On periodically iterated morphisms

We investigate the computational power of periodically iterated morphisms, also known as D0L systems with periodic control; we call them PerD0L systems for short. These systems give rise to a class of one-sided infinite sequences, called PerD0L words. We construct a PerD0L word with exponential subword complexity, thereby answering a question raised by Lepistö [23] on the existence of such words. We solve another open problem concerning the decidability of the first-order theories of PerD0L words [24]; we show it is already undecidable whether a certain letter occurs in a PerD0L word.

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