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On the Complexity of Fibonacci Coding

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Abstract

We show that converting an n-digit number from a binary to Fibonacci representation and backward can be realized by Boolean circuits of complexity O(M(n) log n), where M(n) is the complexity of integer multiplication. For a more general case of r-Fibonacci representations, the obtained complexity estimates are of the form \({2^O}{(\sqrt {\log n} )_n}\).

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Authors and Affiliations

  1. Federal State Unitary Enterprise “Kvant Scientific Research Institute,”, Moscow, Russia

    I. S. Sergeev

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  1. I. S. Sergeev
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Correspondence to I. S. Sergeev.

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Original Russian Text © I.S. Sergeev, 2018, published in Problemy Peredachi Informatsii, 2018, Vol. 54, No. 4, pp. 51–59.

Supported in part by the Russian Foundation for Basic Research, project no. 17-01-00485).

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Sergeev, I.S. On the Complexity of Fibonacci Coding. Probl Inf Transm 54, 343–350 (2018). https://doi.org/10.1134/S0032946018040038

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  • DOI: https://doi.org/10.1134/S0032946018040038

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