Abstract
It is a common problem in the study of stochastic grammars and languages and, in particular, of stochastic L systems that seemingly very little can be said about the probabilities of the word structures derived; in fact, most of the results obtained so far in these areas deal with word lengths and Parikh vectors rather than with the words themselves. Thus the stochastic generating process of the language is hardly reflected by the typical results.
This work was supported by the Natural Science and Engineering Research Council of Canada, Grants A0243 and A3590.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P. Eichhorst, W. Savitch: Growth functions of stochastic Lindenmayer systems. Information and Control 45 (1980), 217–228.
D.H. Greene, D.E. Knuth: Mathematics for the analysis of algorithms. Birkhauser, Boston, 1982 (2nd edition).
J.E. Hopcroft, J.D. Ullman: Introduction to automata theory, languages, and computation. Addison-Wesley Publishing Company, Reading, Mass., 1979.
J. Hromkovié, J. Mertan: Stochastic table Lindenmayer systems. Preprint, Bratislava, about 1984.
H. Jurgensen: Probabilistic L systems. 211–225, Automata, languages, development Edited by A. Lindenmayer, G. Rozenberg. North-Holland Publishing Company, Amsterdam, 1976.
H. Jürgensen, D.E. Matthews, D. Wood: Life and death in Markov deterministic tabled OL systems. Information and Control 48 (1981), 80–93.
H. Jurgensen, H.J. Shyr, G. Thierrin: Codes and compatible partial orders on free monoids. Astérisque, to appear.
C. Lenormand: Opérateurs sur les polynômes non commutatifs. Définitions et notations. Séminaire Schützenberger-Lentin-Nivat, Paris, 1969/70, no. 3.
C. Lenormand: Exponentiation de la dérivation, et intégration des séries en variables non commutatives. Séminaire Schützenherger-Lentin-Nivat, Paris, 1969/70, no. 20
M. Lothaire: Combinatorics on words. Addison-Wesley Publ. Co., Reading, Mass., 1983.
T. Nishida: K0L-system simulating almost but not exactly the same development (case of Japanese cypress). Mem. Fac. Sci., Kyoto Univ., Ser. Biol. 8 (1980), 97–122.
G. Rozenberg, A. Salomaa: The mathematical theory of L systems. Academic Press, New York, 1980.
A. Salomaa, M. Soittola: Automata-theoretic aspects of formal power series. Springer-Verlag, New York, 1978.
A.M. Sandi: A general form for probabilistic Lindenmayer systems. 7th Conf. Probability Theor., Brasov, 1982.
B.A. Sewastjanow: Verzweigungsprozesse. Akademie-Verlag, Berlin, 1974.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Jürgensen, H., Matthews, D.E. (1986). Stochastic OL Systems and Formal Power Series. In: The Book of L. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-95486-3_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-95486-3_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-95488-7
Online ISBN: 978-3-642-95486-3
eBook Packages: Springer Book Archive