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.
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