Abstract
We present a new algorithm for computing the winning region of a parity game played over the configuration graph of a pushdown system. Our method gives the first extension of the saturation technique to the parity condition. Finite word automata are used to represent sets of pushdown configurations. Starting from an initial automaton, we perform a series of automaton transformations to compute a fixed-point characterisation of the winning region. We introduce notions of under-approximation (soundness) and over-approximation (completeness) that apply to automaton transitions rather than runs, and obtain a clean proof of correctness. Our algorithm is simple and direct, and it permits an optimisation that avoids an immediate exponential blow up.
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Bouajjani, A., Esparza, J., Maler, O.: Reachability analysis of pushdown automata: Application to model-checking. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243, pp. 135–150. Springer, Heidelberg (1997)
Finkel, A., Willems, B., Wolper, P.: A direct symbolic approach to model checking pushdown systems. In: INFINITY (1997)
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)
Emerson, E.A., Jutla, C.S.: Tree automata, mu-calculus and determinacy (extended abstract). In: FOCS 1991, pp. 368–377 (1991)
Esparza, J., Kučera, A., Schwoon, S.: Model-checking LTL with regular valuations for pushdown systems. In: Kobayashi, N., Pierce, B.C. (eds.) TACS 2001. LNCS, vol. 2215, pp. 316–339. Springer, Heidelberg (2001)
Hague, M.: Saturation methods for global model-checking pushdown systems. PhD. Thesis, University of Oxford (2009)
Jones, N., Muchnick, S.: Even simple programs are hard to analyse. JACM 24, 338–350 (1977)
Piterman, N., Y. Vardi, M.: Global model-checking of infinite-state systems. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 387–400. Springer, Heidelberg (2004)
Serre, O.: Note on winning positions on pushdown games with ω-regular conditions. Information Processing Letters 85, 285–291 (2003)
Schwoon, S.: Model-checking Pushdown Systems. PhD thesis, Tech. Univ., Munich (2002)
Ball, T., Rajamani, S.K.: Bebop: A Symbolic Model Checker for Boolean Programs. In: Havelund, K., Penix, J., Visser, W. (eds.) SPIN 2000. LNCS, vol. 1885, pp. 113–130. Springer, Heidelberg (2000)
Ball, T., Rajamani, S.K.: The SLAM project: Debugging system software via static analysis. In: POPL, pp. 1–3 (2002)
Cachat, T.: Games on Pushdown Graphs and Extensions. PhD thesis, RWTH Aachen (2003)
Reps, T., Schwoon, S., Jha, S., Melski, D.: Weighted pushdown systems and their application to interprocedural dataflow analysis. Sci. Comput. Program. (2005)
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Hague, M., Ong, C.H.L. (2009). Winning Regions of Pushdown Parity Games: A Saturation Method. In: Bravetti, M., Zavattaro, G. (eds) CONCUR 2009 - Concurrency Theory. CONCUR 2009. Lecture Notes in Computer Science, vol 5710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04081-8_26
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DOI: https://doi.org/10.1007/978-3-642-04081-8_26
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