Advertisement

LTL to Smaller Self-Loop Alternating Automata and Back

  • František Blahoudek
  • Juraj MajorEmail author
  • Jan Strejček
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11884)

Abstract

Self-loop alternating automata (SLAA) with Büchi or co-Büchi acceptance are popular intermediate formalisms in translations of LTL to deterministic or nondeterministic automata. This paper considers SLAA with generic transition-based Emerson-Lei acceptance and presents translations of LTL to these automata and back. Importantly, the translation of LTL to SLAA with generic acceptance produces considerably smaller automata than previous translations of LTL to Büchi or co-Büchi SLAA. Our translation is already implemented in the tool LTL3TELA, where it helps to produce small deterministic or nondeterministic automata for given LTL formulae.

References

  1. 1.
    Babiak, T., et al.: The Hanoi Omega-Automata Format. In: Kroening, D., Păsăreanu, C.S. (eds.) CAV 2015, Part I. LNCS, vol. 9206, pp. 479–486. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-21690-4_31CrossRefGoogle Scholar
  2. 2.
    Babiak, T., Blahoudek, F., Křetínský, M., Strejček, J.: Effective translation of LTL to deterministic Rabin automata: beyond the (F,G)-fragment. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 24–39. Springer, Cham (2013).  https://doi.org/10.1007/978-3-319-02444-8_4CrossRefGoogle Scholar
  3. 3.
    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).  https://doi.org/10.1007/978-3-642-28756-5_8CrossRefzbMATHGoogle Scholar
  4. 4.
    Baier, C., Blahoudek, F., Duret-Lutz, A., Klein, J., Müller, D., Strejček, J.: Generic emptiness check for fun and profit. In: Chen, Y.-F., Cheng, C.-H., Esparza, J. (eds.) ATVA 2019. LNCS, vol. 11781, pp. 445–461. Springer, Cham (2019) Google Scholar
  5. 5.
    Blahoudek, F., Major, J., Strejček, J.: LTL to smaller self-loop alternating automata and back. In: CoRR abs/1908.04645 (2019). http://arxiv.org/abs/1908.04645
  6. 6.
    Chatterjee, K., Gaiser, A., Křetínský, J.: Automata with generalized Rabin pairs for probabilistic model checking and LTL synthesis. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 559–575. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-39799-8_37CrossRefGoogle Scholar
  7. 7.
    Couvreur, J.-M., Duret-Lutz, A., Poitrenaud, D.: On-the-fly emptiness checks for generalized Büchi automata. In: Godefroid, P. (ed.) SPIN 2005. LNCS, vol. 3639, pp. 169–184. Springer, Heidelberg (2005).  https://doi.org/10.1007/11537328_15CrossRefGoogle Scholar
  8. 8.
    Duret-Lutz, A.: Manipulating LTL formulas using Spot 1.0. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 442–445. Springer, Cham (2013).  https://doi.org/10.1007/978-3-319-02444-8_31CrossRefGoogle Scholar
  9. 9.
    Duret-Lutz, A., Lewkowicz, A., Fauchille, A., Michaud, T., Renault, É., Xu, L.: Spot 2.0 — a framework for LTL and \(\omega \)-automata manipulation. In: Artho, C., Legay, A., Peled, D. (eds.) ATVA 2016. LNCS, vol. 9938, pp. 122–129. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-46520-3_8CrossRefGoogle Scholar
  10. 10.
    Dwyer, M.B., Avrunin, G.S., Corbett, J.C.: Property specification patterns for finite-state verification. In: Proceedings of FMSP 1998, pp. 7–15. ACM (1998)Google Scholar
  11. 11.
    Emerson, E.A., Lei, C.-L.: Modalities for model checking: branching time logic strikes back. Sci. Comput. Program. 8(3), 275–306 (1987)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Etessami, K., Holzmann, G.J.: Optimizing Büchi automata. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 153–168. Springer, Heidelberg (2000).  https://doi.org/10.1007/3-540-44618-4_13CrossRefGoogle Scholar
  13. 13.
    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).  https://doi.org/10.1007/3-540-44585-4_6CrossRefGoogle Scholar
  14. 14.
    Hammer, M., Knapp, A., Merz, S.: Truly on-the-fly LTL model checking. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 191–205. Springer, Heidelberg (2005).  https://doi.org/10.1007/978-3-540-31980-1_13CrossRefzbMATHGoogle Scholar
  15. 15.
    Holeček, J., Kratochvíla, T., Řehák, V., Šafránek, D., Šimeček, P.: Verification results in Liberouter project. Technical report 03, 32 pp. CESNET, September 2004Google Scholar
  16. 16.
    Křetínský, J., Meggendorfer, T., Sickert, S., Ziegler, C.: Rabinizer 4: from LTL to your favourite deterministic automaton. In: Chockler, H., Weissenbacher, G. (eds.) CAV 2018. LNCS, vol. 10981, pp. 567–577. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-96145-3_30CrossRefGoogle Scholar
  17. 17.
    Loding, C., Thomas, W.: Alternating automata and logics over infinite words. In: van Leeuwen, J., Watanabe, O., Hagiya, M., Mosses, P.D., Ito, T. (eds.) TCS 2000. LNCS, vol. 1872, pp. 521–535. Springer, Heidelberg (2000).  https://doi.org/10.1007/3-540-44929-9_36CrossRefGoogle Scholar
  18. 18.
    Major, J., Blahoudek, F., Strejček, J., Sasaráková, M., Zbončáková, T.: ltl3tela: LTL to small deterministic or nondeterministic Emerson-Lei automata. In: Chen, Y.-F., Cheng, C.-H., Esparza, J. (eds.) ATVA 2019. LNCS, vol. 11781, pp. 357–365. Springer, Cham (2019)Google Scholar
  19. 19.
    Muller, D.E., Saoudi, A., Schupp, P.E.: Weak alternating automata give a simple explanation of why most temporal and dynamic logics are decidable in exponential time. In: Proceedings of LICS 1988, pp. 422–427. IEEE Computer Society (1988)Google Scholar
  20. 20.
    Müller, D., Sickert, S.: LTL to deterministic Emerson-Lei automata. In: Proceedings of GandALF 2017. EPTCS, vol. 256, pp. 180–194 (2017)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Pelánek, R.: BEEM: benchmarks for explicit model checkers. In: Bošnački, D., Edelkamp, S. (eds.) SPIN 2007. LNCS, vol. 4595, pp. 263–267. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-73370-6_17CrossRefGoogle Scholar
  22. 22.
    Pelánek, R., Strejček, J.: Deeper connections between LTL and alternating automata. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, pp. 238–249. Springer, Heidelberg (2006).  https://doi.org/10.1007/11605157_20CrossRefzbMATHGoogle Scholar
  23. 23.
    Pnueli, A.: The temporal logic of programs. In: Proceedings of FOCS 1977, pp. 46–57. IEEE Computer Society (1977)Google Scholar
  24. 24.
    Renault, E., Duret-Lutz, A., Kordon, F., Poitrenaud, D.: Parallel explicit model checking for generalized Büchi automata. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 613–627. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46681-0_56CrossRefzbMATHGoogle Scholar
  25. 25.
    Rohde, G.S.: Alternating automata and the temporal logic of ordinals. Ph.D. thesis. University of Illinois at Urbana-Champaign (1997). ISBN 0-591-63604-2Google Scholar
  26. 26.
    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).  https://doi.org/10.1007/10722167_21CrossRefGoogle Scholar
  27. 27.
    Tauriainen, H.: Automata and linear temporal logic: translations with transition-based acceptance. Ph.D. thesis. Helsinki University of Technology, Laboratory for Theoretical Computer Science (2006). ISBN 951-22-8343-3Google Scholar
  28. 28.
    Vardi, M.Y.: Nontraditional applications of automata theory. In: Hagiya, M., Mitchell, J.C. (eds.) TACS 1994. LNCS, vol. 789, pp. 575–597. Springer, Heidelberg (1994).  https://doi.org/10.1007/3-540-57887-0_116CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • František Blahoudek
    • 1
  • Juraj Major
    • 2
    Email author
  • Jan Strejček
    • 2
  1. 1.University of MonsMonsBelgium
  2. 2.Masaryk UniversityBrnoCzech Republic

Personalised recommendations