Approximate Regular Expression Matching

Years and Authors of Summarized Original Work

• 1995; Wu, Manber, Myers

Problem Definition

Given a text string T = t₁t₂… t _n and a regular expression R of length m denoting language, $\mathcal{L}(R)$ over an alphabet $\Sigma$ of size $\sigma$, and given a distance function among strings d and a threshold k, the approximate regular expression matching (AREM) problem is to find all the text positions that finish a so-called approximate occurrence of R in T, that is, compute the set $\{j,\,\exists i,\,1,\,\leq \, i\, \leq \, j,\,\exists P\, \in \,\mathcal{L}(R),\,d(P,\,t_{i},\,.\,.\,.\,,\,t_{j})\, \leq \, k\}\ T,R$, and k are given together, whereas the algorithm can be tailored for a specific d.

This entry focuses on the so-called weighted edit distance, which is the minimum sum of weights of a sequence of operations converting one string into the other. The operations are insertions, deletions, and substitutions of characters. The weights are positive real values associated to...