Related papers: An error correcting parser for context free gramma…

We study the problem of efficiently correcting an erroneous product of two $n\times n$ matrices over a ring. Among other things, we provide a randomized algorithm for correcting a matrix product with at most $k$ erroneous entries running in…

We study the problem of approximating the edit distance of two strings in sublinear time, in a setting where one or both string(s) are preprocessed, as initiated by Goldenberg, Rubinstein, Saha (STOC '20). Specifically, in the $(k, K)$-gap…

Let a text $T[1..n]$ be the only string generated by a context-free grammar with $g$ (terminal and nonterminal) symbols, and of size $G$ (measured as the sum of the lengths of the right-hand sides of the rules). Such a grammar, called a…

We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…

The edit distance is a way of quantifying how similar two strings are to one another by counting the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. In this paper we…

We present a unified framework for accelerating edit-distance computation between two compressible strings using straight-line programs. For two strings of total length $N$ having straight-line program representations of total size $n$, we…

We consider the approximate pattern matching problem under edit distance. In this problem we are given a pattern $P$ of length $w$ and a text $T$ of length $n$ over some alphabet $\Sigma$, and a positive integer $k$. The goal is to find all…

Given strings $P$ of length $m$ and $T$ of length $n$ over an alphabet of size $\sigma$, the string matching with $k$-mismatches problem is to find the positions of all the substrings in $T$ that are at Hamming distance at most $k$ from…

The edit distance (a.k.a. the Levenshtein distance) between two strings is defined as the minimum number of insertions, deletions or substitutions of symbols needed to transform one string into another. The problem of computing the edit…

We describe the first self-indexes able to count and locate pattern occurrences in optimal time within a space bounded by the size of the most popular dictionary compressors. To achieve this result we combine several recent findings,…

In this paper we consider the problem of context-free grammars comparison from the analysis point of view. We show that the problem can be reduced to numerical solution of systems of nonlinear matrix equations. The approach presented here…

The algorithmic tasks of computing the Hamming distance between a given pattern of length $m$ and each location in a text of length $n$ is one of the most fundamental algorithmic tasks in string algorithms. Unfortunately, there is evidence…

Edit distance is a measurement of similarity between two sequences such as strings, point sequences, or polygonal curves. Many matching problems from a variety of areas, such as signal analysis, bioinformatics, etc., need to be solved in a…

Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…

Probabilistic context-free grammars (PCFGs) are used to define distributions over strings, and are powerful modelling tools in a number of areas, including natural language processing, software engineering, model checking, bio-informatics,…

The Binary Jumbled String Matching problem is defined as: Given a string $s$ over $\{a,b\}$ of length $n$ and a query $(x,y)$, with $x,y$ non-negative integers, decide whether $s$ has a substring $t$ with exactly $x$ $a$'s and $y$ $b$'s.…

Suppose an oracle knows a string $S$ that is unknown to us and that we want to determine. The oracle can answer queries of the form "Is $s$ a substring of $S$?". In 1995, Skiena and Sundaram showed that, in the worst case, any algorithm…

We introduce annotated grammars, an extension of context-free grammars which allows annotations on terminals. Our model extends the standard notion of regular spanners, and is more expressive than the extraction grammars recently introduced…

The problem of dictionary matching is a classical problem in string matching: given a set S of d strings of total length n characters over an (not necessarily constant) alphabet of size sigma, build a data structure so that we can match in…

We revisit the problem of computing the edit distance of a regular language given via an NFA. This problem relates to the inherent maximal error-detecting capability of the language in question. We present an efficient algorithm for solving…