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International Conference on Developments in Language Theory

DLT 2013: Developments in Language Theory pp 277–288Cite as

Unambiguous Conjunctive Grammars over a One-Letter Alphabet

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7907))

Abstract

It is demonstrated that unambiguous conjunctive grammars over a unary alphabet Σ = {a} have non-trivial expressive power, and that their basic properties are undecidable. The key result is that for every base \(k \geqslant 11\) and for every one-way real-time cellular automaton operating over the alphabet of base-k digits \(\big\{\lfloor\frac{k+9}{4}\rfloor, \ldots, \lfloor\frac{k+1}{2}\rfloor\big\}\), the language of all strings a n with the base-k notation of the form 1 w 1, where w is accepted by the automaton, is generated by an unambiguous conjunctive grammar. Another encoding is used to simulate a cellular automaton in a unary language containing almost all strings. These constructions are used to show that for every fixed unambiguous conjunctive language L 0, testing whether a given unambiguous conjunctive grammar generates L 0 is undecidable.

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Artur Jeż

  2. Institute of Computer Science, University of Wrocław, Poland

    Artur Jeż

  3. Department of Mathematics and Statistics, University of Turku, Finland

    Alexander Okhotin

Authors
  1. Artur Jeż
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  2. Alexander Okhotin
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Editor information

Editors and Affiliations

  1. LIGM, University Paris-Est Marne-la-Vallée, 5 Bd Descartes, Champs-sur-Marne, 77454, Marne-la-Vallée Cedex 2, France

    Marie-Pierre Béal

  2. LIAFA, UMR 7089, University Paris Diderot, 75205, Paris cedex 13, France

    Olivier Carton

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Jeż, A., Okhotin, A. (2013). Unambiguous Conjunctive Grammars over a One-Letter Alphabet. In: Béal, MP., Carton, O. (eds) Developments in Language Theory. DLT 2013. Lecture Notes in Computer Science, vol 7907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38771-5_25

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  • DOI: https://doi.org/10.1007/978-3-642-38771-5_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38770-8

  • Online ISBN: 978-3-642-38771-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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