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Rabinizer 3: Safraless Translation of LTL to Small Deterministic Automata

  • Zuzana Komárková
  • Jan Křetínský
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8837)

Abstract

We present a tool for translating LTL formulae into deterministic ω-automata. It is the first tool that covers the whole LTL that does not use Safra’s determinization or any of its variants. This leads to smaller automata. There are several outputs of the tool: firstly, deterministic Rabin automata, which are the standard input for probabilistic model checking, e.g. for the probabilistic model-checker PRISM; secondly, deterministic generalized Rabin automata, which can also be used for probabilistic model checking and are sometimes by orders of magnitude smaller. We also link our tool to PRISM and show that this leads to a significant speed-up of probabilistic LTL model checking, especially with the generalized Rabin automata.

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References

  1. [BBDL+13]
    Babiak, T., Badie, T., Duret-Lutz, A., Křetínský, M., Strejček, J.: Compositional approach to suspension and other improvements to LTL translation. In: Bartocci, E., Ramakrishnan, C.R. (eds.) SPIN 2013. LNCS, vol. 7976, pp. 81–98. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  2. [BBKS13]
    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, Heidelberg (2013)CrossRefGoogle Scholar
  3. [BK08]
    Baier, C., Katoen, J.-P.: Principles of model checking. MIT Press (2008)Google Scholar
  4. [BKŘS12]
    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. [BKS13]
    Blahoudek, F., Křetínský, M., Strejček, J.: Comparison of LTL to deterministic Rabin automata translators. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR-19 2013. LNCS, vol. 8312, pp. 164–172. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  6. [CGK13]
    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)CrossRefGoogle Scholar
  7. [Cou99]
    Couvreur, J.-M.: On-the-fly verification of linear temporal logic. In: Wing, J.M., Woodcock, J. (eds.) FM 1999. LNCS, vol. 1708, pp. 253–271. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. [DGV99]
    Daniele, M., Giunchiglia, F., Vardi, M.Y.: Improved automata generation for linear temporal logic. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 249–260. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  9. [DL13]
    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, Heidelberg (2013)CrossRefGoogle Scholar
  10. [EH00]
    Etessami, K., Holzmann, G.J.: Optimizing Büchi automata. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 153–167. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  11. [EK14]
    Esparza, J., Křetínský, J.: From LTL to Deterministic Automata: A Safraless Compositional Approach. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 192–208. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  12. [Fri03]
    Fritz, C.: Constructing Büchi automata from linear temporal logic using simulation relations for alternating Büchi automata. In: Ibarra, O.H., Dang, Z. (eds.) CIAA 2003. LNCS, vol. 2759, pp. 35–48. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. [GKE12]
    Gaiser, A., Křetínský, J., Esparza, J.: Rabinizer: Small deterministic automata for LTL(F,G). In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, vol. 7561, pp. 72–76. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. [GL02]
    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
  15. [GO01]
    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), at http://www.lsv.ens-cachan.fr/~gastin/ltl2ba/ CrossRefGoogle Scholar
  16. [KB07]
    Klein, J., Baier, C.: On-the-fly stuttering in the construction of deterministic ω-automata. In: Holub, J., Žďárek, J. (eds.) CIAA 2007. LNCS, vol. 4783, pp. 51–61. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  17. [KE12]
    Křetínský, J., Esparza, J.: Deterministic automata for the (F,G)-fragment of LTL. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 7–22. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  18. [Kle]
    Klein, J.: ltl2dstar - LTL to deterministic Streett and Rabin automata, http://www.ltl2dstar.de/
  19. [KLG13]
    Křetínský, J., Garza, R.L.: Rabinizer 2: Small deterministic automata for LTL∖GU. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 446–450. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  20. [KNP11]
    Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: Verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  21. [KPB95]
    Krishnan, S.C., Puri, A., Brayton, R.K.: Structural complexity of ω-automata. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 143–156. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  22. [KPoR98]
    Kesten, Y., Pnueli, A., Raviv, L.-O.: Algorithmic verification of linear temporal logic specifications. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 1–16. Springer, Heidelberg (1998)Google Scholar
  23. [Pit06]
    Piterman, N.: From nondeterministic Büchi and Streett automata to deterministic parity automata. In: LICS, pp. 255–264 (2006)Google Scholar
  24. [Pnu77]
    Pnueli, A.: The temporal logic of programs. In: FOCS, pp. 46–57 (1977)Google Scholar
  25. [PZ08]
    Pnueli, A., Zaks, A.: On the merits of temporal testers. In: Grumberg, O., Veith, H. (eds.) 25MC Festschrift. LNCS, vol. 5000, pp. 172–195. Springer, Heidelberg (2008)Google Scholar
  26. [R3]
  27. [Saf88]
    Safra, S.: On the complexity of ω-automata. In: FOCS, pp. 319–327 (1988)Google Scholar
  28. [SB00]
    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
  29. [Sch09]
    Schewe, S.: Tighter bounds for the determinisation of Büchi automata. In: de Alfaro, L. (ed.) FOSSACS 2009. LNCS, vol. 5504, pp. 167–181. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  30. [SP]
    Spec Patterns: Property pattern mappings for LTL, http://patterns.projects.cis.ksu.edu/documentation/patterns/ltl.shtml
  31. [TTH13]
    Tsai, M.-H., Tsay, Y.-K., Hwang, Y.-S.: GOAL for games, omega-automata, and logics. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 883–889. Springer, Heidelberg (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Zuzana Komárková
    • 1
  • Jan Křetínský
    • 2
  1. 1.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic
  2. 2.ISTAustria

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