When Simulation Meets Antichains

(On Checking Language Inclusion of Nondeterministic Finite (Tree) Automata)
  • Parosh Aziz Abdulla
  • Yu-Fang Chen
  • Lukáš Holík
  • Richard Mayr
  • Tomáš Vojnar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6015)


We describe a new and more efficient algorithm for checking universality and language inclusion on nondeterministic finite word automata (NFA) and tree automata (TA). To the best of our knowledge, the antichain-based approach proposed by De Wulf et al. was the most efficient one so far. Our idea is to exploit a simulation relation on the states of finite automata to accelerate the antichain-based algorithms. Normally, a simulation relation can be obtained fairly efficiently, and it can help the antichain-based approach to prune out a large portion of unnecessary search paths. We evaluate the performance of our new method on NFA/TA obtained from random regular expressions and from the intermediate steps of regular model checking. The results show that our approach significantly outperforms the previous antichain-based approach in most of the experiments.


Tree Automaton Simulation Relation Maximal Simulation Product Automaton Nondeterministic Finite Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  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 (On Checking Language Inclusion of Nondeterministic Finite (Tree) Automata). Technical report, FIT-TR-2010-001, FIT, Brno University of Technology, Czech Republic (2010)Google Scholar
  3. 3.
    Bouajjani, A., Habermehl, P., Holík, L., Touili, T., Vojnar, T.: Antichain-Based Universality and Inclusion Testing over Nondet. Finite Tree Automata. In: Ibarra, O.H., Ravikumar, B. (eds.) CIAA 2008. LNCS, vol. 5148, pp. 57–67. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Bouajjani, A., Habermehl, P., Moro, P., Vojnar, T.: Verifying Programs with Dynamic 1-Selector-Linked Structures in Regular Model Checking. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 13–29. Springer, Heidelberg (2005)Google Scholar
  5. 5.
    Bouajjani, A., Habermehl, P., Vojnar, T.: Abstract Regular Model Checking. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 372–386. Springer, Heidelberg (2004)Google Scholar
  6. 6.
    Brzozowski, J.A.: Canonical Regular Expressions and Minimal State Graphs for Definite Events. In: Mathematical Theory of Automata (1962)Google Scholar
  7. 7.
    Dill, D.L., Hu, A.J., Wong-Toi, H.: Checking for Language Inclusion Using Simulation Preorders. In: Larsen, K.G., Skou, A. (eds.) CAV 1991. LNCS, vol. 575. Springer, Heidelberg (1992)Google Scholar
  8. 8.
    Henzinger, M.R., Henzinger, T.A., Kopke, P.W.: Computing simulations on finite and infinite graphs. In: Proc. 36th FOCS (1995)Google Scholar
  9. 9.
    Holík, L., Šimáček, J.: Optimizing an LTS-Simulation Algorithm. In: Proc. of MEMICS 2009 (2009)Google Scholar
  10. 10.
    Hopcroft, J.E.: An n.log n Algorithm for Minimizing States in a Finite Automaton. Technical Report CS-TR-71-190, Stanford University (1971)Google Scholar
  11. 11.
    Meyer, A.R., Stockmeyer, L.J.: The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Space. In: Proc. of the 13th Annual Symposium on Switching and Automata Theory. IEEE CS, Los Alamitos (1972)Google Scholar
  12. 12.
    Møller, F. (2004),
  13. 13.
    De Wulf, M., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Antichains: A New Algorithm for Checking Universality of Finite Automata. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 17–30. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Parosh Aziz Abdulla
    • 1
  • Yu-Fang Chen
    • 1
  • Lukáš Holík
    • 2
  • Richard Mayr
    • 3
  • Tomáš Vojnar
    • 2
  1. 1.Uppsala University 
  2. 2.Brno University of Technology 
  3. 3.University of Edinburgh 

Personalised recommendations