# Conditional Lindenmayer systems with subregular conditions: The non-extended case

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2014)

- Volume: 48, Issue: 1, page 127-147
- ISSN: 0988-3754

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topDassow, Jürgen, and Rudolf, Stefan. "Conditional Lindenmayer systems with subregular conditions: The non-extended case." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 48.1 (2014): 127-147. <http://eudml.org/doc/273073>.

@article{Dassow2014,

abstract = {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.},

author = {Dassow, Jürgen, Rudolf, Stefan},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {Lindenmayer systems; controlled derivations},

language = {eng},

number = {1},

pages = {127-147},

publisher = {EDP-Sciences},

title = {Conditional Lindenmayer systems with subregular conditions: The non-extended case},

url = {http://eudml.org/doc/273073},

volume = {48},

year = {2014},

}

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

PB - EDP-Sciences

VL - 48

IS - 1

SP - 127

EP - 147

AB - 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.

LA - eng

KW - Lindenmayer systems; controlled derivations

UR - http://eudml.org/doc/273073

ER -

## References

top- [1] J. Castellanos, C. Martín-Vide, V. Mitrana and J.M. Sempere, 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. Zbl0982.68767
- [2] E. Csuhaj-Varjú and A. Salomaa, Networks of Parallel Language Processors. New Trends in Formal Languages. Vol. 1218 of Lect. Notes Comput. Sci. Springer-Verlag, Berlin (1997) 299–318. Zbl1054.68084MR1605238
- [3] K. Čulik II and H.A. Maurer, 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. Zbl0363.68108MR464718
- [4] J. Dassow, Subregularly controlled derivations: the context-free case. Rostocker Mathematisches Kolloquium34 (1988) 61–70. Zbl0651.68096MR968639
- [5] J. Dassow, 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. MR1914749
- [6] J. Dassow, Subregularly controlled derivations: restrictions by syntactic parameters. Where Math., Comput. Sci., Linguistics and Biology Meet. Kluwer Academic Publishers (2001) 51–61. Zbl1007.68090MR1890680
- [7] J. Dassow, Contextual grammars with subregular choice. Fundamenta Informaticae64 (2005) 109–118. Zbl1102.68041MR2347547
- [8] J. Dassow, 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. Zbl1183.68324MR2553622
- [9] J. Dassow and U. Fest, On regulated L systems. Rostock. Math. Kolloq.25 (1984) 99–118. Zbl0565.68067MR763680
- [10] J. Dassow and H. Hornig, Conditional grammars with subregular conditions, in Proc. Internat. Conf. Words, Languages and Combinatorics II. World Scientific, Singapore (1994) 71–86. Zbl0875.68610MR1351280
- [11] J. Dassow, F. Manea and B. Truthe, 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. Zbl1230.68125
- [12] J. Dassow, F. Manea and B. Truthe, 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. Zbl05934411MR2910372
- [13] J. Dassow and Gh. Păun. Regulated Rrewriting in Formal Language Theory. Springer-Verlag, Berlin (1989). Zbl0697.68067MR1067543
- [14] J. Dassow and St. Rudolf, Conditional Lindenmayer systems with subregular conditions: the extended case (Submitted). Zbl06333645
- [15] J. Dassow, R. Stiebe and B. Truthe, Two collapsing hierarchies of subregularly tree controlled languages. Theoretical Comput. Sci.410 (2009) 3261–3271. Zbl1176.68102MR2546881
- [16] J. Dassow, R. Stiebe and B. Truthe, Generative capacity of subregularly tree controlled grammars. Int. J. Foundations Comput. Sci.21 (2010) 723–740. Zbl1207.68173MR2728321
- [17] J. Dassow and B. Truthe, On networks of evolutionary processors with filters accepted by two-state-automata. Fundamenta Informaticae113 (2011) 1–14. Zbl1263.68098MR2918604
- [18] I. Fris, Grammars with partial ordering. Information and Control12 (1968) 415–425. Zbl0172.30002MR243952
- [19] S. Ginsburg and E.H. Spanier, Control sets on grammars. Math. Syst. Theory2 (1968) 159–177. Zbl0157.33604MR235936
- [20] F. Gécseg and I. Peak, Algebraic Theory of Automata. Academiai kiado, Budapest (1972). Zbl0246.94029MR332374
- [21] A. Gill and L.T. Kou, Multiple-entry finite automata. J. Comput. Syst. Sci.9 (1974) 1–19. Zbl0285.94030MR351666
- [22] Y.-S. Han, K. Salomaa and D. Wood, Nondeterministic state complexity of basic operations for prefix-suffix-free regular languages. Fundamenta Informaticae90 (2009) 93–106. Zbl1161.68534MR2494605
- [23] I.M. Havel, The theory of regular events II. Kybernetika5 (1969) 520–544. Zbl0184.28703MR256787
- [24] S. Istrail, Gramatici contextuale cu selectiva regulata. Stud. Cerc. Mat.30 (1978) 287–294. MR500803
- [25] F. Manea and B. Truthe, Accepting Networks of Evolutionary Processors with Subregular Filters, in Automata and Formal Languages – 13th International Conference AFL 2011. College of Nyíregyháza (2011) 300–314. Zbl1230.68125
- [26] F. Manea and B. Truthe, 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. Zbl1304.68112MR2993347
- [27] S. Marcus, Contextual grammars. Revue Roum. Math. Pures Appl.14 (1969) 1525–1534. Zbl0193.32401MR262026
- [28] C. Martín-Vide and V. Mitrana, Networks of Evolutionary Processors: Results and Perspectives, in Molecular Computational Models: Unconventional Approaches (2005) 78–114. Zbl1060.68046
- [29] R. McNaughton and S. Papert, Counter-Free Languages. M.I.T. Press (1971). Zbl0232.94024MR371538
- [30] M. Perles, M.M. Rabin and E. Shamir, The theory of definite automata. IEEE Trans. Electronic Comput.12 (1963) 233–243. Zbl0158.01002MR153518
- [31] G. Păun, Marcus Contextual Grammars. Kluwer Publ. House, Doordrecht (1998). Zbl0965.68037
- [32] G. Rozenberg and A. Salomaa, The Mathematical Theory of L Systems. Academic Press, New York (1980). Zbl0508.68031MR561711
- [33] G. Rozenberg and A. Salomaa, Handbook of Formal Languages. Springer-Verlag, Berlin (1997). Zbl0866.68057
- [34] G. Rozenberg and S.H. von Solms, Priorities on context conditions in rewriting systems. Inform. Sci.14 (1978) 15–51. Zbl0416.68066MR538667
- [35] A. Salomaa, Formal Languages. Academic Press, New York (1973). Zbl0686.68003MR438755
- [36] H.J. Shyr, Free Monoids and Languages. Hon Min Book Co., Taichung, Taiwan (1991). Zbl0746.20050MR1090325
- [37] H.J. Shyr and G. Thierrin, Ordered automata and associated languages. Tamkang J. Math.5 (1974) 9–20. Zbl0302.68069MR366563
- [38] P.H. Starke, Abstrakte Automaten. Deutscher Verlag der Wissenschaften, Berlin (1969). Zbl0182.02102MR276016
- [39] B. Wiedemann, Vergleich der Leistungsfähigkeit endlicher determinierter Automaten. Diplomarbeit, Universität Rostock (1978).

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