Abstract
In this paper we study the number \(r_{\texttt {bwt}}\) 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 \(r_{\texttt {bwt}}\) 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 whichever purely morphic finite word on a binary alphabet, \(r_{\texttt {bwt}}\) is \(\mathcal {O}(\log n)\), where n is the length of the word. Moreover, we prove that \(r_{\texttt {bwt}}\) is \(\varTheta (\log n)\) 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 bispecial circular factors of such words.
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Frosini, A., Mancini, I., Rinaldi, S., Romana, G., Sciortino, M. (2022). Logarithmic Equal-Letter Runs for BWT of Purely Morphic Words. In: Diekert, V., Volkov, M. (eds) Developments in Language Theory. DLT 2022. Lecture Notes in Computer Science, vol 13257. Springer, Cham. https://doi.org/10.1007/978-3-031-05578-2_11
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