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On the Size of the Universal Automaton of a Regular Language

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STACS 2007 (STACS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4393))

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Abstract

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.

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Authors and Affiliations

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

    Sylvain Lombardy

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  1. Sylvain Lombardy
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Wolfgang Thomas Pascal Weil

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Lombardy, S. (2007). On the Size of the Universal Automaton of a Regular Language. In: Thomas, W., Weil, P. (eds) STACS 2007. STACS 2007. Lecture Notes in Computer Science, vol 4393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70918-3_8

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  • DOI: https://doi.org/10.1007/978-3-540-70918-3_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70917-6

  • Online ISBN: 978-3-540-70918-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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