The Book of L

464 Pages·1986·12.421 MB·English

by  Professor Dr. G. Rozenberg, Professor A. Salomaa (auth.)

G. Rozenberg A. Salomaa
L
The Book of
Springer -Verlag
Berlin Heidelberg New York Tokyo
Professor Dr. G. Rozenberg
Institut of Applied Mathematics and Computer Science
University of Leiden
Wassenaarseweg 80, NL-2300 RA Leiden
Professor A. Salomaa
Department of Mathematics, University of Turky
SF-20500 Turku 50
ISBN-13: 978-3-642-95488-7 e-ISBN-13: 978-3-642-95486-3
DOl: 10.1007/978-3-642-95486-3
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned,
specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying
machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies
are made for other than private use, a fee is payable to "VerwertungsgeseUschaft Wort", Munich.
@by Springer-Verlag Berlin Heidelberg 1986
Softcover reprint of the hardcover 1s t edition 1986
214513140-543210
Preface
This book is dedicated to Aristid Lindenmayer on the occasion of
his 60th birthday on November 17, 1985. Contributions range from
mathematics and theoretical computer science to biology.
Aristid Lindenmayer introduced language-theoretic models for
developmental biology in 1968. Since then the models have been cus
tomarily referred to as L systems. Lindenmayer's invention turned out
to be one of the most beautiful examples of interdisciplinary science:
work in one area (developmental biology) induces most fruitful ideas
in other areas (theory of formal languages and automata, and formal
power series).
As evident from the articles and references in this book, the in
terest in L systems is continuously growing. For newcomers the first
contact with L systems usually happens via the most basic class of L
systems, namely, DOL systems. Here "0" stands for zero context between
developing cells. It has been a major typographical problem that
printers are unable to distinguish between 0 (zero) and 0 (oh). Thus,
DOL was almost always printed with "oh" rather than "zero", and also
pronounced that way.
However, this misunderstanding turned out to be very fortunate.
The wrong spelling "DOL" of "DOL" could be read in the suggestive
way: DO L
Indeed, hundreds of researchers have followed this suggestion.
Some of them appear as contributors to this book. Of the many who
could not contribute, we in particular regret the absence of
A. Ehrenfeucht, G. Herman and H.A. Maurer whose influence in the
theory of L systems has been most significant.
We express our gratitude to all contributors. Special thanks are
due to Jane Lindenmayer for designing the cover of the book and to
Deezy Lindenmayer for getting a picture of Aristid, as well as to both
for providing us with a bibliography of Aristid. Finally, we are
grateful to Springer-Verlag for the timely publication of the book.
November 1985
Grzegorz Rozenberg Arto Salomaa
TABLE OF CONTENTS
Publications of Aristid Lindenmayer XI
Lois A. Abbott
Investigations into Drosophila Wing Development - Results from
a Lindenmayer Model . . . . . . . . . . . . . . . . . . . . .
Jean Berstel
Fibonacci Words - A Survey 13
Jack W. Carlyle, Sheila A. Greibach and Azaria Paz
Planar Map Generation by Parallel Binary Fission/Fusion Grammars 29
A. Cerny and J. Gruska
Modular Trellises 45
K. Culik II and J. Karhumaki
A New Proof for the DOL Sequence Equivalence Problem and its
Implications . • . . . . . . • • . . . . • • . . . . 63
Jlirgen Dassow
On Compound Lindenmayer Systems 75
H. Ehrig and A. Habel
Graph Grammars with Application Conditions • • . • . • . . . .. 87
Joost Engelfriet
The ETOL Hierarchy is in the 01 Hierarchy 101
Ralph O. Erickson
Polyhedral Cell Shapes 111
T. Harju
On Cyclically Overlap-Free Words in Binary Alphabets. . . • .. 123
Cornelia Harte
The Theoretical Basis of the Transplantation Experiment 131
Torn Head and Barbara Lando
Fixed and Stationary w-Words and w-Languages . . . . . . • . .. 147
M. Ito and G. Thierrin
DOL Schemes and Recurrent Words 157
H. Jlirgensen and D.E. Matthews
Stochastic OL Systems and Formal Power Series 167
A. Kelemenova
Complexity of L-Systems 179
VIII
Youichi Kobuchi
Compartmental Hybrid State Production-Diffusion Systems with
Application to Prestalk-Prespore Pattern Regulation in Cellular
Slime Molds • . • . • . • . . . • . • . . • • . • • . • • • .. 193
Robert W. Korn
Hierarchical Aspects of Plant Development . . • . . . • • . .. 207
Hans-Jorg Kreowski
Rule Trees Represent Derivations in Edge Replacement Systems 217
Manfred Kudlek
Languages Defined by Indian Parallel Systems 233
Klaus-Jorn Lange
L Systems and NLOG-Reductions 245
M. Latteux and A. Terlutte
The Parikh-Boundedness of ETOL Languages of Finite Index 253
J. van Leeuwen and R.B. Tan
Computer Networks with Compact Routing Tables • . . • • . . •• 259
Hermann B. LUck and Jacqueline LUck
Unconventional Leaves • . . • . • . 275
Brian H. Mayoh
A Uniform Model for the Growth of Biological Organisms:
Cooperating Sequential Processes . . . . • . . • . • . 291
Manfred Nagl
Graph Technology Applied to a Software Project 303
A. Nakamura, A. Lindenrnayer and K. Aizawa
Some Systems for Map Generation . . . . . 323
Mogens Nielsen
A Programming Language for Lindenmayer Systems 333
Hidenosuke Nishio
A Note on Significance of Cellular Interaction in L-System 345
Thomas Ottmann and Derick Wood
EOL Grammars and Search Trees . 349
D.F. Robinson
Variation in Inflorescence Structure in Cotoneaster Franchetti 361
Azriel Rosenfeld
Partial Path Groups and Parallel Graph Contractions . . • • •. 369
Grzegorz Rozenberg and Arto Salomaa
When L was Young • • . . . . . . . 383
Keijo Ruohonen
Equivalence Problems for Regular Sets of Word Morphisms 393
Walter J. Savitch
Parentheses Grammars and Lindenrnayer Grammars . . • • . . . •• 403
Rani Siromoney
Array Languages and Lindenmayer Systems - A Survey 413
Sven Skyum and Ole Eriksen
Symmetric Distributed Termination 427
Paul M.B. Vitany
Development, Growth and Time 431
Emo Welzl
On the Set of all Subgraphs of the Graphs in a Boundary NLC
Graph Language ••............•.... 445
Takashi Yokomori
Graph-Controlled Systems - An Extension of OL Systems . . . .. 461
PUBLICATIONS OF ARISTID LINDENMAYER UNTIL 1984
F.G. Gustafson & A. Lindenmayer, Determination of Fe55 in plant mate
rial by the thiocyanate method. Plant Physiology, 30: 182-184,
1955.
A. Lindenmayer, Induced biosynthesis of respiratory enzymes in baker's
yeast (abstract). J. Cellular & Compar. Physiol. ~: 345, 1956.
A. Lindenmayer & L. Smith, Some oxidative enzymes of anaerobically
1£:
grown yeast (abstract). Federation Proc., 212, 1957.
A. Lindenmayer & R.W. Estabrook, Low-temperature spectral studies on
the biosynthesis of cytochromes in baker's yeast. Arch. Biochem.
Biophys. 2Q: 66-82, 1958.
A. Lindenmayer, Oxidative metabolism and absorption spectra of anaero
bically grown yeast. J. Cellular & Compar. Physiol. 53: 93-118,
1959.
A. Lindenmayer, The concept of mating compatibility. Amer. Philos.
Soc., Philadelphia, Year Book 1962, pp. 304-307.
A. Lindenmayer & L. Smith, Cytochromes and other pigments of baker's
yeast grown aerobically and anaerobically. Biochim. Biophys.
21:
Acta, 445-461, 1964.
A. Lindenmayer, Life cycles as hierarchical relations. In: "Form and
Strategy in Science", edited by J.R. Gregg & F.T.C. Harris,
D. Reidel Publ. Co., Dordrecht, pp. 416-470, 1964.
A. Lindenmayer, Terminal oxidation and electron transport. In: "The
Fungi, An Advanced Treatise", edited by G.C. Ainsworth &
A.S. Sussman, Academic Press, New York, Vol. 1, pp. 301-348,1965.
A. Lindenmayer, Mathematical models for cellular interactions in
development. Abstracts, 4th Annual Symp. on Biomath. and Computer
Sci. in the Life Sciences, Houston, 1966.
A. Lindenmayer & H.F. Schoen, Selective effects of purine and pyri
midine analogues and of respiratory inhibitors on perithecial
development and branching in Sordaria. Plant Physiology, 42:
1059-1070, 1967.
A. Lindenmayer, Mathematical models for cellular interactions in
development. Part I. Filaments with one-sided inputs. Part II.
Simple and branching filaments with two-sided inputs. J. Theor.
BioI., ~: 280-299, 300-315, 1968.
A. Lindenmayer, Theoretical studies on branching and phyllotactic
patterns. Abstracts, XI Int. Botanical Congress, Seattle, p. 129,
1969.
V. Surapipith & A. Lindenmayer, Thioguanine-dependent light sensitivi
ty of perithecial initiation in Sordaria fimicola. J. Gen. Micro
bioI., 57: 227-237, 1969.
A. Lindenmayer, Developmental systems without cellular interactions,
their languages and grammars. J. Theor. BioI., 30: 455-484, 1971.
XII
A. Lindenmayer & G. Rozenberg, Developmental systems and languages.
In: Proc. 4th A.C.M. Symp. on Theory of Computing, Denver, pp.
214-221, 1972.
G". Rozenberg & A. Lindenmayer, Developmental systems with locally
catenative formulas. Acta Informatica, ~: 214-248, 1973.
A. Lindenmayer, Cellular automata, formal languages and developmental
systems. In: "Logic, Methodology and Philosophy of Science IV",
edited by P. Suppes et al., North-Holland Publ. Co., Amsterdam,
pp. 677-691, 1973.
A. Lindenmayer, Theoretical considerations for the development of com
pound structures (abstract). Acta Botanica Neerlandica, 22: 252,
1973.
A. Lindenmayer, Growth functions of multicellular organisms and cellu
lar programs. Abstracts, 10th Symp. on Biomath. and Computer
Science in the Life Sciences, Houston, 1973.
A. Lindenmayer, Developmental models for the transition from vegeta
tive to flowering condition in shoots (abstract). Amer. J. Bot.
§.Q, Suppl., p. 9, 1973.
A. Lindenmayer, Adding continuous components to L-systems. In:
"L-Systems", edited by G. Rozenberg and A. Salomaa, Lecture Notes
in Computer Science Vol. 15, pp. 53-68, Springer Verlag, Berlin,
1974.
D. Frijters & A. Lindenmayer, A model for the growth and flowering of
Aster novae-angliae on the basis of table (1,0) L-systems. Ibid.,
pp. 24-52, 1974.
P. Hellendoorn and A. Lindenmayer, Phyllotaxis in Bryophyllum tubi
florum: Morphogenetic studies and computer simulations. Acta
Botanica Neerlandica, 23: 473-492, 1974.
A. Lindenmayer, L-systems in their biological context (invited paper).
In: Proc. of Int. Conf. on Biologically Motivated Automata Theory,
McLean, Virginia, pp. 65-69, IEEE, Long Beach, Calif., 1974.
A. Lindenmayer, Computer models for hormonal interactions in the de
velopment of inflorescences (abstract of invited paper at symp.
of Societe Botanique de France). Revue de Cytologie et de Bio
12:
logie Vegetales, 309, 1974.
G.T. Herman, A. Lindenmayer & G. Rozenberg, Description of develop
mental languages using recurrence systems. Math. Systems Theory,
~: 316-341, 1975.
A. Lindenmayer, Developmental systems in their biological context.
Chapter contributed to the book "Developmental Systems and Lan
guages" by G.T. Herman & G. Rozenberg, North-Holland Publ. Co.,
Amsterdam, pp. 1-40, 1975.
A. Lindenmayer, Developmental algorithms for multicellular organisms:
a survey of L-systems. J. Theor. Biol., 2!: 3-22, 1975.
A. Lindenmayer, Algorithms for plant morphogenesis (invited paper).
Abstracts, XII Int. Botanical Congress, Leningrad, p. 223, 1975.