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Average-price-per-reward games on hybrid automata with strong resets

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Abstract

We study price-per-reward games on hybrid automata with strong resets. They generalise average-price games previously studied and have applications in scheduling. We obtain decidability results by a translation to a novel class of finite graphs with price and reward information, and games assigned to edges. The cost and reward of following an edge are determined by the outcome of the edge game that is assigned to it.

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References

  1. Alur R., Courcoubetis C., Henzinger T.A., Ho P.H., Nicollin X., Olivero A., Sifakis J., Yovine S.: The algorithmic analysis of hybrid systems. Theoret. Comput. Sci. 138, 3–34 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alur R., Dill D.: A theory of timed automata. Theoret. Comput. Sci. 126, 183–235 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Henzinger, T.A.: The theory of hybrid automata. In: LICS 1996, pp. 278–292. IEEE Computer Society Press, CA (1996)

  4. Lafferriere G., Pappas G.J., Sastry S.: O-minimal hybrid systems. Math. Contr. Signal. Syst. 13, 1–21 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gentilini, R.: Reachability problems on extended o-minimal hybrid automata. In: FORMATS’05, Volume 3829 of LNCS, pp. 162–176. Springer, Berlin (2005)

  6. Bouyer, P., Brihaye, T., Jurdziński, M., Lazić, R., Rutkowski, M.: Average-price and reachability-price games on hybrid automata with strong resets. In: FORMATS’08, Volume 5215 of LNCS, pp. 63–77. Springer, Berlin (2008)

  7. Brihaye T., Michaux C.: On the expressiveness and decidability of o-minimal hybrid systems. J. Complexity 21, 447–478 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bouyer P., Brinksma E., Larsen K.G.: Optimal infinite scheduling for multi-priced timed automata. Formal Methods Syst. Design 32, 2–23 (2008)

    Google Scholar 

  9. Abdeddam Y., Asarin E., Maler O.: Scheduling with timed automata. Theoret. Comput. Sci. 354, 272–300 (2006)

    Article  MathSciNet  Google Scholar 

  10. Church, A.: Logic, arithmetic and automata. In: Proceedings of the International Congress of Mathematicians, pp. 23–35 (1962)

  11. Thomas, W.: On the synthesis of strategies in infinite games. In: STACS’95, Volume 900 of LNCS, pp. 1–13. Springer, Berlin (2005)

  12. Bouyer, P., Brihaye, T., Chevalier, F.: Control in o-minimal hybrid systems. In: LICS’06, pp. 367–378. IEEE Computer Society Press, CA (2006)

  13. Bouyer P., Brihaye T., Chevalier F.: Weighted o-minimal hybrid systems. Ann. Pure Appl. Logics 161, 268–288 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Jurdziński, M., Trivedi, A.: Reachability-time games on timed automata. In: ICALP’07, Volume 4596 of LNCS, pp. 838–849. Springer, Berlin (2007)

  15. Brihaye T.: A note on the undecidability of the reachability problem for o-minimal dynamical systems. Math. Logic Quart. 52, 165–170 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  16. Tarski A.: A Decision Method for Elementary Algebra and Geometry. University of California Press, CA (1951)

    MATH  Google Scholar 

  17. Weihrauch K.: Computable Analysis. Springer, Berlin (2000)

    Book  MATH  Google Scholar 

  18. Meer, K., Michaux, C.: A survey on real structural complexity theory. Bull. Belgian Math. Soc. 4, 113–148 (1997) (Journées Montoises (Mons, 1994))

    Google Scholar 

  19. Blum L., Shub M., Smale S.: On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines. Am. Math. Soc. Bull. New Ser. 21, 1–46 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  20. Puterman M.L.: Markov Decision Processes, Discrete Stochastic Dynamic Programming. Wiley, New York (1994)

    MATH  Google Scholar 

  21. Vladimerou, V., Prabhakar, P., Viswanathan, M., Dullerud, G.: Stormed hybrid systems. In: ALP’10. Volume 5126 of LNCS, pp. 136–147. Springer, Berlin (2010)

  22. Vladimerou, V., Prabhakar, P., Viswanathan, M., Dullerud, G.: Stormed hybrid games. In: HSCC’09. Volume 5469 of LNCS, pp. 480–484. Springer, Berlin (2009)

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Authors and Affiliations

  1. Department of Computer Science, University of Warwick, Covnetry, UK

    Michał Rutkowski, Ranko Lazić & Marcin Jurdziński

Authors
  1. Michał Rutkowski
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  2. Ranko Lazić
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  3. Marcin Jurdziński
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Corresponding author

Correspondence to Michał Rutkowski.

Additional information

This research was supported in part by EPSRC project EP/E022030/1.

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Rutkowski, M., Lazić, R. & Jurdziński, M. Average-price-per-reward games on hybrid automata with strong resets. Int J Softw Tools Technol Transfer 13, 553–569 (2011). https://doi.org/10.1007/s10009-010-0180-8

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