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Star-Complement-Star on Prefix-Free Languages

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Descriptional Complexity of Formal Systems (DCFS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9118))

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Abstract

We study the star-complement-star operation on prefix-free languages. We get a tight upper bound \(2^{n-3}+2\) for the state complexity of this combined operation on prefix free languages. To prove tightness, we use a binary alphabet. Then we present the results of our computations concerning star-complement-star on binary prefix-free languages. We also show that state complexity of star-complement-star of every unary prefix-free language is one, except for the language \(\{a\}\), where it is two.

M. Palmovský—Research supported by VEGA grant 2/0084/15.

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

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Authors and Affiliations

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

    Matúš Palmovský

  2. Institute of Computer Science, Faculty of Science, P.J. Šafárik University, Jesenná 5, 040 01, Košice, Slovakia

    Juraj Šebej

Authors
  1. Matúš Palmovský
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  2. Juraj Šebej
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Correspondence to Juraj Šebej .

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Editors and Affiliations

  1. School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada

    Jeffrey Shallit

  2. Department of Mathematics, University of Turku, Turku, Finland

    Alexander Okhotin

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Palmovský, M., Šebej, J. (2015). Star-Complement-Star on Prefix-Free Languages. In: Shallit, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2015. Lecture Notes in Computer Science(), vol 9118. Springer, Cham. https://doi.org/10.1007/978-3-319-19225-3_20

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  • DOI: https://doi.org/10.1007/978-3-319-19225-3_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19224-6

  • Online ISBN: 978-3-319-19225-3

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