Description of Generalized Continued Fractions by Finite Automata

Abstract

A generalized continued fraction algorithm associates every real number x with a sequence of integers; x is rational iff the sequence is finite. For a fixed algorithm A, call a sequence of integers valid if it is the result of A on some input x 0. We show that, if the algorithm is sufficiently well behaved, then the set of all valid sequences is accepted by a finite automaton. © Springer Science+Business Media New York 2013.