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International Conference on Language and Automata Theory and Applications

LATA 2019: Language and Automata Theory and Applications pp 190–202Cite as

The Range of State Complexities of Languages Resulting from the Cut Operation

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11417))

Abstract

We investigate the state complexity of languages resulting from the cut operation of two regular languages represented by minimal deterministic finite automata with m and n states. We show that the entire range of complexities, up to the known upper bound, can be produced in the case when the input alphabet has at least two symbols. Moreover, we prove that in the unary case, only complexities up to \(2m-1\) and between n and \(m+n-2\) can be produced, while if \(2m\le n-1\), then the complexities from 2m up to \(n-1\) cannot be produced.

M. Hospodár—Research supported by VEGA grant 2/0132/19 and by grant APVV-15-0091. This work was conducted during a research visit at the Institut für Informatik, Universität Giessen, Germany, funded by the DAAD short-term grant ID 57314022.

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Acknowledgments

We thank Juraj Šebej and Jozef Jirásek Jr. for their help on border values in our theorems. Moreover, also thanks to Galina Jirásková for her support and to all who helped us to improve the presentation of the paper.

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Authors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Markus Holzer

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

    Michal Hospodár

Authors
  1. Markus Holzer
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  2. Michal Hospodár
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Correspondence to Michal Hospodár .

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Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  2. Saint Petersburg State University, St. Petersburg, Russia

    Alexander Okhotin

  3. Ariel University, Ariel, Israel

    Dana Shapira

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Holzer, M., Hospodár, M. (2019). The Range of State Complexities of Languages Resulting from the Cut Operation. In: Martín-Vide, C., Okhotin, A., Shapira, D. (eds) Language and Automata Theory and Applications. LATA 2019. Lecture Notes in Computer Science(), vol 11417. Springer, Cham. https://doi.org/10.1007/978-3-030-13435-8_14

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  • DOI: https://doi.org/10.1007/978-3-030-13435-8_14

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  • Print ISBN: 978-3-030-13434-1

  • Online ISBN: 978-3-030-13435-8

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