Fast Translation from LTL to Büchi Automata via Non-transition-based Automata

  • Shohei Mochizuki
  • Masaya Shimakawa
  • Shigeki Hagihara
  • Naoki Yonezaki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8829)


In model checking, properties are typically defined in linear temporal logic (LTL) and are translated into non-deterministic Büchi automata (NBA). In this paper, we propose a new, efficient translation method that is different from those used in LTL2BA, Spot and LTL3BA. Our method produces non-transition-based generalised Büchi automata (GBA) as an intermediate object, whereas LTL2BA, Spot, and LTL3BA use transition-based generalised Büchi automata (TGBA). Our method enables fast conversion because the data structure representing the object is simpler than that used in conversions via TGBA. Furthermore, we have developed techniques to reduce the number of states, similar to techniques that have heretofore only been available for conversions via TGBA. We also propose a technique to suppress the increase in the number of states that normally occurs while GBA is converted into NBA, using characteristics of strongly connected components of the GBA. We implemented our method with these techniques and experimentally compared our method with LTL2BA, Spot, and LTL3BA, which are the fastest translators to date. Our conversion method was much faster than LTL2BA and Spot, and was competitive with LTL3BA. In addition, the number of states in the NBA resulting from our method was comparable to that produced by LTL2BA, Spot, and LTL3BA.


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  1. 1.
    Abadi, M., Lamport, L., Wolper, P.: Realizable and unrealizable specifications of reactive systems. In: Ronchi Della Rocca, S., Ausiello, G., Dezani-Ciancaglini, M. (eds.) ICALP 1989. LNCS, vol. 372, pp. 1–17. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  2. 2.
    Aoshima, T., Sakuma, K., Yonezaki, N.: An efficient verification procedure supporting evolution of reactive system specifications. In: Proc. of the 4th International Workshop on Principles of Software Evolution, pp. 182–185. ACM (2001)Google Scholar
  3. 3.
    Aoshima, T., Yonezaki, N.: Verification of reactive system specification with outer event conditional formula. In: International Symposium on Principles of Software Evolution (ISPSE2000), pp. 195–199 (2000)Google Scholar
  4. 4.
    Babiak, T., Křetínský, M., Řehák, V., Strejček, J.: LTL to büchi automata translation: Fast and more deterministic. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 95–109. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  5. 5.
    Duret-Lutz, A.: LTL translation improvements in Spot. In: Proc. of the Fifth international conference on Verification and Evaluation of Computer and Communication Systems, VECoS 2011, pp. 72–83. British Computer Society (2011)Google Scholar
  6. 6.
    Duret-Lutz, A., Poitrenaud, D.: Spot: An extensible model checking library using transition-based generalized Büchi automata. In: Proc. of MASCOTS 2004, pp. 76–83. IEEE Computer Society (2004)Google Scholar
  7. 7.
    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
  8. 8.
    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
  9. 9.
    Gerth, R., Peled, D., Vardi, M.Y., Wolper, P.: Simple on-the-fly automatic verification of linear temporal logic. In: Protocol Specification Testing and Verification, pp. 3–18. Chapman & Hall (1995)Google Scholar
  10. 10.
    Giannakopoulou, D., Lerda, F.: From states to transitions: Improving translation of LTL formulae to Büchi automata. In: Peled, D.A., Vardi, M.Y. (eds.) FORTE 2002. LNCS, vol. 2529, pp. 308–326. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Holzmann, G.J.: The model checker SPIN. IEEE Trans. Softw. Eng. 23(5), 279–295 (1997), MathSciNetCrossRefGoogle Scholar
  12. 12.
    Jobstmann, B., Bloem, R.: Optimizations for LTL synthesis. In: Formal Methods in Computer Aided Design, FMCAD 2006, pp. 117–124 (2006)Google Scholar
  13. 13.
    Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: POPL 1989, pp. 179–190 (1989)Google Scholar
  14. 14.
    Rozier, K.Y., Vardi, M.Y.: LTL satisfiability checking. In: Bošnački, D., Edelkamp, S. (eds.) SPIN 2007. LNCS, vol. 4595, pp. 149–167. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  15. 15.
    Somenzi, F., Bloem, R.: Efficient Büchi automata from LTL formulae. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 248–263. Springer, Heidelberg (2000)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Shohei Mochizuki
    • 1
  • Masaya Shimakawa
    • 1
  • Shigeki Hagihara
    • 1
  • Naoki Yonezaki
    • 1
  1. 1.Department of Computer Science, Graduate School of Information Science and EngineeringTokyo Institute of TechnologyMeguro-kuJapan

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