L Systems

  title={L Systems},
  author={Lila Kari and Grzegorz Rozenberg and Arto Salomaa},
  booktitle={Handbook of Formal Languages},
L systems are parallel rewriting systems which were originally introduced in 1968 to model the development of multicellular organisms, [L1]. The basic ideas gave rise to an abundance of language-theoretic problems, both mathematically challenging and interesting from the point of view of diverse applications. After an exceptionally vigorous initial research period (roughly up to 1975; in the book [RSed2], published in 1985, the period up to 1975 is referred to, [RS2], as \when L was young… 
The Linguistic Relevance of Lindenmayer Systems
The interest of applying bio-inspired systems based on bio-inspiration, parallelism and generation of non-context free languages to the description and processing of natural language is pointed out.
F O R M a L L a N G U a G E S
The monograph presents a summary of the state of the theory of developmental systems and languages in 1975 and considers intensively motivation from and application to bilogy, whereas the monograph [24] emphasizes the mathematical theory of such systems.
Iterated morphisms, combinatorics on words and symbolic dynamical systems. (Morphismes itérés, combinatoire des mots et systèmes dynamiques symboliques)
The main subject of the thesis is the recognizability of words generated by primitive morphisms, using a coherent model of combinatorics on words and symbolic dynamical systems.
Inference of bounded L systems with polymorphic P systems
The inference problem of bounded L systems, namely such L systems which work on filaments having length up to a fixed size, is solved by constructing a specific polymorphic P system with target indication which can reproduce the transitions of the examined bounded L system.
On infinite words determined by L systems
Extended linear macro grammars, iteration grammars, and register programs
It is shown that extended macro Grammars have the same language generating power as (parallel) iteration grammars and can be formulated using iterated substitution using IO and OI versions.
Word-Mappings of Level 2
It is shown here that the sequences of level 2 are exactly the rational formal power series over one undeterminate.
Cooperating distributed grammar systems with permitting grammars as components
It is shown that the number of permitting components can be bounded, in the case of left-permitting components with erasing rules even together with the number with nonterminals, and the class of context-sensitive languages is characterized.
A Hierarchy of Automatic $\omega$-Words having a Decidable MSO Theory
  • V. Bárány
  • Mathematics, Linguistics
    RAIRO Theor. Informatics Appl.
  • 2008
It is proved that lexicographic presentations of w-words are canonical, which implies decidability of the MSO theory of every k-lexicographic word as well as closure of these classes under MSO-definable recolorings, e.g. closure under deterministic sequential mappings.
Artificial Life Applications of a Class of P Systems: Abstract Rewriting Systems on Multisets
This work overviews results about a class of artificial chemical systems: Abstract Rewriting Systems on Multisets (ARMS), which are particular types of P Systems and exhibit complex behaviors such as non-linear oscillations.


T0L Systems and Languages
Adult Languages of Propagating Systems with Restricted Parallelism
  • H. Fernau
  • Computer Science
    J. Inf. Process. Cybern.
  • 1993
Some open problems from 2,7,27 are attacked by using propagating ordered grammars and the families of adult languages equal the corresponding families of languages with extensions.
Developmental Systems with Fragmentation
The paper introduces a new class of L systems, where it is possible to continue derivations from certain specified subwords of the words obtained, analogous to those of ultralinearity and finiteness of index for context-free languages.
The Book of L
Investigations into Drosophila Wing Development - Results from a Lindenmayer Model and the Theoretical Basis of the Transplantation Experiment.
Context free languages in biological systems
A set of definitions is proposed which places a dynamic model of growth and stabilization in biological systems in a formal language framework and shows that if every string is considered to be a possible initial string in development, then the class of languages defined is properly included in theclass of regular languages.
Automata-Theoretic Aspects of Formal Power Series
The style has sometimes been characterized as austere or severe, but the author does expect the reader to be able to fill in the more obvious details and the author permits him to present the leading ideas in an uncluttered way.
Dynamical Properties of PWD0L Systems
  • J. Harrison
  • Mathematics, Computer Science
    Theor. Comput. Sci.
  • 1995
The mathematical theory of L systems
A survey of the different areas of the theory of developmental systems and languages in such a way that it discusses typical results obtained in each particular problem area.
DNA computers in vitro and vivo
| We show how DNA molecules and standard lab techniques may be used to create a nonde-terministic Turing machine. This is the rst scheme that shows how to make a universal computer with DNA. We claim