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More on generalized automatic sequences. (English) Zbl 1033.68069

Summary: We give some generalizations of \(k\)-automatic sequences replacing the \(k\)-ary system by an abstract numeration system an a regular language. We study some of the closure properties of these sequences and the possible extension to the multidimensional case or to infinite alphabets. The equivalence of these sequences and morphic predicates is given and the relationship to recognizability is also investigated.

MSC:

68Q45 Formal languages and automata
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