Functional Analysis and Other Mathematics
Volume 1, Number 1, 1-15, DOI: 10.1007/s11853-007-0001-0

Complexity of finite sequences of zeros and ones and geometry of finite spaces of functions

Vladimir I. Arnold

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Abstract

The sequence 001 001 001 001 is simpler than 01 001 0111 001. We present a formal mathematical theory that gives an exact meaning to the preceding (intuitively clear) statement.

Keywords  Arnold’s complexity - Discrete differential operator

Mathematics Subject Classification (2000)  11B50 - 05-99

Supported in part by the RFBR (Grant No. 05-01-00104).

Read at the Moscow Mathematical Society meeting 22 November 2005, homepage: http://www.mms.math-net.ru.

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