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International Conference on Language and Automata Theory and Applications

LATA 2019: Language and Automata Theory and Applications pp 3–30Cite as

Modern Aspects of Complexity Within Formal Languages

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

Abstract

We give a survey on some recent developments and achievements of modern complexity-theoretic investigations of questions in Formal Languages (FL). We will put a certain focus on multivariate complexity analysis, because this seems to be particularly suited for questions concerning typical questions in FL.

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Notes

  1. 1.

    In the literature, is often required that \(|I'|+\kappa (I')\le f(\kappa (I))\), but this is equivalent to the present requirement, because the parameterization can be computed from \(I'\), i.e., \(\kappa (I')\) is also bounded by a function in \(\kappa (I)\) if \(|I'|\) is.

  2. 2.

    The definitions in [52] are a bit different, but this can be neglected in the current discussion.

  3. 3.

    A new survey is announced to appear in [85].

  4. 4.

    The result was phrased in different terminology back in 1975. Wagner actually proved stronger results in the sense that weights on the operations are permitted.

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Acknowledgements

We are grateful to many people giving feedback to the ideas presented in this paper. In particular, Anne-Sophie Himmel, Ulrike Stege, and Petra Wolf commented on earlier versions of the manuscript.

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  1. Fachbereich 4 – Abteilung Informatikwissenschaften, CIRT, Universität Trier, 54286, Trier, Germany

    Henning Fernau

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  1. Henning Fernau
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Correspondence to Henning Fernau .

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  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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Fernau, H. (2019). Modern Aspects of Complexity Within Formal Languages. 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_1

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  • DOI: https://doi.org/10.1007/978-3-030-13435-8_1

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  • Online ISBN: 978-3-030-13435-8

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