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LTL to Smaller Self-Loop Alternating Automata and Back

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Book cover Theoretical Aspects of Computing – ICTAC 2019 (ICTAC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11884))

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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.

F. Blahoudek has been supported by the F.R.S.-FNRS grant F.4520.18 (ManySynth). J. Major and J. Strejček have been supported by the Czech Science Foundation grant GA19-24397S.

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Notes

  1. 1.

    https://github.com/jurajmajor/ltl3tela/blob/master/ATVA19.md.

References

  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_31

    Chapter  Google Scholar 

  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_4

    Chapter  Google Scholar 

  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_8

    Chapter  MATH  Google Scholar 

  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. 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. 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_37

    Chapter  Google Scholar 

  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_15

    Chapter  Google Scholar 

  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_31

    Chapter  Google Scholar 

  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_8

    Chapter  Google Scholar 

  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. Emerson, E.A., Lei, C.-L.: Modalities for model checking: branching time logic strikes back. Sci. Comput. Program. 8(3), 275–306 (1987)

    Article  MathSciNet  Google Scholar 

  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_13

    Chapter  Google Scholar 

  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_6

    Chapter  Google Scholar 

  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_13

    Chapter  MATH  Google Scholar 

  15. Holeček, J., Kratochvíla, T., Řehák, V., Šafránek, D., Šimeček, P.: Verification results in Liberouter project. Technical report 03, 32 pp. CESNET, September 2004

    Google Scholar 

  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_30

    Chapter  Google Scholar 

  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_36

    Chapter  Google Scholar 

  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. 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. Müller, D., Sickert, S.: LTL to deterministic Emerson-Lei automata. In: Proceedings of GandALF 2017. EPTCS, vol. 256, pp. 180–194 (2017)

    Article  MathSciNet  Google Scholar 

  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_17

    Chapter  Google Scholar 

  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_20

    Chapter  MATH  Google Scholar 

  23. Pnueli, A.: The temporal logic of programs. In: Proceedings of FOCS 1977, pp. 46–57. IEEE Computer Society (1977)

    Google Scholar 

  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_56

    Chapter  MATH  Google Scholar 

  25. Rohde, G.S.: Alternating automata and the temporal logic of ordinals. Ph.D. thesis. University of Illinois at Urbana-Champaign (1997). ISBN 0-591-63604-2

    Google Scholar 

  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_21

    Chapter  Google Scholar 

  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 951-22-8343-3

    Google Scholar 

  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_116

    Chapter  Google Scholar 

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Authors and Affiliations

  1. University of Mons, Mons, Belgium

    František Blahoudek

  2. Masaryk University, Brno, Czech Republic

    Juraj Major & Jan Strejček

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  1. František Blahoudek
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  2. Juraj Major
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Correspondence to Juraj Major .

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  1. University of Sheffield, Sheffield, UK

    Robert Mark Hierons

  2. University of Bordeaux, Talence, France

    Mohamed Mosbah

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Blahoudek, F., Major, J., Strejček, J. (2019). LTL to Smaller Self-Loop Alternating Automata and Back. In: Hierons, R., Mosbah, M. (eds) Theoretical Aspects of Computing – ICTAC 2019. ICTAC 2019. Lecture Notes in Computer Science(), vol 11884. Springer, Cham. https://doi.org/10.1007/978-3-030-32505-3_10

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  • DOI: https://doi.org/10.1007/978-3-030-32505-3_10

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