Abstract
Let x be an m-sequence, a maximal length sequence produced by a linear feedback shift register. We show that x has maximal subword complexity function in the sense of Allouche and Shallit. We show that this implies that the nondeterministic automatic complexity \(A_N(x)\) is close to maximal: \(n/2-A_N(x)=O(\log ^2n)\), where n is the length of x. In contrast, Hyde has shown \(A_N(y)\le n/2+1\) for all sequences y of length n.
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Acknowledgments
This work was partially supported by a grant from the Simons Foundation (#315188 to Bjørn Kjos-Hanssen). This material is based upon work supported by the National Science Foundation under Grant No. 1545707.
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Kjos-Hanssen, B. (2017). Shift Registers Fool Finite Automata. In: Kennedy, J., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2017. Lecture Notes in Computer Science(), vol 10388. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55386-2_12
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DOI: https://doi.org/10.1007/978-3-662-55386-2_12
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