Related papers: Which Regular Expression Patterns are Hard to Matc…
Regular expressions with backreferences (regex, for short), as supported by most modern libraries for regular expression matching, have an NP-complete matching problem. We define a complexity parameter of regex, called active variable…
The classical pattern matching asks for locating all occurrences of one string, called the pattern, in another, called the text, where a string is simply a sequence of characters. Due to the potential practical applications, it is desirable…
Regular expression matching is of practical importance due to its widespread use in real-world applications. In practical use, regular expressions are often used with real-world extensions. Accordingly, the matching problem of regular…
In the problem of $\texttt{Generalised Pattern Matching}\ (\texttt{GPM})$ [STOC'94, Muthukrishnan and Palem], we are given a text $T$ of length $n$ over an alphabet $\Sigma_T$, a pattern $P$ of length $m$ over an alphabet $\Sigma_P$, and a…
Motivated by the imminent growth of massive, highly redundant genomic databases, we study the problem of compressing a string database while simultaneously supporting fast random access, substring extraction and pattern matching to the…
In the present paper, we study the match test for extended regular expressions. We approach this NP-complete problem by introducing a novel variant of two-way multihead automata, which reveals that the complexity of the match test is…
The explosive rate of information growth and availability often makes it increasingly difficult to locate information pertinent to your needs. These problems are often compounded when keyword based search methodologies are not adequate for…
The Kleene star operator is an important pattern construct for representing a pattern that repeats multiple times. Due to its simplicity and usefulness, it is imported into various pattern-matching systems other than regular expressions.…
We present an algorithm for searching regular expression matches in compressed text. The algorithm reports the number of matching lines in the uncompressed text in time linear in the size of its compressed version. We define efficient data…
Fast matching of regular expressions with bounded repetition, aka counting, such as (ab){50,100}, i.e., matching linear in the length of the text and independent of the repetition bounds, has been an open problem for at least two decades.…
Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation graphs…
This paper is devoted to finite state automata, regular expression matching, pattern recognition, and the exponential blow-up problem, which is the growing complexity of automata exponentially depending on regular expression length. This…
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…
The classic exact pattern matching problem, given two strings -- a pattern $P$ of length $m$ and a text $T$ of length $n$ -- asks whether $P$ occurs as a substring of $T$. A property tester for the problem needs to distinguish (with high…
We revisit the complexity of approximate pattern matching in an elastic-degenerate string. Such a string is a sequence of $n$ finite sets of strings of total length $N$, and compactly describes a collection of strings obtained by first…
The $k$-mismatch problem consists in computing the Hamming distance between a pattern $P$ of length $m$ and every length-$m$ substring of a text $T$ of length $n$, if this distance is no more than $k$. In many real-world applications, any…
Set constraints provide a highly general way to formulate program analyses. However, solving arbitrary boolean combinations of set constraints is NEXPTIME-hard. Moreover, while theoretical algorithms to solve arbitrary set constraints…
We present a trichotomy theorem for the quantum query complexity of regular languages. Every regular language has quantum query complexity Theta(1), ~Theta(sqrt n), or Theta(n). The extreme uniformity of regular languages prevents them from…
Classic similarity measures of strings are longest common subsequence and Levenshtein distance (i.e., the classic edit distance). A classic similarity measure of curves is dynamic time warping. These measures can be computed by simple…
An elastic-degenerate (ED) string is a sequence of $n$ sets of strings of total length $N$, which was recently proposed to model a set of similar sequences. The ED string matching (EDSM) problem is to find all occurrences of a pattern of…