Description of Generalized Continued Fractions by Finite Automata

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 43)


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.


Continue Fraction Finite Automaton Irrational Number Finite Union Continue Fraction Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I am very grateful to the referee for many suggestions that considerably improved the chapter.

Supported by a grant from NSERC.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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