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Playing Games with Counter Automata

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Reachability Problems (RP 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7550))

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Abstract

We survey recent results about subclasses of multi-counter games that are either equipped with more than one counter or allow for stochastic control states.

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References

  1. Abdulla, P.A., Ben Henda, N., de Alfaro, L., Mayr, R., Sandberg, S.: Stochastic Games with Lossy Channels. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 35–49. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  2. Baier, C., Bertrand, N., Schnoebelen, P.: On Computing Fixpoints in Well-Structured Regular Model Checking, with Applications to Lossy Channel Systems. In: Hermann, M., Voronkov, A. (eds.) LPAR 2006. LNCS (LNAI), vol. 4246, pp. 347–361. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  3. Berger, N., Kapur, N., Schulman, L., Vazirani, V.: Solvency games. In: Proceedings of FST&TCS 2008. Leibniz International Proceedings in Informatics, vol. 2, pp. 61–72. Schloss Dagstuhl–Leibniz-Zentrum für Informatik (2008)

    Google Scholar 

  4. Bouyer, P., Fahrenberg, U., Larsen, K., 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)

    Chapter  Google Scholar 

  5. Brázdil, T., Brožek, V., Etessami, K.: One-counter stochastic games. In: Proceedings of FST&TCS 2010. Leibniz International Proceedings in Informatics, vol. 8, pp. 108–119. Schloss Dagstuhl–Leibniz-Zentrum für Informatik (2010)

    Google Scholar 

  6. Brázdil, T., Brožek, V., Etessami, K., Kučera, A.: Approximating the Termination Value of One-Counter MDPs and Stochastic Games. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 332–343. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  7. Brázdil, T., Brožek, V., Etessami, K., Kučera, A., Wojtczak, D.: One-counter Markov decision processes. In: Proceedings of SODA 2010, pp. 863–874. SIAM (2010)

    Google Scholar 

  8. Brázdil, T., Brožek, V., Forejt, V., Kučera, A.: Reachability in recursive Markov decision processes. Information and Computation 206(5), 520–537 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Brázdil, T., Brožek, V., Kučera, A., Obdržálek, J.: Qualitative reachability in stochastic BPA games. Information and Computation 208(7), 772–796 (2010)

    Article  MathSciNet  Google Scholar 

  10. Brázdil, T., Chatterjee, K., Kučera, A., Novotný, P.: Efficient Controller Synthesis for Consumption Games with Multiple Resource Types. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 23–38. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  11. 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, Part II. LNCS, vol. 6199, pp. 478–489. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  12. Brázdil, T., Kučera, A., Novotný, P., Wojtczak, D.: Minimizing Expected Termination Time in One-Counter Markov Decision Processes. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part II. LNCS, vol. 7392, pp. 141–152. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  13. 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)

    Chapter  Google Scholar 

  14. 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, Part II. LNCS, vol. 6199, pp. 599–610. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  15. Chatterjee, K., Doyen, L.: Energy and Mean-Payoff Parity Markov Decision Processes. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 206–218. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  16. Chatterjee, K., Doyen, L., Henzinger, T., Raskin, J.F.: Generalized mean-payoff and energy games. In: Proceedings of FST&TCS 2010. Leibniz International Proceedings in Informatics, vol. 8, pp. 505–516. Schloss Dagstuhl–Leibniz-Zentrum für Informatik (2010)

    Google Scholar 

  17. Condon, A.: The complexity of stochastic games. Information and Computation 96(2), 203–224 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  18. Etessami, K., Wojtczak, D., Yannakakis, M.: Recursive Stochastic Games with Positive Rewards. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 711–723. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  19. Etessami, K., Yannakakis, M.: Recursive Markov Decision Processes and Recursive Stochastic Games. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 891–903. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  20. Etessami, K., Yannakakis, M.: Efficient Qualitative Analysis of Classes of Recursive Markov Decision Processes and Simple Stochastic Games. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 634–645. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  21. Etessami, K., Yannakakis, M.: Recursive Concurrent Stochastic Games. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006, Part II. LNCS, vol. 4052, pp. 324–335. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  22. Fahrenberg, U., Juhl, L., Larsen, K., Srba, J.: Energy Games in Multiweighted Automata. In: Cerone, A., Pihlajasaari, P. (eds.) ICTAC 2011. LNCS, vol. 6916, pp. 95–115. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  23. Filar, J., Vrieze, K.: Competitive Markov Decision Processes. Springer (1996)

    Google Scholar 

  24. Kučera, A.: The complexity of bisimilarity-checking for one-counter processes. Theoretical Computer Science 304(1-3), 157–183 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  25. Maitra, A., Sudderth, W.: Finitely additive stochastic games with Borel measurable payoffs. International Journal of Game Theory 27, 257–267 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  26. Martin, D.: The determinacy of Blackwell games. Journal of Symbolic Logic 63(4), 1565–1581 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  27. Puterman, M.: Markov Decision Processes. Wiley (1994)

    Google Scholar 

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Kučera, A. (2012). Playing Games with Counter Automata. In: Finkel, A., Leroux, J., Potapov, I. (eds) Reachability Problems. RP 2012. Lecture Notes in Computer Science, vol 7550. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33512-9_4

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  • DOI: https://doi.org/10.1007/978-3-642-33512-9_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33511-2

  • Online ISBN: 978-3-642-33512-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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