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Problems on Finite Automata and the Exponential Time Hypothesis

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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 several classical decision problems on finite automata under the (Strong) Exponential Time Hypothesis. We focus on three types of problems: universality, equivalence, and emptiness of intersection. All these problems are known to be CoNP-hard for nondeterministic finite automata, even when restricted to unary input alphabets. A different type of problems on finite automata relates to aperiodicity and to synchronizing words. We also consider finite automata that work on commutative alphabets and those working on two-dimensional words.

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Notes

  1. 1.

    Even tighter descriptions of the complexities can be given within classical complexity theory, but this is not so important for our presentation here, as we mostly focus on polynomial versus exponential time.

  2. 2.

    Recall that the \(O^*\) notation suppresses polynomial factors.

  3. 3.

    In this proof, we neglect the use of some ceiling functions for the sake of readability.

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Author information

Authors and Affiliations

  1. Fachbereich 4 – Abteilung Informatik, Universität Trier, 54286, Trier, Germany

    Henning Fernau

  2. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, 72076, Tübingen, Germany

    Andreas Krebs

Authors
  1. Henning Fernau
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  2. Andreas Krebs
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Correspondence to Henning Fernau or Andreas Krebs .

Editor information

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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Fernau, H., Krebs, A. (2016). Problems on Finite Automata and the Exponential Time Hypothesis. 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_8

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  • DOI: https://doi.org/10.1007/978-3-319-40946-7_8

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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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