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Conjunctive Grammars over a Unary Alphabet: Undecidability and Unbounded Growth

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Abstract

It has recently been proved (Jeż, DLT 2007) that conjunctive grammars (that is, context-free grammars augmented by conjunction) generate some non-regular languages over a one-letter alphabet. The present paper improves this result by constructing conjunctive grammars for a larger class of unary languages. The results imply undecidability of a number of decision problems of unary conjunctive grammars, as well as non-existence of a recursive function bounding the growth rate of the generated languages. An essential step of the argument is a simulation of a cellular automaton recognizing positional notation of numbers using language equations.

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Authors and Affiliations

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

    Artur Jeż

  2. Department of Mathematics, University of Turku, Turku, Finland

    Alexander Okhotin

  3. Academy of Finland, Helsinki, Finland

    Alexander Okhotin

Authors
  1. Artur Jeż
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  2. Alexander Okhotin
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Corresponding author

Correspondence to Alexander Okhotin.

Additional information

A. Jeż supported by MNiSW grant number N206 024 31/3826, 2006–2008.

A. Okhotin supported by the Academy of Finland under grant 118540.

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Jeż, A., Okhotin, A. Conjunctive Grammars over a Unary Alphabet: Undecidability and Unbounded Growth. Theory Comput Syst 46, 27–58 (2010). https://doi.org/10.1007/s00224-008-9139-5

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  • DOI: https://doi.org/10.1007/s00224-008-9139-5

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