Abstract
We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating functions or from their generating finite automatons, respectively.
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Acknowledgment
The authors would like to thank Christian Mauduit for helpful discussions.
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This article is part of the Topical Collection on Special Issue on Sequences and Their Applications
The authors are partially supported by the Austrian Science Fund FWF Project 5511-N26 which is part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications”.
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Mérai, L., Winterhof, A. On the pseudorandomness of automatic sequences. Cryptogr. Commun. 10, 1013–1022 (2018). https://doi.org/10.1007/s12095-017-0260-7
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DOI: https://doi.org/10.1007/s12095-017-0260-7
Keywords
- Finite automaton
- Automatic sequences
- Correlation measure
- Pseudorandom sequences
- Thue-Morse sequence
- State complexity