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The Equivalence Problem of Finite Substitutions on ab*c, with Applications

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Book cover Automata, Languages and Programming (ICALP 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2380))

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Abstract

We show that it is undecidable whether or not two finite substitutions are equivalent on the fixed regular language ab*c. This gives an unexpected answer to a question proposed in 1985 by Culik II and Karhumäki. At the same time it can be seen as the final result in a series of undecidability results for finite transducers initiated in 1968 by Griffiths. An application to systems of equations over finite languages is given.

Research was supported by the grant 44087 of the Academy of Finland

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Author information

Authors and Affiliations

  1. Department of Mathematics and Turku Centre for Computer Science, University of Turku, FIN-20014, Turku, Finland

    J. Karhumäki

  2. Department of Cybernetics, Kiev National University, Kiev, 252017, Ukraine

    L. P. Lisovik

Authors
  1. J. Karhumäki
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  2. L. P. Lisovik
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Editor information

Editors and Affiliations

  1. Institute of Theoretical Computer Science, ETH Zentrum, ETH Zürich, 8092, Zürich, Switzerland

    Peter Widmayer  & Stephan Eidenbenz  & 

  2. Department of Languages and Sciences of the Computation E.T.S. de Ingeniería Informática, University of Málaga, Campus de Teatinos, 29071, Málaga, Spain

    Francisco Triguero , Rafael Morales  & Ricardo Conejo ,  & 

  3. School of Cognitive and Computing Sciences, University of Sussex, Falmer, Brighton, BN1 9QN, UK

    Matthew Hennessy

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© 2002 Springer-Verlag Berlin Heidelberg

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Karhumäki, J., Lisovik, L.P. (2002). The Equivalence Problem of Finite Substitutions on ab*c, with Applications. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_69

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  • DOI: https://doi.org/10.1007/3-540-45465-9_69

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43864-9

  • Online ISBN: 978-3-540-45465-6

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