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Decision Questions Concerning Semilinearity, Morphisms, and Commutation of Languages

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Automata, Languages and Programming (ICALP 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2076))

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Abstract

Let ℭ be a class of automata (in a precise sense to be defined) and ℭc the class obtained by augmenting each automaton in ℭ with finitely many reversal-bounded counters. We first show that if the languages defined by ℭ are effectively semilinear, then so are the languages defined by ℭc, and, hence, their emptiness problem is decidable. This result is then used to show the decidability of various problems concerning morphisms and commutation of languages. We also prove a surprising undecidability result: given a fixed two element code K, it is undecidable whether a given context-free language L commutes with K, i.e., LK = KL.

Supported under 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

    Tero Harju

  2. Department of Computer Science, University of California, Santa Barbara, CA, 93106

    Oscar Ibarra

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

    Juhani Karhumäki

  4. Turku Centre for Computer Science, Lemminkäisenkatu 14A, FIN-20520, Turku, Finland

    Arto Salomaa

Authors
  1. Tero Harju
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  2. Oscar Ibarra
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  3. Juhani Karhumäki
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  4. Arto Salomaa
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Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informátics, Univ. Politècnica de Catalunya, C/Jordi Girona Salgado 1-3, 08034, Barcelona, Spain

    Fernando Orejas

  2. Computer Technology Institute (CTI), University of Patras, 61 Riga Feraiou street, 26221, Patras, Greece

    Paul G. Spirakis

  3. Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584, CH, Utrecht, The Netherlands

    Jan van Leeuwen

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© 2001 Springer-Verlag Berlin Heidelberg

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Harju, T., Ibarra, O., Karhumäki, J., Salomaa, A. (2001). Decision Questions Concerning Semilinearity, Morphisms, and Commutation of Languages. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_48

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  • DOI: https://doi.org/10.1007/3-540-48224-5_48

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  • Print ISBN: 978-3-540-42287-7

  • Online ISBN: 978-3-540-48224-6

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