On the equivalence of linear conjunctive grammars and trellis automata

Alexander Okhotin

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 38, Issue: 1, page 69-88
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Okhotin, Alexander. "On the equivalence of linear conjunctive grammars and trellis automata." RAIRO - Theoretical Informatics and Applications 38.1 (2010): 69-88. <http://eudml.org/doc/92734>.

@article{Okhotin2010,
abstract = { 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. },
author = {Okhotin, Alexander},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Conjunctive grammar; trellis automaton; cellular automaton; language equation; Turing machine.},
language = {eng},
month = {3},
number = {1},
pages = {69-88},
publisher = {EDP Sciences},
title = {On the equivalence of linear conjunctive grammars and trellis automata},
url = {http://eudml.org/doc/92734},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Okhotin, Alexander
TI - On the equivalence of linear conjunctive grammars and trellis automata
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 1
SP - 69
EP - 88
AB - 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.
LA - eng
KW - Conjunctive grammar; trellis automaton; cellular automaton; language equation; Turing machine.
UR - http://eudml.org/doc/92734
ER -

References

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  11. A. Okhotin, On the closure properties of linear conjunctive languages. Theoret. Comput. Sci.299 (2003) 663-685.  
  12. A. Okhotin, Whale Calf, a parser generator for conjunctive grammars, in Implementation and Application of Automata, Proc. CIAA 2002, Tours, France, July 3–5, 2002. Lect. Notes Comput. Sci. (2002). 2608 213-220.  
  13. A. Okhotin, Boolean grammars, in Developments in Language Theory, Proc. DLT 2003, Szeged, Hungary, July 7–11, 2003. Lect. Notes Comput. Sci.2710 (2003) 398-410.  
  14. A.R. Smith III, Cellular automata and formal languages, in Proc. 11th IEEE Annual Sympo. Switching and Automata Theory (1970) 216-224.  
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