A generalization of automatic sequences. (English) Zbl 0662.68052

The paper deals with sequences of strings from a word semigroup \(A^*\) and gives a connection between the following ideas: (1) generalized systems of enumeration, (2) locally catenative formulas, (3) automata with generalized digits as inputs and (4) fixed points of (certain) morphisms. There has been considerable interest in the cases (1)-(4) in the theory of combinatorics on words and in the theory of automata. The author unifies this problem area in the present work.
Reviewer: T.J.Harju


68Q45 Formal languages and automata
11B83 Special sequences and polynomials
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