Linear Grammars with One-Sided Contexts and Their Automaton Representation

  • Mikhail Barash
  • Alexander Okhotin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)


The paper considers a family of formal grammars that extends linear context-free grammars with an operator for referring to the left context of a substring being defined, as well as with a conjunction operation (as in linear conjunctive grammars). These grammars are proved to be computationally equivalent to an extension of one-way real-time cellular automata with an extra data channel. The main result is the undecidability of the emptiness problem for grammars restricted to a one-symbol alphabet, which is proved by simulating a Turing machine by a cellular automaton with feedback. The same construction proves the \(\Sigma^0_2\)-completeness of the finiteness problem for these grammars.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Mikhail Barash
    • 1
    • 2
  • Alexander Okhotin
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland
  2. 2.Turku Centre for Computer ScienceTurkuFinland

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