Robustness of Pisot-regular sequences
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We consider numeration systems based on a d-tuple π=(U_1,β¦,U_d) of sequences of integers and we define (π,π)-regular sequences through π-recognizable formal series, where π is any semiring. We show that, for any d-tuple π of Pisot numeration systems and any commutative semiring π, this definition does not depend on the greediness of the π-representations of integers. The proof is constructive and is based on the fact that the normalization is realizable by a 2d-tape finite automaton. In particular, we use an ad hoc operation mixing a 2d-tape automaton and a π-automaton in order to obtain a new π-automaton.
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