Elsevier

Discrete Mathematics

Volume 340, Issue 3, March 2017, Pages 524-531
Discrete Mathematics

A simple shift rule for k-ary de Bruijn sequences

https://doi.org/10.1016/j.disc.2016.09.008Get rights and content
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Abstract

A k-ary de Bruijn sequence of order n is a cyclic sequence of length kn in which each k-ary string of length n appears exactly once as a substring. A shift rule for a de Bruijn sequence of order n is a function that maps each length n substring to the next length n substring in the sequence. We present the first known shift rule for k-ary de Bruijn sequences that runs in O(1)-amortized time per symbol using O(n) space. Our rule generalizes the authors’ recent shift rule for the binary case (A surprisingly simple de Bruijn sequence construction, Discrete Math. 339, 127–131).

Keywords

k-ary de Bruijn sequence
De Bruijn sequence
Universal cycle
Necklaces
Shift Gray code
CAT algorithm
Generate
Shift rule
Successor rule

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