Logarithmic Equal-Letter Runs for BWT of Purely Morphic Words

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 whichever purely morphic finite word on a binary alphabet, r(bwt) is 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 bispecial circular factors of such words.