Linear grammars with one-sided contexts and their automaton representation
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 49 (2015) no. 2, pp. 153-178.

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 Σ02-completeness of the finiteness problem for these grammars and automata.

Reçu le :
Accepté le :
DOI : 10.1051/ita/2015004
Classification : 68Q42, 68Q80
Mots-clés : Context-free grammars, conjunctive grammars, contexts, cellular automata, trellis automata, undecidability.
Barash, Mikhail 1 ; Okhotin, Alexander 2

1 Turku Centre for Computer Science, Turku 20014, Finland.
2 Department of Mathematics and Statistics, University of Turku, Turku 20014, Finland.
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Barash, Mikhail; Okhotin, Alexander. Linear grammars with one-sided contexts and their automaton representation. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 49 (2015) no. 2, pp. 153-178. doi : 10.1051/ita/2015004. http://archive.numdam.org/articles/10.1051/ita/2015004/

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