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Unambiguous Conjunctive Grammars over a One-Letter Alphabet

  • Artur Jeż
  • Alexander Okhotin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7907)

Abstract

It is demonstrated that unambiguous conjunctive grammars over a unary alphabet Σ = {a} have non-trivial expressive power, and that their basic properties are undecidable. The key result is that for every base \(k \geqslant 11\) and for every one-way real-time cellular automaton operating over the alphabet of base-k digits \(\big\{\lfloor\frac{k+9}{4}\rfloor, \ldots, \lfloor\frac{k+1}{2}\rfloor\big\}\), the language of all strings a n with the base-k notation of the form 1 w 1, where w is accepted by the automaton, is generated by an unambiguous conjunctive grammar. Another encoding is used to simulate a cellular automaton in a unary language containing almost all strings. These constructions are used to show that for every fixed unambiguous conjunctive language L 0, testing whether a given unambiguous conjunctive grammar generates L 0 is undecidable.

Keywords

Cellular Automaton Expressive Power Input Alphabet Nonterminal Symbol Start Symbol 
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 2013

Authors and Affiliations

  • Artur Jeż
    • 1
    • 2
  • Alexander Okhotin
    • 3
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.Institute of Computer ScienceUniversity of WrocławPoland
  3. 3.Department of Mathematics and StatisticsUniversity of TurkuFinland

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