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.
Supported by the VKR Center of Excellence MT-LAB.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alur, R., La Torre, S., Pappas, G.J.: Optimal paths in weighted timed automata. Theoretical Computer Science 318(3), 297–322 (2004)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Ehrenfeucht, A., Mycielski, J.: Positional strategies for mean payoff games. International Journal of Game Theory 8(2), 109–113 (1979)
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)
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)
Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)
Yen, H.C.: A unified approach for deciding the existence of certain Petri net paths. Information and Computation 96(1), 119–137 (1992)
Zwick, U., Paterson, M.: The complexity of mean payoff games on graphs. Theorertical Computer Science 158(1&2), 343–359 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fahrenberg, U., Juhl, L., Larsen, K.G., Srba, J. (2011). Energy Games in Multiweighted Automata. In: Cerone, A., Pihlajasaari, P. (eds) Theoretical Aspects of Computing – ICTAC 2011. ICTAC 2011. Lecture Notes in Computer Science, vol 6916. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23283-1_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-23283-1_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23282-4
Online ISBN: 978-3-642-23283-1
eBook Packages: Computer ScienceComputer Science (R0)