We consider conditional tabled Lindenmayer sytems without interaction, where each table is associated with a regular set and a table can only be applied to a sentential form which is contained in its associated regular set. We study the effect to the generative power, if we use instead of arbitrary regular languages only finite, nilpotent, monoidal, combinational, definite, ordered, union-free, star-free, strictly locally testable, commutative regular, circular regular, and suffix-closed regular languages. Essentially, we prove that the hierarchy of language families obtained from conditional Lindenmayer systems with subregular conditions is almost identical to the hierarchy of families of subregular languages.
Mots-clés : Lindenmayer systems, controlled derivations
@article{ITA_2014__48_1_127_0,
author = {Dassow, J\"urgen and Rudolf, Stefan},
title = {Conditional {Lindenmayer} systems with subregular conditions: {The} non-extended case},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {127--147},
publisher = {EDP-Sciences},
volume = {48},
number = {1},
year = {2014},
doi = {10.1051/ita/2014007},
mrnumber = {3195792},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ita/2014007/}
}
TY - JOUR AU - Dassow, Jürgen AU - Rudolf, Stefan TI - Conditional Lindenmayer systems with subregular conditions: The non-extended case JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2014 SP - 127 EP - 147 VL - 48 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita/2014007/ DO - 10.1051/ita/2014007 LA - en ID - ITA_2014__48_1_127_0 ER -
%0 Journal Article %A Dassow, Jürgen %A Rudolf, Stefan %T Conditional Lindenmayer systems with subregular conditions: The non-extended case %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2014 %P 127-147 %V 48 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita/2014007/ %R 10.1051/ita/2014007 %G en %F ITA_2014__48_1_127_0
Dassow, Jürgen; Rudolf, Stefan. Conditional Lindenmayer systems with subregular conditions: The non-extended case. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 1, pp. 127-147. doi : 10.1051/ita/2014007. http://archive.numdam.org/articles/10.1051/ita/2014007/
[1] , , and , Solving NP-Complete Problems With Networks of Evolutionary Processors. IWANN'01: Proc. of the 6th International Work-Conference on Artificial and Natural Neural Networks. Vol. 2084 of Lect. Notes Comput. Sci. Springer-Verlag, Berlin (2001) 621-628. | Zbl
[2] and , Networks of Parallel Language Processors. New Trends in Formal Languages. Vol. 1218 of Lect. Notes Comput. Sci. Springer-Verlag, Berlin (1997) 299-318. | MR
[3] and , Tree controlled grammars. Comput. 19 (1977) 129-139. New Trends in Formal Languages - Control, Cooperation, and Combinatorics. Vol.1218 of Lect. Notes Comput. Sci. Springer-Verlag Berlin (1997) 299-318. | MR | Zbl
[4] , Subregularly controlled derivations: the context-free case. Rostocker Mathematisches Kolloquium 34 (1988) 61-70. | MR | Zbl
[5] , Conditional grammars with restrictions by syntactic parameters. Words, Semigroups, Transductions, edited by M. Ito, Gh. Păun and Sh. Yu. World Scientific, Singapore (2001) 59-68. | MR
[6] , Subregularly controlled derivations: restrictions by syntactic parameters. Where Math., Comput. Sci., Linguistics and Biology Meet. Kluwer Academic Publishers (2001) 51-61. | MR | Zbl
[7] , Contextual grammars with subregular choice. Fundamenta Informaticae 64 (2005) 109-118. | MR | Zbl
[8] , Grammars with commutative, circular, and locally testable conditions. Automata, Formal Languages, and Related Topics - Dedicated to Ferenc Gécseg on the occasion of his 70th birthday. University of Szeged (2009) 27-37. | MR | Zbl
[9] and , On regulated L systems. Rostock. Math. Kolloq. 25 (1984) 99-118. | MR | Zbl
[10] and , Conditional grammars with subregular conditions, in Proc. Internat. Conf. Words, Languages and Combinatorics II. World Scientific, Singapore (1994) 71-86. | MR | Zbl
[11] , and , Networks of evolutionary processors with subregular filters, in Languages and Automata Theory and Applications. Vol. 6638 of Lect. Notes Comput. Sci. Springer-Verlag, Berlin (2011) 262-273. | Zbl
[12] , and , On Contextual Grammars with Subregular Selection Languages, in Descriptional Complexity of Formal Systems. Vol. 6808 of Lect. Notes Comput. Sci. Springer-Verlag, Berlin (2011) 135-146. | MR
[13] and . Regulated Rrewriting in Formal Language Theory. Springer-Verlag, Berlin (1989). | MR | Zbl
[14] and , Conditional Lindenmayer systems with subregular conditions: the extended case (Submitted).
[15] , and , Two collapsing hierarchies of subregularly tree controlled languages. Theoretical Comput. Sci. 410 (2009) 3261-3271. | MR | Zbl
[16] , and , Generative capacity of subregularly tree controlled grammars. Int. J. Foundations Comput. Sci. 21 (2010) 723-740. | MR | Zbl
[17] and , On networks of evolutionary processors with filters accepted by two-state-automata. Fundamenta Informaticae 113 (2011) 1-14. | MR | Zbl
[18] , Grammars with partial ordering. Information and Control 12 (1968) 415-425. | MR | Zbl
[19] and , Control sets on grammars. Math. Syst. Theory 2 (1968) 159-177. | MR | Zbl
[20] and , Algebraic Theory of Automata. Academiai kiado, Budapest (1972). | MR | Zbl
[21] and , Multiple-entry finite automata. J. Comput. Syst. Sci. 9 (1974) 1-19. | MR | Zbl
[22] , and , Nondeterministic state complexity of basic operations for prefix-suffix-free regular languages. Fundamenta Informaticae 90 (2009) 93-106. | MR | Zbl
[23] , The theory of regular events II. Kybernetika 5 (1969) 520-544. | MR | Zbl
[24] , Gramatici contextuale cu selectiva regulata. Stud. Cerc. Mat. 30 (1978) 287-294. | MR
[25] and , Accepting Networks of Evolutionary Processors with Subregular Filters, in Automata and Formal Languages - 13th International Conference AFL 2011. College of Nyíregyháza (2011) 300-314. | Zbl
[26] and , On internal contextual grammars with subregular selection languages, in Descriptional Complexity of Formal Systems. Vol. 7386 of Lect. Notes Comput. Sci. Springer-Verlag, Berlin (2012) 222-235. | MR
[27] , Contextual grammars. Revue Roum. Math. Pures Appl. 14 (1969) 1525-1534. | MR | Zbl
[28] and , Networks of Evolutionary Processors: Results and Perspectives, in Molecular Computational Models: Unconventional Approaches (2005) 78-114. | Zbl
[29] and , Counter-Free Languages. M.I.T. Press (1971). | MR
[30] , and , The theory of definite automata. IEEE Trans. Electronic Comput. 12 (1963) 233-243. | MR | Zbl
[31] , Marcus Contextual Grammars. Kluwer Publ. House, Doordrecht (1998). | Zbl
[32] and , The Mathematical Theory of L Systems. Academic Press, New York (1980). | MR | Zbl
[33] and , Handbook of Formal Languages. Springer-Verlag, Berlin (1997). | Zbl
[34] and , Priorities on context conditions in rewriting systems. Inform. Sci. 14 (1978) 15-51. | MR | Zbl
[35] , Formal Languages. Academic Press, New York (1973). | MR | Zbl
[36] , Free Monoids and Languages. Hon Min Book Co., Taichung, Taiwan (1991). | MR | Zbl
[37] and , Ordered automata and associated languages. Tamkang J. Math. 5 (1974) 9-20. | MR | Zbl
[38] , Abstrakte Automaten. Deutscher Verlag der Wissenschaften, Berlin (1969). | MR | Zbl
[39] , Vergleich der Leistungsfähigkeit endlicher determinierter Automaten. Diplomarbeit, Universität Rostock (1978).
Cité par Sources :
