Theoretical Computer Science 301(1-3), pp. 285-312.
ISSN/ISBN: Not available at this time. DOI: 10.1016/S0304-3975(02)00587-X
Abstract: In an automatic sequence an element need not have an asymptotic density. In this paper a necessary and sufficient criterion is proved for the existence of the asymptotic density of a given element. If it does not exist the asymptotic distribution of the element can be described in terms of a function H whose graph is self-similar. An algorithm is given to decide whether H is piecewise continuously differentiable, and in this case it can be computed effectively. Finally, it is shown that the H_{∞}-density of an element in an automatic sequence always exists and equals its logarithmic density.
Bibtex:
@article{,
title={The asymptotic distribution of elements in automatic sequences},
author={Peter, Manfred},
journal={Theoretical computer science},
volume={301},
number={1},
pages={285--312},
year={2003},
publisher={Elsevier},
DOI={10.1016/S0304-3975(02)00587-X},
}
Reference Type: Journal Article
Subject Area(s): Computer Science