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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
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
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
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
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)
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
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
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
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
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
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)
Emerson, E.A., Lei, C.-L.: Modalities for model checking: branching time logic strikes back. Sci. Comput. Program. 8(3), 275–306 (1987)
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
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
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
Holeček, J., Kratochvíla, T., Řehák, V., Šafránek, D., Šimeček, P.: Verification results in Liberouter project. Technical report 03, 32 pp. CESNET, September 2004
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
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
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)
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)
Müller, D., Sickert, S.: LTL to deterministic Emerson-Lei automata. In: Proceedings of GandALF 2017. EPTCS, vol. 256, pp. 180–194 (2017)
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
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
Pnueli, A.: The temporal logic of programs. In: Proceedings of FOCS 1977, pp. 46–57. IEEE Computer Society (1977)
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
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
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
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
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
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-030-32505-3_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32504-6
Online ISBN: 978-3-030-32505-3
eBook Packages: Computer ScienceComputer Science (R0)