# Descriptive Complexity of Computable Sequences

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## Abstract

Our goal is to study the complexity of infinite binary recursive sequences. We introduce several measures of the quantity of information they contain. Some measures are based on size of programs that generate the sequence, the others are based on the Kolmogorov complexity of its finite prefixes. The relations between these complexity measures are established. The most surprising among them are obtained using a specific two-players game.

## Keywords

Complexity Measure Binary String Computable Function Special Node Kolmogorov Complexity
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© Springer-Verlag Berlin Heidelberg 1999