一个有效的广义移位定则
An Efficient Generalized Shift-Rule for the Prefer-Max De Bruijn Sequence
摘要：
构造De Bruijn序列的基本方法之一是使用移位规则。移位规则接收一个单词作为参数，并计算序列中出现在它之后的符号。$(n,k)$ -De Bruijn序列的最优移位规则在时间上运行$O(n)$。我们提出了一个扩展的概念，我们命名为一个广义移位规则，它接收一个字，$w$，和一个整数，$c$，并输出的$c$符号后，$w$。$(n,k)$ Bruijn序列的最优广义移位规则在时间上运行$O(n+c)$ .我们表明，不同于在移位规则的情况下，时间最优的广义移位规则允许有效地构建整个序列。我们为著名的prefer-max和prefer-min De Bruijn序列提供了一个时间最优的广义移位规则。
英文摘要：
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 symbol 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 $c$ symbols that comes after $w$. An optimal generalized-shift-rule for an $(n,k)$-De Bruijn sequence runs in time $O(n+c)$. We show that, unlike in the case of a shift-rule, a time optimal generalized-shift-rule allows to construct the entire sequence efficiently. We provide a time optimal generalized-shift-rule for the well-known prefer-max and prefer-min De Bruijn sequences.
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