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On continued fractions and finite automata. (English) Zbl 0251.10024


MSC:

11J70 Continued fractions and generalizations
11C20 Matrices, determinants in number theory
68Q45 Formal languages and automata
15B36 Matrices of integers
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References:

[1] Detlovs, V. K.: Equivalence of normal algorithms and recursive functions. (Russian). Trudy Mat. Inst. Steklov.52, 75–139 (1958)
[2] Hall, M.: On the sum and product of continued fractions. Ann. of Math.48, 966–993 (1947) · Zbl 0030.02201
[3] Hurwitz, A.: Über die Kettenbruch-Entwicklung der Zahl e. Phys.-ökon. Ges., Königsberg (1891). Mathematische Werke, Bd. 2, 129–133, Basel: Birkhäuser 1933
[4] Hurwitz, A.: Über die angenäherte Darstellungen der Zahlen durch rationale Brüche. Math. Ann.44, 417–436 (1894) · JFM 25.0322.04
[5] Raney, G. N.: Generalization of the Fibonacci sequence ton dimensions. Canad. J. Math.18, 332–349 (1966) · Zbl 0151.02406
[6] Salomaa, A.: Theory of Automata. (International Series of Monographs in Pure and Applied Mathematics, vol. 100.) Oxford: Pergamon Press, 1969
[7] Sanov, I. N.: A property of a representation of a free group. (Russian). Doklady Akad. Nauk SSSR57, 657–659 (1947)
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