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Counting Minimal Symmetric Difference NFAs

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Book cover Language and Automata Theory and Applications (LATA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7810))

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Abstract

A result of Nicaud states that the number of distinct unary regular string languages recognized by minimal deterministic finite automata (DFAs) with n states is asymptotically equal to n2n − 1. We consider the analogous question for symmetric difference automata (ℤ2-NFAs), and show that precisely 22n − 1 unary languages are recognized by n-state minimal ℤ2-NFAs.

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Author information

Authors and Affiliations

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

    Brink van der Merwe & Jaco Geldenhuys

  2. Department of Mathematics, Fairleigh Dickinson University, 1000 River Rd., Teaneck, NJ, 07666, USA

    Mark Farag

Authors
  1. Brink van der Merwe
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  2. Mark Farag
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  3. Jaco Geldenhuys
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Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

  2. Fakultät für Informatik, Institut für Wissens- und Sprachverarbeitung, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Bianca Truthe

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van der Merwe, B., Farag, M., Geldenhuys, J. (2013). Counting Minimal Symmetric Difference NFAs. In: Dediu, AH., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2013. Lecture Notes in Computer Science, vol 7810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37064-9_37

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  • DOI: https://doi.org/10.1007/978-3-642-37064-9_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37063-2

  • Online ISBN: 978-3-642-37064-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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