Elastic-degenerate (ED) strings generalize classic strings by allowing each position to store a set of up to$h$strings of arbitrary lengths [2]. An ED string is a restricted version of a regular expression whose expressiveness still causes a combinatorial explosion of possible resolutions (i.e., the members of its language), making classical pattern matching and indexing techniques either inefficient or inapplicable. A position in an ED string is called solid if it stores a single symbol, otherwise elastic. We introduce the Min/Max wavelet tree (MM-WT), a variant of the wavelet tree supporting semantics-aware rank and select on ED strings. Each leaf stores two arrays per symbol$c, \min _{c}$and$\max _{c}$, giving for each position the minimum and maximum symbol count across all alternatives. Prefix sums bound the number of occurrences in any resolution of a prefix, so sm-rank$(c, i)$returns an interval$\left[r_{\min}, r_{\max}\right]$of possible ranks, and sm-select$(c, j)$returns an interval for the$j$-th occurrence of$c$. On classic strings, min and max collapse to the same counts and the structure becomes a standard wavelet tree. The structure uses the same space as a subset wavelet tree [1] internally, plus$\mathcal{O}(n \sigma \log h)$bits for the min/max arrays, and supports both queries in$\mathcal{O}(\log \sigma)$time.

We introduce Attractor Matching, a new framework for structural string comparison built upon the theory of string attractors. Given a pattern$x$of length$m$and one of its attractors$\Gamma_{x}$, the problem asks for all substrings$y[i. . i+m-1]$of a text$y$such that$\Gamma_{x}$is also an attractor of$y[i. . i+m-1]$. Unlike classical notions of string matching, which rely on character equality or distance measures, attractor matching focuses on the structural properties that govern repetitiveness and compressibility. Our contribution is fourfold. First, we adapt the IsAttractor algorithm of Béal et al. by combining the DAWG with the slidingwindow technique of Blumer, enabling online attractor verification as the window advances over the text. Second, we reformulate the verification procedure on the Compressed DAWG (CDAWG), obtaining a more compact representation that preserves correctness. Third, we employ the sliding-window CDAWG method of Inenaga et al., which allows efficient attractor matching on sliding-window maintained CDAWGs with incremental updates. Finally, we introduce a relaxed variant, Attractor Matching with Mismatches, where the pattern attractor may be extended by at most$\rho$additional positions, enabling structurally tolerant matching. This paradigm bridges compression and similarity, opening new directions for structure-aware pattern matching.