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The Boundary of Prefix-Free Languages

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Developments in Language Theory (DLT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9168))

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Abstract

We investigate the boundary operation on the class of prefix-free regular languages. We show that if a prefix-free language is recognized by a deterministic finite automaton of n states, then its boundary is recognized by a deterministic automaton of at most \((n-1)\cdot 2^{n-4}+n+1\) states. We prove that this bound is tight, and to describe worst-case examples, we use a three-letter alphabet. Next we show that the tight bound for boundary on binary prefix-free languages is \(2n-2\), and that in the unary case, the tight bound is \(n-2\).

J. Jirásek—Research supported by VEGA grant 1/0142/15.

G. Jirásková—Research supported by VEGA grant 2/0084/15.

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Authors and Affiliations

  1. Institute of Computer Science, Faculty of Science, P.J. Šafárik University, Jesenná 5, 04001, Košice, Slovakia

    Jozef Jirásek

  2. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 04001, Košice, Slovakia

    Galina Jirásková

Authors
  1. Jozef Jirásek
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  2. Galina Jirásková
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Corresponding author

Correspondence to Galina Jirásková .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Igor Potapov

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Jirásek , J., Jirásková, G. (2015). The Boundary of Prefix-Free Languages. In: Potapov, I. (eds) Developments in Language Theory. DLT 2015. Lecture Notes in Computer Science(), vol 9168. Springer, Cham. https://doi.org/10.1007/978-3-319-21500-6_24

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  • DOI: https://doi.org/10.1007/978-3-319-21500-6_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21499-3

  • Online ISBN: 978-3-319-21500-6

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