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Kuratowski Algebras Generated by Factor-, Subword-, and Suffix-Free Languages

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Descriptional Complexity of Formal Systems (DCFS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10316))

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Abstract

We study Kuratowski algebras generated by suffix-, factor-, and subword-free languages under the operations of star and complementation. We examine 12 possible algebras, and for each of them, we provide an answer to the question whether or not it can be generated by a suffix-, factor-, or subword-free language. In each case when an algebra can be generated by such a language, we show that this language may be taken to be regular, and we compute upper bounds on the state complexities of all the generated languages. Finally, we find generators that maximize these complexities.

M. Palmovský—Research supported by VEGA grant 2/0084/15 and grant APVV-15-0091. This work was conducted as a part of PhD study of Matúš Palmovský at the Faculty of Mathematics, Physics and Informatics of the Commenius University in Bratislava.

J. Šebej—Research supported by VEGA grant 1/0142/15 and grant APVV-15-0091.

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Authors and Affiliations

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

    Jozef Jirásek Jr. & Matúš Palmovský

  2. Faculty of Science, Institute of Computer 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. Matúš Palmovský
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  3. Juraj Šebej
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Corresponding author

Correspondence to Juraj Šebej .

Editor information

Editors and Affiliations

  1. Università degli Studi di Milano, Milan, Italy

    Giovanni Pighizzini

  2. University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada

    Cezar Câmpeanu

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Jirásek, J., Palmovský, M., Šebej, J. (2017). Kuratowski Algebras Generated by Factor-, Subword-, and Suffix-Free Languages. In: Pighizzini, G., Câmpeanu, C. (eds) Descriptional Complexity of Formal Systems. DCFS 2017. Lecture Notes in Computer Science(), vol 10316. Springer, Cham. https://doi.org/10.1007/978-3-319-60252-3_15

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  • DOI: https://doi.org/10.1007/978-3-319-60252-3_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60251-6

  • Online ISBN: 978-3-319-60252-3

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