Descriptive complexity of computable sequences

Authors:
Bruno Durand;Alexander Shen;Nikolai Vereshchagin
Affiliations:
Univ. de Provence, Marseille, France;Institute of Problems of Information Transmission, Moscow, Russia;Moscow State Univ., Moscow, Russia
Venue:
Theoretical Computer Science
Year:
2002

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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 game2.