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Parity Games on Bounded Phase Multi-pushdown Systems

  • Mohamed Faouzi Atig
  • Ahmed Bouajjani
  • K. Narayan Kumar
  • Prakash SaivasanEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10299)

Abstract

In this paper we address the problem of solving parity games over the configuration graphs of bounded phase multi-pushdown systems. A non-elementary decision procedure was proposed for this problem by A. Seth. In this paper, we provide a simple and inductive construction to solve this problem. We also prove a non-elementary lower-bound, answering a question posed by A. Seth.

Keywords

Strategy Function Atomic Formula Winning Strategy Valuation Function Game Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Cachat, T.: Uniform solution of parity games on prefix-recognizable graphs. Electr. Notes Theor. Comput. Sci. 68, 1–15 (2002)zbMATHGoogle Scholar
  2. 2.
    Emerson, E.A., Jutla, C.S.: Tree automata, mu-calculus and determinacy (extended abstract). In: 32nd Annual Symposium on Foundations of Computer Science, San Juan, Puerto Rico, 1–4 October (1991)Google Scholar
  3. 3.
    Kupferman, O., Piterman, N., Vardi, M.Y.: An automata-theoretic approach to infinite-state systems. In: Manna, Z., Peled, D.A. (eds.) Time for Verification. LNCS, vol. 6200, pp. 202–259. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-13754-9_11 CrossRefGoogle Scholar
  4. 4.
    Martin, D.A.: Borel determinacy. Ann. Math. 102, 363–371 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Qadeer, S., Rehof, J.: Context-bounded model checking of concurrent software. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 93–107. Springer, Heidelberg (2005). doi: 10.1007/978-3-540-31980-1_7 CrossRefGoogle Scholar
  6. 6.
    Saivasan, P.: Analysis of Automata-theoretic models of Concurrent Recursive Programs. Ph.D. thesis, Chennai Mathematical Institute (2016)Google Scholar
  7. 7.
    Serre, O.: Note on winning positions on pushdown games with [omega]-regular conditions. Inf. Process. Lett. 85, 285–291 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Seth, A.: Games on multi-stack pushdown systems. In: Artemov, S., Nerode, A. (eds.) LFCS 2009. LNCS, vol. 5407, pp. 395–408. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-92687-0_27 CrossRefGoogle Scholar
  9. 9.
    Stockmeyer, L.J.: The Complexity of Decision Problems in Automata Theory and Logic. Ph.D. thesis. MIT, Cambridge (1974)Google Scholar
  10. 10.
    Torre, S.L., Madhusudan, P., Parlato, G.: A robust class of context-sensitive languages. In: LICS. IEEE Computer Society (2007)Google Scholar
  11. 11.
    Torre, S., Madhusudan, P., Parlato, G.: Reducing context-bounded concurrent reachability to sequential reachability. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 477–492. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-02658-4_36 CrossRefGoogle Scholar
  12. 12.
    Walukiewicz, I.: Pushdown processes: games and model checking. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 62–74. Springer, Heidelberg (1996). doi: 10.1007/3-540-61474-5_58 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Mohamed Faouzi Atig
    • 1
  • Ahmed Bouajjani
    • 2
  • K. Narayan Kumar
    • 3
  • Prakash Saivasan
    • 4
    Email author
  1. 1.Uppsala UniversityUppsalaSweden
  2. 2.IRIF, Université Paris DiderotParisFrance
  3. 3.Chennai Mathematical InstituteChennaiIndia
  4. 4.TU BraunschweigBraunschweigGermany

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