Iterated Morphisms with Complementarity on the DNA Alphabet

Watson-Crick complementarity can be viewed as a language-theoretic operation: "bad" words obtained through a generative process are replaced by their complementary ones. This idea seems particularly suitable for Linden- mayer systems. D0L systems augmented with a specific complementarity transition, Watson-Crick D0L systems, have turned out to be a most interesting model and have already been extensively studied. In the present paper, attention is focused on Watson-Crick D0L systems, where the alphabet is the original four-letter DNA alphabet {A, G, T , C}. Growth functions and various decision problems will be investigated. Previously known cases about growth functions that are not Z-rational deal with alphabets bigger than the DNA alphabet, and it has been an open problem whether similar constructions can be carried out for the DNA alphabet. The main result in this paper shows that this is indeed the case.

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