Matching statistics were introduced to solve the approximate string matching problem, which is a recurrent subroutine in bioinformatics applications. In 2010, Ohlebusch et al. [SPIRE 2010] proposed a time and space efficient algorithm for computing matching statistics which relies on some components of a compressed suffix tree - notably, the longest common prefix (LCP) array. In this paper, we show how their algorithm can be generalized from strings to Wheeler deterministic finite automata. Most importantly, we introduce a notion of LCP array for Wheeler automata, thus establishing a first clear step towards extending (compressed) suffix tree functionalities to labeled graphs.

The study of the compressibility of repetitive sequences is an issue that is attracting great interest. We consider purely morphic words, which are highly repetitive sequences generated by iterating a morphism$\varphi$that admits a fixed point (denoted by$\varphi^{\infty}(a)$) starting from a given character$a$belonging to the finite alphabet$A$, i.e.$\varphi^{\infty}(a)=\lim\nolimits_{i\rightarrow\infty}\varphi^{i}(a)$. Such morphisms are called prolongable on$a$. Here we focus on the compressibility via the Burrows-Wheeler Transform ($BWT$) of infinite families of finite sequences generated by morphisms. In particular, denoted by$r(w)$the number of equal-letter runs of a word$w$, we provide new upper bounds on$r(\mathsf{bwt} (\varphi^{i}(a)))$, i.e. the number of equal-letter runs produced when$BWT$is applied on$\varphi^{i}(a)$. Such bounds depend on the factor complexity$f_{x}(n)$of the infinite word$x=\varphi^{\infty}(a)$, that counts, for each$n\geq 0$, the number of distinct factors of$x$having length$n$.

Summary form only given. We introduce an extension of the Burrows-Wheeler transform to a multiset of primitive words. Primitiveness is not actually a restrictive hypothesis, since in practice almost all the processed texts are primitive (or become primitive by adding an end-of-string symbol). We prove that such a transformation as the BWT is reversible. We show how to use the transformation as a preprocessing for the simultaneous compression of different texts.