1. Logarithmic equal-letter runs for BWT of purely morphic words
- Author
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Frosini, Andrea, Mancini, Ilaria, Rinaldi, Simone, Romana, Giuseppe, and Sciortino, Marinella
- Subjects
Computer Science - Formal Languages and Automata Theory ,Computer Science - Data Structures and Algorithms - Abstract
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 $\Theta(\log n)$ 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.
- Published
- 2022