On the pseudorandomness of Parry--Bertrand automatic sequences
<|reference_start|>On the pseudorandomness of Parry--Bertrand automatic sequences: The correlation measure is a testimony of the pseudorandomness of a sequence $\infw{s}$ and provides information about the independence of some parts of $\infw{s}$ and their shifts. Combined with the well-distribution measure, a sequence possesses good pseudorandomness properties if both measures are relatively small. In combinatorics on words, the famous $b$-automatic sequences are quite far from being pseudorandom, as they have small factor complexity on the one hand and large well-distribution and correlation measures on the other. This paper investigates the pseudorandomness of a specific family of morphic sequences, including classical $b$-automatic sequences. In particular, we show that such sequences have large even-order correlation measures; hence, they are not pseudorandom. We also show that even- and odd-order correlation measures behave differently when considering some simple morphic sequences.<|reference_end|>
@article{popoli2024on,
    title={On the pseudorandomness of Parry--Bertrand automatic sequences},
    author={Pierre Popoli and Manon Stipulanti},
    journal={arXiv preprint arXiv:2408.14059},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.14059},
    primaryClass={math.CO cs.DM}
}