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Peter, M (2003)

The asymptotic distribution of elements in automatic sequences

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.

@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