This paper establishes computational equivalence of two seemingly unrelated concepts: linear conjunctive grammars and trellis automata. Trellis automata, also studied under the name of one-way real-time cellular automata, have been known since early 1980s as a purely abstract model of parallel computers, while linear conjunctive grammars, introduced a few years ago, are linear context-free grammars extended with an explicit intersection operation. Their equivalence implies the equivalence of several other formal systems, including a certain restricted class of Turing machines and a certain type of language equations, thus giving further evidence for the importance of the language family they all generate.
@article{ITA_2004__38_1_69_0,
author = {Okhotin, Alexander},
title = {On the equivalence of linear conjunctive grammars and trellis automata},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
volume = {38},
year = {2004},
pages = {69-88},
doi = {10.1051/ita:2004004},
mrnumber = {2059029},
zbl = {1084.68079},
language = {en},
url = {http://dml.mathdoc.fr/item/ITA_2004__38_1_69_0}
}
Okhotin, Alexander. On the equivalence of linear conjunctive grammars and trellis automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 38 (2004) pp. 69-88. doi : 10.1051/ita:2004004. http://gdmltest.u-ga.fr/item/ITA_2004__38_1_69_0/
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