论文标题
在每个单词的摊销polyogarithmic时间中生成灰色代码
Generating a Gray code for prefix normal words in amortized polylogarithmic time per word
论文作者
论文摘要
前缀普通词是一个二进制单词，其属性没有子字符串的$ 1 $ S超过相同长度的前缀。通过证明前缀普通词是一种气泡语言，我们可以详尽地列出所有长度$ n $的前缀普通单词作为组合灰色代码，其中连续的字符串最多有两个交换或flips。该灰色代码可以以$ \ oh（\ log^2 n）$每个单词的摊销时间生成，而迄今为止最好的一代算法hitherto具有$ \ oh（n）$每个单词的运行时间。我们还提出了一个会员测试仪，用于前缀普通单词，以及泡泡语言的新颖表征。
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.
