Antichains: A New Algorithm for Checking Universality of Finite Automata

  • M. De Wulf
  • L. Doyen
  • T. A. Henzinger
  • J. -F. Raskin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4144)


We propose and evaluate a new algorithm for checking the universality of nondeterministic finite automata. In contrast to the standard algorithm, which uses the subset construction to explicitly determinize the automaton, we keep the determinization step implicit. Our algorithm computes the least fixed point of a monotone function on the lattice of antichains of state sets. We evaluate the performance of our algorithm experimentally using the random automaton model recently proposed by Tabakov and Vardi. We show that on the difficult instances of this probabilistic model, the antichain algorithm outperforms the standard one by several orders of magnitude. We also show how variations of the antichain method can be used for solving the language-inclusion problem for nondeterministic finite automata, and the emptiness problem for alternating finite automata.


Monotone Function Finite Automaton Average Execution Time Dual Lattice Nondeterministic 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. [BL80]
    Brzozowski, J.A., Leiss, E.L.: On equations for regular languages, finite automata, and sequential networks. Theoretical Computer Science 10, 19–35 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  2. [CCGR99]
    Cimatti, A., Clarke, E.M., Giunchiglia, F., Roveri, M.: NUSMV: A new symbolic model verifier. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 495–499. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  3. [CKS81]
    Chandra, A.K., Kozen, D., Stockmeyer, L.J.: Alternation. J. ACM 28, 114–133 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  4. [DDR06]
    De Wulf, M., Doyen, L., Raskin, J.-F.: A lattice theory for solving games of imperfect information. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 153–168. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. [HMU01]
    Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (2001)zbMATHGoogle Scholar
  6. [KV01]
    Kupferman, O., Vardi, M.Y.: Weak alternating automata are not that weak. ACM Trans. Computational Logic 2, 408–429 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  7. [Mø04]
    Møller, A.: dk.brics.automaton (2004),
  8. [MS72]
    Meyer, A.R., Stockmeyer, L.J.: The equivalence problem for regular expressions with squaring requires exponential space. In: Symp. Foundations of Computer Science, pp. 125–129. IEEE Computer Society, Los Alamitos (1972)Google Scholar
  9. [Rei84]
    Reif, J.H.: The complexity of two-player games of incomplete information. J. Computer and System Sciences 29, 274–301 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  10. [Som98]
    Somenzi, F.: CUDD: CU Decision Diagram Package Release 2.3.0. University of Colorado at Boulder (1998)Google Scholar
  11. [TV05]
    Tabakov, D., Vardi, M.Y.: Experimental evaluation of classical automata constructions. In: Sutcliffe, G., Voronkov, A. (eds.) LPAR 2005. LNCS (LNAI), vol. 3835, pp. 396–411. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • M. De Wulf
    • 1
  • L. Doyen
    • 1
  • T. A. Henzinger
    • 2
    • 3
  • J. -F. Raskin
    • 1
  1. 1.CSUniversité Libre de BruxellesBelgium
  2. 2.I&CEcole Polytechnique Fédérale de Lausanne (EPFL)Switzerland
  3. 3.EECSUniversity of California at BerkeleyU.S.A.

Personalised recommendations