Theory of L systems: From the point of view of formal language theory

Developmental Systems with Fragmentation

DAIMI Report Series ◽

10.7146/dpb.v3i36.6457 ◽

1974 ◽

Vol 3 (36) ◽

Author(s):

Grzegorz Rozenberg ◽

K. Rouhonen ◽

Arto Salomaa

Keyword(s):

Formal Language ◽

Point Of View ◽

Formal Language Theory ◽

Language Theory ◽

Developmental Systems ◽

Basic Properties ◽

New Class ◽

Theory Point ◽

L Systems ◽

Context Free

The paper introduces a new class of L systems, where it is possible to continue derivations from certain specified subwords of the words obtained. Such L systems (called L systems with fragmentation or just JL systems) are of interest both from biological and formal language theory point of view. The paper deals with JL systems without interactions, discusses the basic properties of the language families obtained, as well as their position in the L hierarchy. Finalhy, two infinite hierarchies of language families are obtained by limited fragmentation, the notions being analogous to those of ultralinearity and finiteness of index for context-free languages.

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COMPOSITION OF INFLATION RULES FOR APERIODIC STRUCTURES WITH NINE-FOLD SYMMETRY

International Journal of Modern Physics B ◽

10.1142/s0217979299000217 ◽

1999 ◽

Vol 13 (04) ◽

pp. 363-373 ◽

Cited By ~ 10

Author(s):

JUAN GARCÍa ESCUDERO

Keyword(s):

Finite Number ◽

Formal Language ◽

Point Of View ◽

Formal Language Theory ◽

Language Theory ◽

Formal Grammars ◽

Size And Shape ◽

Selective Approach ◽

Theory Point ◽

Inflation Rules

Deterministic aperiodic planar patterns with nine-fold symmetry have been interpreted recently in terms of a class of formal grammars known as D0L systems. A wider class of patterns with the same symmetry can be generated by composing two inflation rules. They are described with the help of ET0L systems. From the formal language theory point of view this corresponds to a selective approach, due to the fact that we need to introduce nonterminal symbols in the alphabet. From the point of view of quasicrystal structures, instead of having only one pattern of a given size and shape, we now have a finite number of them. This allows to construct nondeterministic models of aperiodic structures.

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THE DEVELOPMENT OF FORMAL LANGUAGE THEORY SINCE 1956

International Journal of Foundations of Computer Science ◽

10.1142/s0129054190000254 ◽

1990 ◽

Vol 01 (04) ◽

pp. 355-368

Author(s):

ROBERT McNAUGHTON

Keyword(s):

Formal Language ◽

Formal Languages ◽

Early Years ◽

Formal Language Theory ◽

Language Theory ◽

Personal Interest

This brief survey will discuss the early years of the theory of formal languages through about 1970, treating only the most fundamental of the concepts. The paper will conclude with a brief discussion of a small number of topics, the choice reflecting only the personal interest of the author.

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