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International Conference on Implementation and Application of Automata

CIAA 2017: Implementation and Application of Automata pp 138–150Cite as

Nondeterministic Complexity of Operations on Free and Convex Languages

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10329))

Abstract

We study the nondeterministic state complexity of basic regular operations on the classes of prefix-, suffix-, factor-, and subword-free and -convex regular languages. For the operations of intersection, union, concatenation, square, star, reversal, and complementation, we get the tight upper bounds for all considered classes except for complementation on factor- and subword-convex languages. Most of our witnesses are described over optimal alphabets. The most interesting result is the describing of a proper suffix-convex language over a five-letter alphabet meeting the upper bound \(2^n\) for complementation.

Research supported by VEGA grant 2/0084/15 and grant APVV-15-0091. This work was conducted as a part of PhD study of Michal Hospodár and Peter Mlynárčik at the Faculty of Mathematics, Physics and Informatics of the Comenius University.

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Acknowledgment

We would like to thank Jozef Jirásek, Jr., for his help with finding the suffix-convex witness for complementation and for fruitful discussions on the topic.

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Authors and Affiliations

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

    Michal Hospodár, Galina Jirásková & Peter Mlynárčik

Authors
  1. Michal Hospodár
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  2. Galina Jirásková
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  3. Peter Mlynárčik
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Corresponding author

Correspondence to Michal Hospodár .

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Editors and Affiliations

  1. LIGM (UMR 8049), CNRS, Université Paris-Est, Marne-la-Vallée Cedex 2, France

    Arnaud Carayol

  2. LIGM (UMR 8049), Université Paris-Est, Marne-la-Vallée Cedex 2, France

    Cyril Nicaud

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Hospodár, M., Jirásková, G., Mlynárčik, P. (2017). Nondeterministic Complexity of Operations on Free and Convex Languages. In: Carayol, A., Nicaud, C. (eds) Implementation and Application of Automata. CIAA 2017. Lecture Notes in Computer Science(), vol 10329. Springer, Cham. https://doi.org/10.1007/978-3-319-60134-2_12

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  • DOI: https://doi.org/10.1007/978-3-319-60134-2_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60133-5

  • Online ISBN: 978-3-319-60134-2

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