TOL systems and languages
TLDR
TOL languages form an infinite hierarchy with respect to “natural” complexity measures introduced in this paper, and are contained in the family of context-free programmed languages.Abstract:
We discuss a family of systems and languages (called TOL) which have originally arisen from the study of mathematical models for the development of some biological organisms. From a formal language theory point of view, a TOL system is a rewriting system where at each step of a derivation every symbol in a string is rewritten in a context-free way, but different rewriting steps may use different sets of production rules and the language consists of all strings derivable from the single fixed string (the axiom). The family of TOL languages (as well as its different subfamilies considered here) is not closed with respect to usually considered operations; it is “incomparable” with context-free languages, but it is contained in the family of context-free programmed languages. TOL languages form an infinite hierarchy with respect to “natural” complexity measures introduced in this paper.read more
Citations
More filters
Book
The mathematical theory of L systems
Grzegorz Rozenberg,Arto Salomaa +1 more
TL;DR: 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.
Proceedings ArticleDOI
Visual models of plants interacting with their environment
TL;DR: A modeling framework is introduced that makes it possible to simulate and visualize a wide range of interactions at the level of plant architecture and extends the formalism of Lindenmayer systems with constructs needed to model bi−directional information exchange between plants and their environment.
Journal ArticleDOI
Developmental algorithms for multicellular organisms: A survey of L-systems
TL;DR: A survey of biologically relevant mathematical results available on algorithmic systems modelled by algorithmic rules for multicellular organisms, thus defining a hierarchy of language families.
Book
L Systems
TL;DR: The fundamental L families constitute a similar testing ground as the Chomsky hierarchy when new devices (grammars, automata, etc.) and new phenomena are investigated in language theory.
References
More filters
Book
Formal Languages and Their Relation to Automata
TL;DR: The theory of formal languages as a coherent theory is presented and its relationship to automata theory is made explicit, including the Turing machine and certain advanced topics in language theory.
Journal ArticleDOI
Mathematical models for cellular interactions in development. I. Filaments with one-sided inputs.
TL;DR: A theory is proposed for the development of filamentous organisms, based on the assumptions that the filaments are composed of cells which undergo changes of state under inputs they receive from their neighbors, and the cells produce outputs as determined by their state and the input they receive.
Journal ArticleDOI
On Context-Free Languages
TL;DR: In this report, certain properties of context-free (CF or type 2) Grammars are investigated, like that of Chomsky, and it is shown that this type of grammar is essentially stronger than type 2 grammars and has the advantage over type 1 grammARS that the phrase structure of a grammatical sentence is unique, once the derivation is given.
Journal ArticleDOI
Developmental systems without cellular interactions, their languages and grammars.
TL;DR: Theorems were obtained concerning partial characterizations of the class of developmental systems without cellular interactions, and some of the mathematical properties of this class are discussed.