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Magic Numbers and Ternary Alphabet

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Developments in Language Theory (DLT 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5583))

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Abstract

A number α, in the range from n to 2n, is magic for n with respect to a given alphabet size s, if there is no minimal nondeterministic finite automaton of n states and s input letters whose equivalent minimal deterministic finite automaton has α states. We show that in the case of a ternary alphabet, there are no magic numbers. For all n and α satisfying that \(n \leqslant \alpha \leqslant 2^n\), we describe an n-state nondeterministic automaton with a three-letter input alphabet that needs α deterministic states.

Research supported by VEGA grant 2/0111/09.

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Author information

Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovakia

    Galina Jirásková

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  1. Galina Jirásková
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Editors and Affiliations

  1. Institut für Formale Methoden der Informatik, FMI, Universität Stuttgart, Universitätsstrasse 38, 70569, Stuttgart, Germany

    Volker Diekert  & Dirk Nowotka  & 

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Jirásková, G. (2009). Magic Numbers and Ternary Alphabet. In: Diekert, V., Nowotka, D. (eds) Developments in Language Theory. DLT 2009. Lecture Notes in Computer Science, vol 5583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02737-6_24

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  • DOI: https://doi.org/10.1007/978-3-642-02737-6_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02736-9

  • Online ISBN: 978-3-642-02737-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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