An efficient generalized shift-rule for the prefer-max De Bruijn sequence
نویسندگان
چکیده
منابع مشابه
An Efficient Generalized Shift-Rule for the Prefer-Max De Bruijn Sequence
One of the fundamental ways to construct De Bruijn sequences is by using a shift-rule. A shift-rule receives a word as an argument and computes the digit that appears after it in the sequence. An optimal shift-rule for an (n, k)-De Bruijn sequence runs in time O(n). We propose an extended notion we name a generalized-shift-rule, which receives a word, w, and an integer, c, and outputs the c dig...
متن کاملAn Efficient Shift Rule for the Prefer-Max De Bruijn Sequence
A shift rule for the prefer-max De Bruijn sequence is formulated, for all sequence orders, and over any finite alphabet. An efficient algorithm for this shift rule is presented, which has linear (in the sequence order) time and memory complexity.
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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...
متن کاملA simple shift rule for k-ary de Bruijn sequences
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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The skew of a binary string is the difference between the number of zeroes and the number of ones, while the length of the string is the sum of these two numbers. We consider certain suffixes of the lexicographicallyleast de Bruijn sequence at natural breakpoints of the binary string. We show that the skew and length of these suffixes are enumerated by sequences generalizing the Fibonacci and L...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2020
ISSN: 0012-365X
DOI: 10.1016/j.disc.2019.111657