De Bruijn序列的偏好函数的跨度
Spans of Preference Functions for De Bruijn Sequences
摘要：
非二进制福特序列是由简单规则生成的de Bruijn序列，该规则确定首先尝试哪些符号的优先级，给定大小为$n$的初始字，这是生成序列的顺序。这组规则通过span $n-1$的偏好函数的概念来推广，span给出了在遇到大小为$n-1$的子串之后出现什么符号的优先级。在本文中，我们的偏好函数生成完整的de Bruijn序列的特征。更重要的是，我们建立了任何偏好函数，生成一个德Bruijn序列的顺序$n$也生成德Bruijn序列的所有订单高于$n$，从而使福特序列没有特殊情况。因此，我们定义的偏好函数的复杂性的德布鲁因序列的偏好函数，生成这个德布鲁因序列的最小可能的跨度。
英文摘要：
A nonbinary Ford sequence is a de Bruijn sequence generated by simple rules that determine the priorities of what symbols are to be tried first, given an initial word of size $n$ which is the order of the sequence being generated. This set of rules is generalized by the concept of a preference function of span $n-1$, which gives the priorities of what symbols to appear after a substring of size $n-1$ is encountered. In this paper we characterize preference functions that generate full de Bruijn sequences. More significantly, We establish that any preference function that generates a de Bruijn sequence of order $n$ also generates de Bruijn sequences of all orders higher than $n$, thus making the Ford sequence no special case. Consequently, we define the preference function complexity of a de Bruijn sequence to be the least possible span of a preference function that generates this de Bruijn sequence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
