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.
Accepté le :
DOI : 10.1051/ita/2015004
Mots-clés : Context-free grammars, conjunctive grammars, contexts, cellular automata, trellis automata, undecidability.
@article{ITA_2015__49_2_153_0,
author = {Barash, Mikhail and Okhotin, Alexander},
title = {Linear grammars with one-sided contexts and their automaton representation},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {153--178},
publisher = {EDP-Sciences},
volume = {49},
number = {2},
year = {2015},
doi = {10.1051/ita/2015004},
mrnumber = {3373813},
zbl = {1328.68100},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ita/2015004/}
}
TY - JOUR AU - Barash, Mikhail AU - Okhotin, Alexander TI - Linear grammars with one-sided contexts and their automaton representation JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2015 SP - 153 EP - 178 VL - 49 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita/2015004/ DO - 10.1051/ita/2015004 LA - en ID - ITA_2015__49_2_153_0 ER -
%0 Journal Article %A Barash, Mikhail %A Okhotin, Alexander %T Linear grammars with one-sided contexts and their automaton representation %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2015 %P 153-178 %V 49 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita/2015004/ %R 10.1051/ita/2015004 %G en %F ITA_2015__49_2_153_0
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://www.numdam.org/articles/10.1051/ita/2015004/
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