A surprisingly simple de Bruijn sequence construction

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A surprisingly simple de Bruijn sequence construction

Pick any length n binary string b1b2 · · · bn and remove the first bit b1. If b2b3 · · · bn1 is a necklace then append the complement of b1 to the end of the remaining string; otherwise append b1. By repeating this process, eventually all 2 binary strings will be visited cyclically. This shift rule leads to a new de Bruijn sequence construction that can be generated in O(1)-amortized time per b...

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A (non-circular) de Bruijn sequence w of order n is a word such that every word of length n appears exactly once in w as a factor. In this paper, we generalize the concept to a multi-shift setting: a m-shift de Bruijn sequence of order n is a word such that every word of length n appears exactly once in w as a factor that starts at an index im+ 1 for some integer i ≥ 0. We show the number of th...

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A k-ary de Bruijn sequence of order n is a cyclic sequence of length k 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 ...

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2016

ISSN: 0012-365X

DOI: 10.1016/j.disc.2015.08.002