纯形态词的BWT的对数等字母运行
Logarithmic equal-letter runs for BWT of purely morphic words
摘要：
本文研究了当Burrows-Wheeler变换（$BWT$）应用于纯态射有限字（由可迭代态射生成的字）时产生的等字母游程数$r_{bwt}$。这样的参数$r_{bwt}$是非常重要的，因为它提供了$BWT$在可压缩性和索引方面的性能的量度。特别是，我们证明，当$BWT$被应用到任何纯形态有限字的二进制字母表，$r_{bwt}$是$\mathcal{O}(\log n)$，其中$n$是字的长度。此外，我们证明了$r_{bwt}$是$Θ(\log n)$的二进制字所产生的一大类可压缩的二元态射。这些界限是通过提供一些新的结构性质的\emph{bispecial circular factors}这样的话证明。
英文摘要：
In this paper we study the number $r_{bwt}$ of equal-letter runs produced by the Burrows-Wheeler transform ($BWT$) when it is applied to purely morphic finite words, which are words generated by iterating prolongable morphisms. Such a parameter $r_{bwt}$ is very significant since it provides a measure of the performances of the $BWT$, in terms of both compressibility and indexing. In particular, we prove that, when $BWT$ is applied to any purely morphic finite word on a binary alphabet, $r_{bwt}$ is $\mathcal{O}(\log n)$, where $n$ is the length of the word. Moreover, we prove that $r_{bwt}$ is $Θ(\log n)$ for the binary words generated by a large class of prolongable binary morphisms. These bounds are proved by providing some new structural properties of the \emph{bispecial circular factors} of such words.
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