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Generating a Gray code for prefix normal words in amortized polylogarithmic time per word
Theoretical Computer Science ( IF 0.9 ) Pub Date : 2020-08-04 , DOI: 10.1016/j.tcs.2020.07.035
Péter Burcsi , Gabriele Fici , Zsuzsanna Lipták , Rajeev Raman , Joe Sawada

A prefix normal word is a binary word with the property that no substring has more 1s 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 O(log2n) amortized time per word, while the best generation algorithm hitherto has O(n) running time per word. We also present a membership tester for prefix normal words, as well as a novel characterization of bubble languages.



中文翻译:

生成格雷码以在每个单词的摊余对数时间内为普通单词添加前缀

前缀普通字是一个二进制字,其属性是子字符串的长度不能比相同长度的前缀多1。通过证明前缀普通词集合是冒泡语言,我们可以穷尽所有长度为n的前缀普通词作为组合格雷码列出,其中连续的字符串最多相差两次交换或位翻转。此格雷码可以在Ø日志2ñ 摊分每个单词的时间,而迄今为止最好的生成算法 Øñ每个单词的运行时间。我们还介绍了一种用于普通单词前缀的成员资格测试器,以及一种泡泡语言的新颖表征。

更新日期:2020-09-30
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