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.
The authors acknowledge partial support by Indo-French Project AVeCSo, TCS-Fellowship, Indo-Swedish DST-VR Project P-02/2014, Infosys Foundation.
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References
Cachat, T.: Uniform solution of parity games on prefix-recognizable graphs. Electr. Notes Theor. Comput. Sci. 68, 1–15 (2002)
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)
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
Martin, D.A.: Borel determinacy. Ann. Math. 102, 363–371 (1975)
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
Saivasan, P.: Analysis of Automata-theoretic models of Concurrent Recursive Programs. Ph.D. thesis, Chennai Mathematical Institute (2016)
Serre, O.: Note on winning positions on pushdown games with [omega]-regular conditions. Inf. Process. Lett. 85, 285–291 (2003)
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
Stockmeyer, L.J.: The Complexity of Decision Problems in Automata Theory and Logic. Ph.D. thesis. MIT, Cambridge (1974)
Torre, S.L., Madhusudan, P., Parlato, G.: A robust class of context-sensitive languages. In: LICS. IEEE Computer Society (2007)
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
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
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Atig, M.F., Bouajjani, A., Narayan Kumar, K., Saivasan, P. (2017). Parity Games on Bounded Phase Multi-pushdown Systems. In: El Abbadi, A., Garbinato, B. (eds) Networked Systems. NETYS 2017. Lecture Notes in Computer Science(), vol 10299. Springer, Cham. https://doi.org/10.1007/978-3-319-59647-1_21
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