## An automata theoretic decidability proof for first-order theory of $$\langle\mathbb{N},<,P\rangle$$ with morphic predicate $$P$$.(English)Zbl 0937.68078

Summary: We show connections between morphisms on words and pictures on a finite alphabet and finite deterministic incomplete automata. We use these connections to re-prove, in terms of automata, a decidability result about the first-order theory of the structures $$\langle \mathbb{N}, <, P\rangle$$ for multi-ary morphic predicates $$P$$.

### MSC:

 68Q45 Formal languages and automata