Description of Generalized Continued Fractions by Finite Automata [chapter]

Jeffrey Shallit
2013 Number Theory and Related Fields  
A generalized continued fraction algorithm associates with every real number x a sequence of integers; x is rational iff the sequence is finite. For a fixed algorithm, call a sequence of integers valid if it is the result of that algorithm 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.
doi:10.1007/978-1-4614-6642-0_17 fatcat:jap44mzzi5ewdkrf7xqatwgvim