Summary
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.
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Rozenberg, G., Lindenmayer, A. Developmental systems with locally catenative formulas. Acta Informatica 2, 214–248 (1973). https://doi.org/10.1007/BF00289079
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DOI: https://doi.org/10.1007/BF00289079