Logarithmic equal-letter runs for BWT of purely morphic words

02/05/2022
by   Andrea Frosini, et al.
0

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 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 bispecial circular factors of such words.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/04/2023

Ranking and unranking bordered and unbordered words

A border of a word w is a word that is both a non-empty proper prefix an...
research
01/22/2019

Palindromic Subsequences in Finite Words

In 1999 Lyngsø and Pedersen proposed a conjecture stating that every bin...
research
08/05/2021

Counting scattered palindromes in a finite word

We investigate the scattered palindromic subwords in a finite word. We s...
research
06/22/2020

On morphisms preserving palindromic richness

Droubay, Justin and Pirillo that each word of length n contains at most ...
research
06/28/2022

Asymptotic bounds for the number of closed and privileged words

A word w has a border u if u is a non-empty proper prefix and suffix of ...
research
01/07/2020

VC-dimensions of nondeterministic finite automata for words of equal length

Ishigami and Tani studied VC-dimensions of deterministic finite automata...
research
10/03/2021

Words that almost commute

The Hamming distance ham(u,v) between two equal-length words u, v is the...

Please sign up or login with your details

Forgot password? Click here to reset