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International Conference on Language and Automata Theory and Applications

LATA 2017: Language and Automata Theory and Applications pp 261–272Cite as

Lower Bound Methods for the Size of Nondeterministic Finite Automata Revisited

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10168))

Abstract

We revisit the following lower bound methods for the size of a nondeterministic finite automaton: the fooling set technique, the extended fooling set technique, and the biclique edge cover technique, presenting these methods in terms of quotients and atoms of regular languages. Although the lower bounds obtained by these methods are not necessarily tight, some classes of languages for which tight bounds can be achieved, are known. We show that languages with maximal reversal complexity belong to the class of languages for which the fooling set technique provides a tight bound. We also show that the extended fooling set technique is tight for a subclass of unary cyclic languages.

This work was supported by the Estonian Ministry of Education and Research institutional research grant IUT33-13 and by the ERDF funded ICT National Programme project “Coinduction”.

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Authors and Affiliations

  1. Institute of Cybernetics, Tallinn University of Technology, Akadeemia tee 21, 12618, Tallinn, Estonia

    Hellis Tamm

  2. Department of Computer Science, Stellenbosch University, Private Bag X1, Matieland, 7602, South Africa

    Brink van der Merwe

Authors
  1. Hellis Tamm
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  2. Brink van der Merwe
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Corresponding author

Correspondence to Hellis Tamm .

Editor information

Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Frank Drewes

  2. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  3. University of Giessen, Giessen, Germany

    Bianca Truthe

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Tamm, H., van der Merwe, B. (2017). Lower Bound Methods for the Size of Nondeterministic Finite Automata Revisited. In: Drewes, F., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2017. Lecture Notes in Computer Science(), vol 10168. Springer, Cham. https://doi.org/10.1007/978-3-319-53733-7_19

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  • DOI: https://doi.org/10.1007/978-3-319-53733-7_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53732-0

  • Online ISBN: 978-3-319-53733-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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