Abstract
In this paper we provide a broad investigation of the symbolic approach for solving Parity Games. Specifically, we implement in a fresh tool, called , four symbolic algorithms to solve Parity Games and compare their performances to the corresponding explicit versions for different classes of games. By means of benchmarks, we show that for random games, even for constrained random games, explicit algorithms actually perform better than symbolic algorithms. The situation changes, however, for structured games, where symbolic algorithms seem to have the advantage. This suggests that when evaluating algorithms for parity-game solving, it would be useful to have real benchmarks and not only random benchmarks, as the common practice has been.
Work supported by NSF grants CCF-1319459 and IIS-1527668, NSF Expeditions in Computing project “ExCAPE: Expeditions in Computer Augmented Program Engineering” and GNCS 2018: Logica, Automi e Giochi per Sistemi Auto-adattivi.
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Notes
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The tool is available for download from https://github.com/antoniodistasio/sympgsolver.
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References
Iris Bahar, R., Frohm, E.A., Gaona, C.M., Hachtel, G.D., Macii, E., Pardo, A., Somenzi, F.: Algebraic decision diagrams and their applications. Formal Methods Syst. Des. 10, 171–206 (1997)
Bakera, M., Edelkamp, S., Kissmann, P., Renner, C.D.: Solving \(\mu \)-calculus parity games by symbolic planning. In: Peled, D.A., Wooldridge, M.J. (eds.) MoChArt 2008. LNCS (LNAI), vol. 5348, pp. 15–33. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00431-5_2
Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Comput. 35, 677–691 (1986)
Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic model checking: \(10^{20}\) states and beyond. In: LICS 1990, pp. 428–439 (1990)
Bustan, D., Kupferman, O., Vardi, M.Y.: A measured collapse of the modal \(\mu \)-calculus alternation hierarchy. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 522–533. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24749-4_46
Calude, C.S., Jain, S., Khoussainov, B., Li, W., Stephan, F.: Deciding parity games in quasipolynomial time. In: STOC 2017, pp. 252–263 (2017)
Cermák, P., Lomuscio, A., Murano, A.: Verifying and synthesising multi-agent systems against one-goal strategy logic specifications. In: AAAI 2015, pp. 2038–2044 (2015)
Chatterjee, K., Dvorák, W., Henzinger, M., Loitzenbauer, V.: Improved set-based symbolic algorithms for parity games. In: CSL 2017, pp. 18:1–18:21 (2017)
Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Kozen, D. (ed.) LP 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982). https://doi.org/10.1007/BFb0025774
Di Stasio, A., Murano, A., Perelli, G., Vardi, M.Y.: Solving parity games using an automata-based algorithm. In: Han, Y.-S., Salomaa, K. (eds.) CIAA 2016. LNCS, vol. 9705, pp. 64–76. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40946-7_6
Eisner, C., Peled, D.: Comparing symbolic and explicit model checking of a software system. In: Bošnački, D., Leue, S. (eds.) SPIN 2002. LNCS, vol. 2318, pp. 230–239. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46017-9_18
Emerson, E.A., Jutla, C.: Tree automata, \(\mu \)-calculus and determinacy. In: FOCS 1991, pp. 368–377 (1991)
Jurdzinski, M.: Deciding the winner in parity games is in UP \(\cap \) co-Up. Inf. Process. Lett. 68(3), 119–124 (1998)
Jurdziński, M.: Small progress measures for solving parity games. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 290–301. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-46541-3_24
Jurdzinski, M., Lazic, R.: Succinct progress measures for solving parity games. In: LICS 2017, pp. 1–9 (2017)
Kant, G., van de Pol, J.: Generating and solving symbolic parity games. In: GRAPHITE 2014, pp. 2–14 (2014)
Keiren, J.J.A.: Benchmarks for parity games. In: Dastani, M., Sirjani, M. (eds.) FSEN 2015. LNCS, vol. 9392, pp. 127–142. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24644-4_9
Kupferman, O., Vardi, M.Y.: Weak alternating automata and tree automata emptiness. In: STOC 1998, pp. 224–233 (1998)
Kupferman, O., Vardi, M.Y., Wolper, P.: An automata theoretic approach to branching-time model checking. J. ACM 47(2), 312–360 (2000)
McMillan, K.L.: Symbolic Model Checking. Kluwer Academic Publishers, Norwell (1993)
Tabakov, D.: Evaluation of explicit and symbolic automata-theoretic algorithm. Master’s thesis, Rice University (2005)
van Dijk, T.: Oink: an implementation and evaluation of modern parity game solvers. In: Beyer, D., Huisman, M. (eds.) TACAS 2018. LNCS, vol. 10805, pp. 291–308. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89960-2_16
Wilke, T.: Alternating tree automata, parity games, and modal \(\mu \)-calculus. Bull. Belg. Math. Soc. Simon Stevin 8(2), 359 (2001)
Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theor. Comput. Sci. 200(1–2), 135–183 (1998)
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Di Stasio, A., Murano, A., Vardi, M.Y. (2018). Solving Parity Games: Explicit vs Symbolic. In: Câmpeanu, C. (eds) Implementation and Application of Automata. CIAA 2018. Lecture Notes in Computer Science(), vol 10977. Springer, Cham. https://doi.org/10.1007/978-3-319-94812-6_14
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