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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)

Abstract

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.

Keywords

Regular Language Input Alphabet Nonterminal Symbol Unary Language Language Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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