Linear grammars with one-sided contexts and their automaton representation

Mikhail Barash, Alexander Okhotin

Research output

4 Citations (Scopus)


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 Σ2-completeness of the finiteness problem for these grammars and automata.

Original languageEnglish
Pages (from-to)153-158
Number of pages6
JournalRAIRO - Theoretical Informatics and Applications
Issue number2
Publication statusPublished - 1 Apr 2015

Scopus subject areas

  • Software
  • Mathematics(all)
  • Computer Science Applications

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