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Showing papers by "Grzegorz Rozenberg published in 1973"


Journal ArticleDOI
TL;DR: 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.

84 citations


Journal ArticleDOI
01 Dec 1973
TL;DR: A new family of languages is introduced which originated from a study of some mathematical models for the development of biological organisms and it is proved that it forms a full abstractfamily of languages.
Abstract: This paper introduces a new family of languages which originated from a study of some mathematical models for the development of biological organisms. Various properties of this family are established and in particular it is proved that it forms a full abstract family of languages. It is compared with some other families of languages which have already been studied and which either originated from the study of models for biological development or belong to the now standard Chomsky hierarchy. A characterization theorem for context-free languages is also established.

73 citations


Journal ArticleDOI
TL;DR: It is shown that dependent PDOL systems can produce sequences for every locally catenative formula (PDOL systems are propagating, deterministic developmental systems without interactions).
Abstract: A locally catenative sequence of strings of letters is such that each string in the sequence, after an initial stretch, is formed by concatenating strings which occurred at some specified distances previously in the sequence These kinds of structures are frequently encountered in biological development, particularly in the case of compound branching structures or compound leaves Developmental systems have been formally defined in previous publications One of the present results is that dependent PDOL systems can produce sequences for every locally catenative formula (PDOL systems are propagating, deterministic developmental systems without interactions) Every dependent PDOL system produces a sequence which satisfies an infinite class of locally catenative formulas Some of these formulas can be derived from a minimum formula, but a sequence may satisfy more than one minimum formulas

52 citations


Journal ArticleDOI
TL;DR: This paper investigates unary developmental systems and languages, which are distinguished by the property that the alphabet involved in their definition has only one symbol in it.

26 citations