Logarithmic equal-letter runs for BWT of purely morphic words

Abstract

In this paper we study the number rbwt of equal-letter runs produced by the Burrows-Wheeler transform (BW T ) when it is applied to purely morphic finite words, which are words generated by iterating prolongable morphisms. Such a parameter rbwt is very significant since it provides a measure of the performances of the BW T , in terms of both compressibility and indexing. In particular, we prove that, when BW T is applied to any purely morphic finite word on a binary alphabet, rbwt is O(log n), where n is the length of the word. Moreover, we prove that rbwt 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 bispecial circular factors of such words.