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 


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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.

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