Abstract
Lee has shown that ifL is aDOL language, then πink(L) <C · k2 for some constantC, where πink(L) denotes the number of subwords of lengthk inL. We show that the result does not hold forDIL languages. It is also shown that each everywhere growing (uniform)DIL language is the image under a coding of an everywhere growing (uniform)DOL language. A similar result holds for languages generated by systems with tables. These enable us to solve the subword complexity problems for developmental languages with interactions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Van Dalen, “A note on some systems of Lindenmayer,”Math. Systems Theory 5:128–140 (1971).
P. Doucet, “On the membership question in some Lindenmayer systems,”Indagationes Mathematicae 34:45–52 (1972).
A. Ehrenfeucht and G. Rozenberg, “A limit theorem for sets of sub words in deterministic TOL systems,”Information and Control 2:70–73 (1973).
G. T. Herman and G. Rozenberg, Developmental Systems and Languages (North-Holland Publishing Co., Amsterdam, to be published).
K. P. Lee, “Subwords of developmental languages,” Ph.D. dissertation, State University of New York at Buffalo, 1975.
A. Lindenmayer, “Mathematical models for cellular interactions in development, Parts I and II,” /.Theoret. Biol. 8:280–315 (1968).
A. Lindenmayer, “Developmental systems without cellular interactions, their languages and grammars,”J. Theoret. Biol. 30:455–484 (1971).
A. Lindenmayer and G. Rozenberg, “Developmental systems and languages,” inProc. 4th ACM Symp. on Theory of Computing (1972), pp. 214–221.
A. Paz and A. Salomaa, “Integral sequential word functions and growth equivalence of Lindenmayer systems,”Information and Control 23:313–343 (1973).
G. Rozenberg, “DOL sequences,”Discrete Mathematics 7:323–347 (1974).
G. Rozenberg and A. Lindenmayer, “Developmental systems with locally catenative formulas,”Acta Informatica 2:214–248 (1973).
A. Salomaa, “On exponential growth in Lindenmayer systems,”Indagationes Mathematicae 35:23–30 (1973).
A. Salomaa, “On some recent problems concerning developmental languages,” to appear inProc. Conf. on Automata and Formal Languages.
Author information
Authors and Affiliations
Additional information
This paper is based on part of K.P.L.'s Ph.D. thesis.
Rights and permissions
About this article
Cite this article
Ehrenfeucht, A., Lee, K.P. & Rozenberg, G. Subword complexities of various classes of deterministic developmental languages with interactions. International Journal of Computer and Information Sciences 4, 219–236 (1975). https://doi.org/10.1007/BF01007760
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01007760