Diophantine properties of real numbers generated by finite automata

By Boris Adamczewski, Julien Cassaigne. Compositio Mathematica, 2006

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We study some Diophantine properties of automatic real numbers and we present a method to derive irrationality measures for such numbers. As a consequence, we prove that the $b$-adic expansion of a Liouville number cannot be generated by a finite automaton, a conjecture due to Shallit.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dae81af1d89a5c03c610ccd0012dee2d9ea79934