Conjunctive Grammars over a Unary Alphabet: Undecidability and Unbounded Growth

Article

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.

Keywords

Conjunctive grammars Unary languages Language equations Trellis automata Cellular automata 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland
  2. 2.Department of MathematicsUniversity of TurkuTurkuFinland
  3. 3.Academy of FinlandHelsinkiFinland

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