Reduction of Nondeterministic Tree Automata

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9636)

Abstract

We present an efficient algorithm to reduce the size of nondeterministic tree automata, while retaining their language. It is based on new transition pruning techniques, and quotienting of the state space w.r.t. suitable equivalences. It uses criteria based on combinations of downward and upward simulation preorder on trees, and the more general downward and upward language inclusions. Since tree-language inclusion is EXPTIME-complete, we describe methods to compute good approximations in polynomial time.

We implemented our algorithm as a module of the well-known libvata tree automata library, and tested its performance on a given collection of tree automata from various applications of libvata in regular model checking and shape analysis, as well as on various classes of randomly generated tree automata. Our algorithm yields substantially smaller and sparser automata than all previously known reduction techniques, and it is still fast enough to handle large instances.

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References

  1. 1.
    Abdulla, P.A., Bouajjani, A., Holík, L., Kaati, L., Vojnar, T.: Computing simulations over tree automata. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 93–108. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Abdulla, P.A., Chen, Y.-F., Holík, L., Mayr, R., Vojnar, T.: When simulation meets antichains. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 158–174. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Abdulla, P.A., Holík, L., Jonsson, B., Lengál, O., Trinh, C.Q., Vojnar, T.: Verification of heap manipulating programs with ordered data by extended forest automata. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 224–239. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  4. 4.
    Abdulla, P.A., Holík, L., Kaati, L., Vojnar, T.: A uniform (bi-)simulation-based framework for reducing tree automata. Electr. Notes Theor. Comput. Sci. 251, 27–48 (2009)CrossRefMATHGoogle Scholar
  5. 5.
    Abdulla, P.A., Legay, A., d’Orso, J., Rezine, A.: Simulation-based iteration of tree transducers. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 30–44. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Abdulla, P.A., Legay, A., d’Orso, J., Rezine, A.: Tree regular model checking: a simulation-based approach. J. Log. Algebr. Program. 69(1–2), 93–121 (2006)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Almeida, R., Holík, L., Mayr, R.: HeavyMinOTAut (2015). http://tinyurl.com/pm2b4qk
  8. 8.
    Almeida, R., Holík, L., Mayr, R.: Reduction of nondeterministic tree automata. Technical report EDI-INF-RR-1421, University of Edinburgh (2016). arXiv 1512.08823Google Scholar
  9. 9.
    Basin, D., Karlund, N., Møller, A.: Mona (2015). http://www.brics.dk/mona
  10. 10.
    Bonchi, F., Pous, D.: Checking NFA equivalence with bisimulations up to congruence. In: Principles of Programming Languages (POPL), Rome, Italy. ACM (2013)Google Scholar
  11. 11.
    Bouajjani, A., Habermehl, P., Holík, L., Touili, T., Vojnar, T.: Antichain-based universality and inclusion testing over nondeterministic finite tree automata. In: Ibarra, O.H., Ravikumar, B. (eds.) CIAA 2008. LNCS, vol. 5148, pp. 57–67. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Bouajjani, A., Habermehl, P., Rogalewicz, A., Vojnar, T.: Abstract regular tree model checking of complex dynamic data structures. In: Yi, K. (ed.) SAS 2006. LNCS, vol. 4134, pp. 52–70. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Clemente, L., Mayr, R.: Advanced automata minimization. In: 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL, pp. 63–74. ACM (2013)Google Scholar
  14. 14.
    Comon, H., Dauchet, M., Gilleron, R., Löding, C., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (2008). http://www.grappa.univ-lille3.fr/tata. Release 18 November 2008
  15. 15.
    Durand, I.: Autowrite (2015). http://dept-info.labri.fr/~idurand/autowrite
  16. 16.
    Genet, T., et al.: Timbuk (2015). http://www.irisa.fr/celtique/genet/timbuk/
  17. 17.
    Etessami, K.: A hierarchy of polynomial-time computable simulations for automata. In: Brim, L., Jančar, P., Křetínský, M., Kučera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 131–144. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  18. 18.
    Habermehl, P., Holík, L., Rogalewicz, A., Šimáček, J., Vojnar, T.: Forest automata for verification of heap manipulation. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 424–440. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  19. 19.
    Holík, L.: Simulations and Antichains for Efficient Handling of Finite Automata. Ph.D. thesis, Faculty of Information Technology of Brno University of Technology (2011)Google Scholar
  20. 20.
    Holík, L., Lengál, O., Rogalewicz, A., Šimáček, J., Vojnar, T.: Fully automated shape analysis based on forest automata. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 740–755. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  21. 21.
    Holík, L., Lengál, O., Šimáček, J., Vojnar, T.: Efficient inclusion checking on explicit and semi-symbolic tree automata. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 243–258. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  22. 22.
    Lengál, O., Simácek, J., Vojnar, T.: Libvata: highly optimised non-deterministic finite tree automata library (2015). http://www.fit.vutbr.cz/research/groups/verifit/tools/libvata/
  23. 23.
    Lengál, O., Simácek, J., Vojnar, T., Habermehl, P., Holík, L., Rogalewicz, A.: Forester: tool for verification of programs with pointers (2015). http://www.fit.vutbr.cz/research/groups/verifit/tools/forester/
  24. 24.
    Tabakov, D., Vardi, M.: Model Checking Büchi Specifications. In LATA, volume Report 35/07. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Tarragona (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.University of EdinburghEdinburghUK
  2. 2.Brno University of TechnologyBrnoCzech Republic

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