On the invariance of the Kolmogorov complexity of $\beta$-expansions
<|reference_start|>On the invariance of the Kolmogorov complexity of $\beta$-expansions: We establish a relationship between the algorithmic (Kolmogorov) complexity of the prefixes of any binary expansion and a specific $\beta$-expansion, for every computable $\beta \in (1,2)$. The proof of the main statement crucially hinges on the development of a new dynamical system that generates this specific $\beta$-expansion. This dynamical system can be implemented on a computer.<|reference_end|>
@article{abadie2024on,
    title={On the invariance of the Kolmogorov complexity of $\beta$-expansions},
    author={Valentin Abadie and Helmut Boelcskei},
    journal={arXiv preprint arXiv:2405.03816},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.03816},
    primaryClass={cs.IT math.IT}
}