On the Size of the Universal Automaton of a Regular Language

  • Sylvain Lombardy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4393)


The universal automaton of a regular language is the maximal NFA without merging states that recognizes this language. This automaton is directly inspired by the factor matrix defined by Conway thirty years ago. We prove in this paper that a tight bound on its size with respect to the size of the smallest equivalent NFA is given by Dedekind’s numbers. At the end of the paper, we deal with the unary case. Chrobak has proved that the size of the minimal deterministic automaton with respect to the smallest NFA is tightly bounded by the Landau’s function; we show that the size of the universal automaton is in this case an exponential of the Landau’s function.


Regular languages Universal Automaton NFA Minimization. 


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© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Sylvain Lombardy
    • 1
  1. 1.Université de Marne-la-Valle, Institut Gaspard-Monge, UMR CNRS 8049, 77454 Marne-la-Valle Cedex 2 

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