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On the Number of Nonterminal Symbols in Unambiguous Conjunctive Grammars

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Descriptional Complexity of Formal Systems (DCFS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7386))

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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.

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Author information

Authors and Affiliations

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

    Artur Jeż

  2. Department of Mathematics, 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. Institut für Informatik, Universität Giessen, Arndtstraße 2, 35392, Giessen, Germany

    Martin Kutrib

  2. Departamento de Ciência de Computadores, Universidade do Porto, Faculdade de Ciências, Rua do Campo Alegre 1021-1055, 4169-007, Porto, Portugal

    Nelma Moreira  & Rogério Reis  & 

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Jeż, A., Okhotin, A. (2012). On the Number of Nonterminal Symbols in Unambiguous Conjunctive Grammars. In: Kutrib, M., Moreira, N., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2012. Lecture Notes in Computer Science, vol 7386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31623-4_14

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  • DOI: https://doi.org/10.1007/978-3-642-31623-4_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31622-7

  • Online ISBN: 978-3-642-31623-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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