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Kuratowski Algebras Generated by Prefix-Free Languages

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Implementation and Application of Automata (CIAA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9705))

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Abstract

We study Kuratowski algebras generated by prefix-free languages under the operations of star and complement. Our results are as follows. Five of 12 possible algebras cannot be generated by any prefix-free language. Two algebras are generated only by trivial prefix-free languages, the empty set and the language \(\{\varepsilon \}\). Each of the remaining five algebras can be generated, for every \(n\ge 4\), by a regular prefix-free language of state complexity n, which meets the upper bounds on the state complexities of all the languages in the resulting algebra.

J. Šebej was supported by the Slovak Grant Agency for Science under contracts VEGA 1/0142/15 and VEGA 2/0084/15.

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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 Jr. & Juraj Šebej

Authors
  1. Jozef Jirásek Jr.
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  2. Juraj Šebej
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Correspondence to Juraj Šebej .

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Editors and Affiliations

  1. Yonsei University, Seoul, Korea (Republic of)

    Yo-Sub Han

  2. Queen's University , Kingston, Ontario, Canada

    Kai Salomaa

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Jirásek, J., Šebej, J. (2016). Kuratowski Algebras Generated by Prefix-Free Languages. In: Han, YS., Salomaa, K. (eds) Implementation and Application of Automata. CIAA 2016. Lecture Notes in Computer Science(), vol 9705. Springer, Cham. https://doi.org/10.1007/978-3-319-40946-7_13

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  • DOI: https://doi.org/10.1007/978-3-319-40946-7_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40945-0

  • Online ISBN: 978-3-319-40946-7

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