On the Number of Nonterminal Symbols in Unambiguous Conjunctive Grammars

  • Artur Jeż
  • Alexander Okhotin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7386)


It is demonstrated that the family of languages generated by unambiguous conjunctive grammars with 1 nonterminal symbol is strictly included in the languages generated by 2-nonterminal grammars, which is in turn a proper subset of the family generated using 3 or more nonterminal symbols. This hierarchy is established by considering grammars over a one-letter alphabet, for which it is shown that 1-nonterminal grammars generate only regular languages, 2-nonterminal grammars generate some non-regular languages, but all of them have upper density zero, while 3-nonterminal grammars may generate some non-regular languages of non-zero density. It is also shown that the equivalence problem for 2-nonterminal grammars is undecidable.


Regular Language Input Alphabet Nonterminal Symbol Unary Language Language Equation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Artur Jeż
    • 1
  • Alexander Okhotin
    • 2
  1. 1.Institute of Computer ScienceUniversity of WrocławPoland
  2. 2.Department of MathematicsUniversity of TurkuFinland

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