Abstract
In this paper, we consider factor complexity/topological entropy of infinite binary sequences. In particular, we show that for any real number \(\alpha \) with \(0 \leqslant \alpha \leqslant 1\), there is a subset of the Cantor space with Hausdorff dimension \(\alpha \), such that each one of its elements has factor complexity \(\alpha \). This result partially generalises to the multidimensional case where sequences are replaced by their d-dimensional analogs.
This work is partially supported by the Singapore Ministry of Education Academic Research Fund Tier 2 Grant MOE2016-T2-1-019/R146-000-234-112 (PI Frank Stephan).
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Acknowledgments
The authors would like to thank the anonyomous referees of CIAA 2018 and Hugh Anderson for very helpful comments on the mathematics and the English of this paper.
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Moldagaliyev, B., Staiger, L., Stephan, F. (2018). On the Values for Factor Complexity. In: Câmpeanu, C. (eds) Implementation and Application of Automata. CIAA 2018. Lecture Notes in Computer Science(), vol 10977. Springer, Cham. https://doi.org/10.1007/978-3-319-94812-6_23
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