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On the Construction of a Family of Automata That Are Generically Non-minimal

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Language and Automata Theory and Applications (LATA 2013)

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

Abstract

One way to generate an accessible deterministic finite automaton is to first generate a spanning tree and then complete it to an automaton. We introduce the ideas of a sequential automaton, that are automata with sequential trees as breadth-first spanning subtrees. We introduce the concept of elementary equivalent states and explore combinatorial properties of non-minimal sequential automata. We then show that minimality is negligible among sequential automata by calculating the probability that an automaton has two elementary equivalent states and showing that this probability approach 1 as the size of the automaton increases.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, York College of the City University of New York, 94-20 Guy R. Brewer Blvd, Jamaica, NY, USA

    Parisa Babaali

  2. Department of Mathematics, Graduate Center of the City University of New York, 365 5th Avenue, New York, NY, USA

    Christopher Knaplund

Authors
  1. Parisa Babaali
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  2. Christopher Knaplund
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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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Babaali, P., Knaplund, C. (2013). On the Construction of a Family of Automata That Are Generically Non-minimal. 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_9

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  • DOI: https://doi.org/10.1007/978-3-642-37064-9_9

  • 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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