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Computability by finite automata and Pisot bases. (English) Zbl 0819.11005
This paper gives additional results to C. Frougny [Math. Syst. Theory 25, 37-60 (1992; Zbl 0776.11005)]. An algebraic integer \(>1\) is a Pisot number if all its Galois conjugates have modulus less than 1. Main results: “the function of normalization in base \(\theta\) which maps any \(\theta\)-representation of a real number onto its \(\theta\)-development, obtained by a greedy algorithm, is a function computable by a finite automaton over any alphabet if and only if \(\theta\) is a Pisot number.

MSC:
11A67 Other number representations
68Q45 Formal languages and automata
11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
11Y40 Algebraic number theory computations
Keywords:
Pisot number
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References:
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