Advertisement

ACTL ∩ LTL Synthesis

  • Rüdiger Ehlers
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7358)

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.

Keywords

Synthesis Problem Winning Strategy Decision Sequence Computation Tree Logic Common Fragment 
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.
Download to read the full conference paper text

References

  1. 1.
    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)CrossRefGoogle Scholar
  2. 2.
    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)Google Scholar
  3. 3.
    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)CrossRefGoogle Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    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)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    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)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    Ehlers, R.: Symbolic Bounded Synthesis. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 365–379. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Ehlers, R.: Experimental aspects of synthesis. In: Reich, J., Finkbeiner, B. (eds.) iWIGP. EPTCS, vol. 50, pp. 1–16 (2011)Google Scholar
  12. 12.
    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)CrossRefGoogle Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    Emerson, E.A., Jutla, C.S.: Tree automata, mu-calculus and determinacy (extended abstract). In: FOCS, pp. 368–377. IEEE Computer Society (1991)Google Scholar
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    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)CrossRefGoogle Scholar
  18. 18.
    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)CrossRefGoogle Scholar
  19. 19.
    Hashiguchi, K.: Representation theorems on regular languages. J. Comput. Syst. Sci. 27(1), 101–115 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    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)MathSciNetzbMATHGoogle Scholar
  21. 21.
    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)CrossRefGoogle Scholar
  22. 22.
    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)CrossRefGoogle Scholar
  23. 23.
    Klein, J., Baier, C.: Experiments with deterministic ω-automata for formulas of linear temporal logic. Theor. Comput. Sci. 363(2), 182–195 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    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)CrossRefGoogle Scholar
  25. 25.
    Maidl, M.: The common fragment of CTL and LTL. In: FOCS, pp. 643–652 (2000)Google Scholar
  26. 26.
    McNaughton, R.: Infinite games played on finite graphs. Ann. Pure Appl. Logic 65(2), 149–184 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    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)CrossRefGoogle Scholar
  28. 28.
    Sohail, S., Somenzi, F.: Safety first: A two-stage algorithm for LTL games. In: FMCAD, pp. 77–84. IEEE (2009)Google Scholar
  29. 29.
    Somenzi, F.: CUDD: CU decision diagram package, release 2.4.2 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Rüdiger Ehlers
    • 1
  1. 1.Reactive Systems GroupSaarland UniversityGermany

Personalised recommendations

Cite paper