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://archive.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://archive.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://archive.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://archive.numdam.org/articles/10.1051/ita/2015004/
T. Aizikowitz and M. Kaminski, . Comput. Sci. Russia (CSR 2011, St. Petersburg, Russia, 14–18 June 2011). Vol. 6651 of Lect. Notes Comput. Sci. (2011) 345–358. | DOI
M. Barash, Recursive descent parsing for grammars with contexts. SOFSEM 2013 student research forum Špindlerův Mlýn, Czech Republic, 26-31 January, 2013. Local Proceedings II, 10–21, Institute of Computer Science AS CR (2013).
M. Barash, Programming language specification by a grammar with contexts. In Fifth Workshop on Non-Classical Models of Automata and Applications, NCMA 2013, Umeå, Sweden, 13–14 August, 2013, edited by S. Bensch, F. Drewes, R. Freund, F. Otto. books@ocg.at 294, Österreichische Computer Gesellschaft (2013) 51–67. http://users.utu.fi/mikbar/kieli/
and , An extension of context-free grammars with one-sided context specifications. Inform. Comput. 237 (2014) 268–293. | DOI | MR | Zbl
M. Barash and A. Okhotin, LATIN 2014: Theoretical Informatics, Montevideo, Uruguay, 31 March–4 April 2014. In vol. 8392, Lect. Notes Comput. Sci. (2014) 190–201. | DOI
and , Parsing algorithms with backtrack. Inform. Control 23 (1973) 1–34. | DOI | MR | Zbl
, and , Systolic trellis automata I. Int. J. Comput. Math. 15 (1984) 195–212. | DOI | MR | Zbl
, and , Systolic trellis automata II. Int. J. Comput. Math. 16 (1984) 3–22. | DOI | MR | Zbl
, One-way bounded cellular automata. Inform. Control 44 (1980) 261–281. | DOI | MR | Zbl
and , Characterizations and computational complexity of systolic trellis automata. Theoret. Comput. Sci. 29 (1984) 123–153. | DOI | MR | Zbl
, and , Sequential machine characterizations of trellis and cellular automata and applications. SIAM J. Comput. 14 (1985) 426–447. | DOI | MR | Zbl
, Conjunctive grammars can generate non-regular unary languages. Int. J. Found. Comput. Sci. 19 (2008) 597–615. | DOI | MR | Zbl
and , Conjunctive grammars over a unary alphabet: undecidability and unbounded growth. Theory Comput. Syst. 46 (2010) 27–58. | DOI | MR | Zbl
R. Kowalski, Logic for Problem Solving. North-Holland, Amsterdam (1979). | MR | Zbl
, Conjunctive grammars. J. Autom. Lang. Comb. 6 (2001) 519–535. | MR | Zbl
, On the closure properties of linear conjunctive languages. Theoret. Comput. Sci. 299 (2003) 663–685. | DOI | MR | Zbl
, On the equivalence of linear conjunctive grammars to trellis automata. RAIRO: ITA 38 (2004) 69–88. | DOI | Numdam | MR | Zbl
, Homomorphisms preserving linear conjunctive languages. J. Autom. Lang. Comb. 13 (2008) 299–305. | MR | Zbl
, Conjunctive and Boolean grammars: the true general case of the context-free grammars. Comput. Sci. Rev. 9 (2013) 27–59. | DOI | Zbl
, Improved normal form for grammars with one-sided contexts. Theoret. Comput. Sci. 588 (2015) 52–72. | DOI | MR | Zbl
H. Rogers, Jr., Theory of Recursive Functions and Effective Computability. McGraw-Hill (1967). | MR | Zbl
, LFP: A logic for linguistic descriptions and an analysis of its complexity. Comput. Linguistics 14 (1988) 1–9.
, On real-time one-way cellular array. Theoret. Comput. Sci. 141 (1995) 331–335. | DOI | MR | Zbl
I. Törmä. Personal communication. February 2013.
, A property of real-time trellis automata. Discrete Appl. Math. 15 (1986) 117–119. | DOI | MR | Zbl
Cité par Sources :
