The Shannon function for calculating the Arnold complexity of length $2^n$ binary words for arbitrary $n$

Yu. V. Merekin

S. L. Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia

Abstract: The exact value of the Shannon function for fast calculating the Arnold complexity of length $2^n$ binary words is obtained for $n=m^2$, $n=m^2+m$, and $n=m^2+2m$, $m\geq2$. Thus the exact value of the Shannon function is determined for an arbitrary $n$. Bibliogr. 6.

Keywords: binary word, complexity of word, Arnold complexity, Shannon function.

UDC: 519.714

Received: 11.02.2013
Revised: 25.12.2013

 English version: Journal of Applied and Industrial Mathematics, 2015, 9:1, 98–109

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