Energy Games in Multiweighted Automata

  • Uli Fahrenberg
  • Line Juhl
  • Kim G. Larsen
  • Jiří Srba
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6916)

Abstract

Energy games have recently attracted a lot of attention. These are games played on finite weighted automata and concern the existence of infinite runs subject to boundary constraints on the accumulated weight, allowing e.g only for behaviours where a resource is always available (nonnegative accumulated weight), yet does not exceed a given maximum capacity. We extend energy games to a multiweighted and parameterized setting, allowing us to model systems with multiple quantitative aspects. We present reductions between Petri nets and multiweighted automata and among different types of multiweighted automata and identify new complexity and (un)decidability results for both one- and two-player games. We also investigate the tractability of an extension of multiweighted energy games in the setting of timed automata.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alur, R., La Torre, S., Pappas, G.J.: Optimal paths in weighted timed automata. Theoretical Computer Science 318(3), 297–322 (2004)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Atig, M.F., Habermehl, P.: On Yen’s Path Logic for Petri Nets. In: Bournez, O., Potapov, I. (eds.) RP 2009. LNCS, vol. 5797, pp. 51–63. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Behrmann, G., Fehnker, A., Hune, T., Larsen, K.G., Pettersson, P., Romijn, J.M.T., Vaandrager, F.W.: Minimum-Cost Reachability for Priced Timed Automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 147–161. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N.: Timed automata with observers under energy constraints. In: Johansson, K.H., Yi, W. (eds.) HSCC, pp. 61–70. ACM, New York (2010)CrossRefGoogle Scholar
  5. 5.
    Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N., Srba, J.: Infinite Runs in Weighted Timed Automata with Energy Constraints. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 33–47. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Brázdil, T., Jančar, P., Kučera, A.: Reachability games on extended vector addition systems with states. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 478–489. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Chakrabarti, A., de Alfaro, L., Henzinger, T.A., Stoelinga, M.: Resource Interfaces. In: Alur, R., Lee, I. (eds.) EMSOFT 2003. LNCS, vol. 2855, pp. 117–133. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Chaloupka, J.: Z-reachability problem for games on 2-dimensional vector addition systems with states is in P. In: Kučera, A., Potapov, I. (eds.) RP 2010. LNCS, vol. 6227, pp. 104–119. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Chatterjee, K., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Generalized mean-payoff and energy games. In: Proceedings of FSTTCS 2010. LIPIcs, vol. 8, pp. 505–516. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2010)Google Scholar
  10. 10.
    Chatterjee, K., Doyen, L.: Energy Parity Games. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 599–610. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Degorre, A., Doyen, L., Gentilini, R., Raskin, J.-F., Toruńczyk, S.: Energy and Mean-Payoff Games with Imperfect Information. In: Dawar, A., Veith, H. (eds.) CSL 2010. LNCS, vol. 6247, pp. 260–274. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Ehrenfeucht, A., Mycielski, J.: Positional strategies for mean payoff games. International Journal of Game Theory 8(2), 109–113 (1979)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    Kosaraju, S.R., Sullivan, G.: Detecting cycles in dynamic graphs in polynomial time. In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing (STOC 1988), pp. 398–406. ACM, New York (1988)Google Scholar
  15. 15.
    Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)MATHGoogle Scholar
  16. 16.
    Yen, H.C.: A unified approach for deciding the existence of certain Petri net paths. Information and Computation 96(1), 119–137 (1992)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Zwick, U., Paterson, M.: The complexity of mean payoff games on graphs. Theorertical Computer Science 158(1&2), 343–359 (1996)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Uli Fahrenberg
    • 1
  • Line Juhl
    • 2
  • Kim G. Larsen
    • 2
  • Jiří Srba
    • 2
  1. 1.INRIA/IRISARennes CedexFrance
  2. 2.Department of Computer ScienceAalborg UniversityDenmark

Personalised recommendations