A family of Lempel-Ziv factorizations is a well-studied string structure. The LZ-End factorization is a member of the family that achieved faster extraction of any substrings (Kreft & Navarro, TCS 2013). One of the interests for LZ-End factorizations is the possible difference between the size of LZ-End and LZ77 factorizations. They also showed families of strings where the approximation ratio of the number of LZ-End phrases to the number of LZ77 phrases asymptotically approaches 2. However, the alphabet size of these strings is unbounded. In this paper, we analyze the LZ-End factorization of the period-doubling sequence. We also show that the approximation ratio for the period-doubling sequence asymptotically approaches 2 for the binary alphabet.

翻译：Lempel-Ziv因子化的家族是一个研究周密的字符串结构。LZ-End因子化是能够更快提取任何子字符串(Kreft & Navarro, TCS, 2013)的家庭成员。LZ-End因子化的利益之一是LZ-End因子化的大小和LZ77因子化的大小之间可能的差异。它们还显示了字符串的家族,其中LZ-End的词组数目与LZ77的词组数目的近似比。2 但这些字符组的字母大小是无界的。在本文件中,我们分析了周期多动序列的LZ-End因子化。我们还表明,对于二进字母,周期的振动序列的近似比率是无序式的2。