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International Workshop on Descriptional Complexity of Formal Systems

DCFS 2014: Descriptional Complexity of Formal Systems pp 210–221Cite as

Prefix-Free Languages: Right Quotient and Reversal

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8614))

Abstract

We investigate the right quotient and the reversal operations on the class of prefix-free languages. We get the tight bounds n − 1 and 2n − 2 + 1 on the state complexity of right quotient and reversal, respectively. To prove the tightness of the bound for reversal, we use a ternary alphabet. Moreover, we prove that this bound cannot be met by any binary language. In the binary case, we get a lower bound 2n − 2 − 7 infinitely often. Our calculations show that this lower bound cannot be exceeded.

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Authors and Affiliations

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

    Jozef Jirásek, Monika Krausová & Juraj Šebej

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

    Galina Jirásková & Peter Mlynárčik

Authors
  1. Jozef Jirásek
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  2. Galina Jirásková
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  3. Monika Krausová
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  4. Peter Mlynárčik
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  5. Juraj Šebej
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Editor information

Editors and Affiliations

  1. Department of Computer Science, The University of Western Ontario, N6A 5B7, London, Ontario, Canada

    Helmut Jürgensen

  2. Department of Mathematics and TUCS, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  3. University of Turku, Fi-20014, Turku, Finland

    Alexander Okhotin

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Jirásek, J., Jirásková, G., Krausová, M., Mlynárčik, P., Šebej, J. (2014). Prefix-Free Languages: Right Quotient and Reversal. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2014. Lecture Notes in Computer Science, vol 8614. Springer, Cham. https://doi.org/10.1007/978-3-319-09704-6_19

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  • DOI: https://doi.org/10.1007/978-3-319-09704-6_19

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09703-9

  • Online ISBN: 978-3-319-09704-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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