Geodesic
Linear grammars with one-sided contexts and their automaton representation
Barash, Mikhail1 ; Okhotin, Alexander2
1 Turku Centre for Computer Science, Turku 20014, Finland.
2 Department of Mathematics and Statistics, University of Turku, Turku 20014, Finland.
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 49 (2015) no. 2, pp. 153-178

Voir la notice de l'article provenant de la source Numdam

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
Keywords: 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. 
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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

Cité par Sources :