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Languages Alive pp 221–235Cite as

Undecidability of State Complexities Using Mirror Images

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7300))

Abstract

We establish the undecidability of the state complexity of compositions of the operation mirror image and two other regularity-preserving operations. The undecidability of Hilbert’s Tenth Problem is not needed; the weaker Davis-Putnam-Robinson Theorem suffices for the reduction. Special attention is paid to the maximal state complexity of mirror images and the maximal deterministic state complexity of nondeterministic finite automata.

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Author information

Authors and Affiliations

  1. Turku Centre for Computer Science, Joukahaisenkatu 3–5 B, 20520, Turku, Finland

    Arto Salomaa

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  1. Arto Salomaa
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Editors and Affiliations

  1. Institut für Informatik, Universität Potsdam, August-Bebel-Straße 89, 14482, Potsdam, Germany

    Henning Bordihn

  2. Institut für Informatik, Universität Giessen, Arndtstraße 2, 35392, Giessen, Germany

    Martin Kutrib

  3. Fakultät für Informatik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39016, Magdeburg, Germany

    Bianca Truthe

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Salomaa, A. (2012). Undecidability of State Complexities Using Mirror Images. In: Bordihn, H., Kutrib, M., Truthe, B. (eds) Languages Alive. Lecture Notes in Computer Science, vol 7300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31644-9_15

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  • DOI: https://doi.org/10.1007/978-3-642-31644-9_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31643-2

  • Online ISBN: 978-3-642-31644-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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