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Linear Grammars with One-Sided Contexts and Their Automaton Representation

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LATIN 2014: Theoretical Informatics (LATIN 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8392))

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Abstract

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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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Turku, Turku, FI-20014, Finland

    Mikhail Barash

  2. Turku Centre for Computer Science, Turku, FI-20520, Finland

    Mikhail Barash & Alexander Okhotin

Authors
  1. Mikhail Barash
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  2. Alexander Okhotin
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Editor information

Editors and Affiliations

  1. Facultad de Ingeniería, Instituto de Computación, Universidad de la República, Julio Herrera y Reissig 565, 11300, Montevideo, Uruguay

    Alberto Pardo  & Alfredo Viola  & 

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Barash, M., Okhotin, A. (2014). Linear Grammars with One-Sided Contexts and Their Automaton Representation. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_17

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  • DOI: https://doi.org/10.1007/978-3-642-54423-1_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54422-4

  • Online ISBN: 978-3-642-54423-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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