以每个单词摊销多对数时间生成前缀正规字的格雷码
Generating a Gray code for prefix normal words in amortized polylogarithmic time per word
AI总结：
本研究证明前缀正规字集合是bubble language，据此生成其组合格雷码，将每个单词的生成摊销时间从此前的O(n)降至O(log²n)，还提出成员测试器与bubble language的新刻画。
摘要：
前缀正规字是一种二元字，其性质为任意子串中1的数量都不超过长度相同的前缀中的1的数量。通过证明前缀正规字集合是一种bubble language（冒泡语言），我们可将所有长度为n的前缀正规字穷举排列为组合格雷码，相邻字符串至多相差两次交换或位翻转。该格雷码可按每个单词O(log²n)的摊销时间生成，而此前最优的生成算法每个单词运行时间为O(n)。我们还提出了前缀正规字的成员测试器，以及bubble language的一种全新刻画。
英文摘要：
A prefix normal word is a binary word with the property that no substring has more $1$s than the prefix of the same length. By proving that the set of prefix normal words is a bubble language, we can exhaustively list all prefix normal words of length $n$ as a combinatorial Gray code, where successive strings differ by at most two swaps or bit flips. This Gray code can be generated in $\Oh(\log^2 n)$ amortized time per word, while the best generation algorithm hitherto has $\Oh(n)$ running time per word. We also present a membership tester for prefix normal words, as well as a novel characterization of bubble languages.
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。
