled, D.A., Tsay, Y.-K. (eds.) ATVA 2005. LNCS, vol. 3707, pp. 248–262. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  12. Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  13. Godefroid, P., Wolper, P.: A partial approach to model checking. Inform. and Comput. 110(2), 305–326 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  14. Jurdzinski, M., Paterson, M., Zwick, U.: A deterministic subexponential algorithm for solving parity games. In: SODA, pp. 117–123 (2006)

    Google Scholar 

  15. Kamp, H.: Tense Logic and the Theory of Linear Order. PhD thesis, University of California at Los Angeles (1968)

    Google Scholar 

  16. Löding, C.: Methods for the transformation of omega-automata: Complexity and connection to second order logic. Master’s thesis, Christian-Albrechts-University of Kiel (1998)

    Google Scholar 

  17. Martin, D.A.: Borel Determinacy. Annals of Math. 102, 363–371 (1975)

    Article  Google Scholar 

  18. Maurin, F.: Exact complexity bounds for ordinal addition. Theor. Comput. Sci. 165(2), 247–273 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  19. Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: POPL 1989, pp. 179–190. ACM Press, New York (1989)

    Chapter  Google Scholar 

  20. Reif, J.H.: The complexity of two-player games of incomplete information. J. Comput. System Sci. 29(2), 274–301 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  21. Rosenstein, J.G.: Linear orderings. Academic Press, London (1982)

    MATH  Google Scholar 

  22. Ramadge, P.J., Wonham, W.M.: The control of discrete event systems. Proceedings of IEEE 77(1), 81–98 (1989)

    Article  Google Scholar 

  23. Thomas, W.: On the synthesis of strategies in infinite games. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 1–13. Springer, Heidelberg (1995)

    Google Scholar 

  24. Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification. In: LICS 1986, pp. 332–344 (1986)

    Google Scholar 

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Cachat, T. (2006). Controller Synthesis and Ordinal Automata. In: Graf, S., Zhang, W. (eds) Automated Technology for Verification and Analysis. ATVA 2006. Lecture Notes in Computer Science, vol 4218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11901914_18

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  • DOI: https://doi.org/10.1007/11901914_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-47237-7

  • Online ISBN: 978-3-540-47238-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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