An automatic sequence is a letter-to-letter coding of fixed point uniform morphism. More generally, morphic sequences are codings points arbitrary morphisms. There many examples where an, priori, with non-uniform morphism happens to be an sequence. example the Lysënok \(a \to aca\), \(b d\), \(c b\), \(d c\), which also \(2\)-automatic Such identification useful for describing dynamical systems...

We investigate automatic presentations of infinite words. Starting points of our study are the works of Rigo and Maes, and Carton and Thomas concerning the lexicographic presentation, respectively the decidability of the MSO theory of morphic words. Refining their techniques we observe that the lexicographic presentation of a (morphic) word is canonical in a certain sense. We then go on to gene...

We study finite state transduction of automatic and morphic sequences. Dekking [4] proved that morphic sequences are closed under transduction and in particular morphic images. We present a simple proof of this fact, and use the construction in the proof to show that non-erasing transductions preserve a condition called α-substitutivity. Roughly, a sequence is α-substitutive if the sequence can...

We prove a pumping lemma in order to characterize the infinite words determined by indexed languages. An infinite language L determines an infinite word α if every string in L is a prefix of α. If L is regular or context-free, it is known that α must be ultimately periodic. We show that if L is an indexed language, then α is a morphic word, i.e., α can be generated by iterating a morphism under...