Averages of automatic sequences

Authors:
A. Barbé;F. von Haeseler
Affiliations:
Department of Electrical Engineering, K.U. Leuven, Kasteelpark Arenberg, Leuven, Belgium;Department of Electrical Engineering, K.U. Leuven, Kasteelpark Arenberg, Leuven, Belgium
Venue:
Theoretical Computer Science
Year:
2006

Citing 5
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Abstract

We give some sufficient criteria for the existence of certain averages (mean, correlation functions) of generalized higher-dimensional automatic sequences and show how to calculate these averages. Then follows an exploration of the nature of necessary and sufficient conditions for the existence of averages. Some of these criteria are applied to averages which play a central role in the determination of the correlation function of an automatic sequence.