Abstract
We study the synthesis problem for specifications of the common fragment of ACTL (computation tree logic with only universal path quantification) and LTL (linear-time temporal logic). Key to this setting is a novel construction for translating properties from LTL to very-weak automata, whenever possible. Such automata are structurally simple and thus amenable to optimizations as well as symbolic implementations.
Based on this novel construction, we describe a synthesis approach that inherits the efficiency of generalized reactivity(1) synthesis [27], but is significantly richer in terms of expressivity.
This work was supported by the DFG as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS).
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References
Bloem, R., Chatterjee, K., Greimel, K., Henzinger, T.A., Jobstmann, B.: Robustness in the Presence of Liveness. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 410–424. Springer, Heidelberg (2010)
Bloem, R., Galler, S.J., Jobstmann, B., Piterman, N., Pnueli, A., Weiglhofer, M.: Interactive presentation: Automatic hardware synthesis from specifications: a case study. In: Lauwereins, R., Madsen, J. (eds.) DATE, pp. 1188–1193. ACM (2007)
Bloem, R., Galler, S.J., Jobstmann, B., Piterman, N., Pnueli, A., Weiglhofer, M.: Specify, compile, run: Hardware from PSL. Electr. Notes Theor. Comput. Sci. 190(4), 3–16 (2007)
Bojańczyk, M.: The Common Fragment of ACTL and LTL. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 172–185. Springer, Heidelberg (2008)
Browne, A., Clarke, E.M., Jha, S., Long, D.E., Marrero, W.R.: An improved algorithm for the evaluation of fixpoint expressions. Theor. Comput. Sci. 178(1-2), 237–255 (1997)
Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic model checking: 1020 states and beyond. Inf. Comput. 98(2), 142–170 (1992)
Cimatti, A., Clarke, E., Giunchiglia, E., Giunchiglia, F., Pistore, M., Roveri, M., Sebastiani, R., Tacchella, A.: NuSMV 2: An OpenSource Tool for Symbolic Model Checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 359–364. Springer, Heidelberg (2002)
de Alfaro, L., Faella, M.: An Accelerated Algorithm for 3-Color Parity Games with an Application to Timed Games. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 108–120. Springer, Heidelberg (2007)
Ehlers, R.: Minimising Deterministic Büchi Automata Precisely Using SAT Solving. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 326–332. Springer, Heidelberg (2010)
Ehlers, R.: Symbolic Bounded Synthesis. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 365–379. Springer, Heidelberg (2010)
Ehlers, R.: Experimental aspects of synthesis. In: Reich, J., Finkbeiner, B. (eds.) iWIGP. EPTCS, vol. 50, pp. 1–16 (2011)
Ehlers, R.: Generalized Rabin(1) Synthesis with Applications to Robust System Synthesis. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 101–115. Springer, Heidelberg (2011)
Ehlers, R.: Unbeast: Symbolic Bounded Synthesis. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 272–275. Springer, Heidelberg (2011)
Emerson, E.A., Jutla, C.S.: Tree automata, mu-calculus and determinacy (extended abstract). In: FOCS, pp. 368–377. IEEE Computer Society (1991)
Etessami, K., Wilke, T., Schuller, R.A.: Fair Simulation Relations, Parity Games, and State Space Reduction for Büchi Automata. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 694–707. Springer, Heidelberg (2001)
Filiot, E., Jin, N., Raskin, J.-F.: An Antichain Algorithm for LTL Realizability. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 263–277. Springer, Heidelberg (2009)
Filiot, E., Jin, N., Raskin, J.-F.: Compositional Algorithms for LTL Synthesis. In: Bouajjani, A., Chin, W.-N. (eds.) ATVA 2010. LNCS, vol. 6252, pp. 112–127. Springer, Heidelberg (2010)
Gastin, P., Oddoux, D.: Fast LTL to Büchi Automata Translation. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 53–65. Springer, Heidelberg (2001)
Hashiguchi, K.: Representation theorems on regular languages. J. Comput. Syst. Sci. 27(1), 101–115 (1983)
Janin, D., Lenzi, G.: On the relationship between monadic and weak monadic second order logic on arbitrary trees, with applications to the mu-calculus. Fundam. Inform. 61(3-4), 247–265 (2004)
Jobstmann, B., Galler, S., Weiglhofer, M., Bloem, R.: Anzu: A Tool for Property Synthesis. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 258–262. Springer, Heidelberg (2007)
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)
Klein, J., Baier, C.: Experiments with deterministic ω-automata for formulas of linear temporal logic. Theor. Comput. Sci. 363(2), 182–195 (2006)
Kukula, J.H., Shiple, T.R.: Building Circuits from Relations. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 113–123. Springer, Heidelberg (2000)
Maidl, M.: The common fragment of CTL and LTL. In: FOCS, pp. 643–652 (2000)
McNaughton, R.: Infinite games played on finite graphs. Ann. Pure Appl. Logic 65(2), 149–184 (1993)
Piterman, N., Pnueli, A., Sa’ar, Y.: Synthesis of Reactive(1) Designs. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 364–380. Springer, Heidelberg (2006)
Sohail, S., Somenzi, F.: Safety first: A two-stage algorithm for LTL games. In: FMCAD, pp. 77–84. IEEE (2009)
Somenzi, F.: CUDD: CU decision diagram package, release 2.4.2 (2009)
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Ehlers, R. (2012). ACTL ∩ LTL Synthesis. In: Madhusudan, P., Seshia, S.A. (eds) Computer Aided Verification. CAV 2012. Lecture Notes in Computer Science, vol 7358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31424-7_9
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