Related papers: String Representation in Suffixient Set Size Space
The problem of finding factors of a text string which are identical or similar to a given pattern string is a central problem in computer science. A generalised version of this problem consists in implementing an index over the text to…
Weighted automata (WA) are an important formalism to describe quantitative properties. Obtaining equivalent deterministic machines is a longstanding research problem. In this paper we consider WA with a set semantics, meaning that the…
We consider subsequences with gap constraints, i.e., length-k subsequences p that can be embedded into a string w such that the induced gaps (i.e., the factors of w between the positions to which p is mapped to) satisfy given gap…
The central result of this paper is the small-is-very-small principle for restricted sequential theories. The principle says roughly that whenever the given theory shows that a property has a small witness, i.e. a witness in every definable…
In this paper we describe a data structure that supports pattern matching queries on a dynamically arriving text over an alphabet ofconstant size. Each new symbol can be prepended to $T$ in O(1) worst-case time. At any moment, we can report…
The suffix tree is arguably the most fundamental data structure on strings: introduced by Weiner (SWAT 1973) and McCreight (JACM 1976), it allows solving a myriad of computational problems on strings in linear time. Motivated by its large…
String attractors [STOC 2018] are combinatorial objects recently introduced to unify all known dictionary compression techniques in a single theory. A set $\Gamma\subseteq [1..n]$ is a $k$-attractor for a string $S\in[1..\sigma]^n$ if and…
Compressed indexing is a powerful technique that enables efficient querying over data stored in compressed form, significantly reducing memory usage and often accelerating computation. While extensive progress has been made for…
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…
We consider the Consensus Patterns problem, where, given a set of input strings, one is asked to extract a long-enough pattern which appears (with some errors) in all strings. We prove that this problem is W[1]-hard when parameterized by…
We define a suffixient set for a text $T [1..n]$ to be a set $S$ of positions between 1 and $n$ such that, for any edge descending from a node $u$ to a node $v$ in the suffix tree of $T$, there is an element $s \in S$ such that $u$'s path…
For a sequence $S$ of terms from an abelian group $G$ of length $|S|$, let $\Sigma_n(S)$ denote the set of all elements that can be represented as the sum of terms in some $n$-term subsequence of $S$. When the subsum set is very small,…
A key principle in string processing is local consistency: using short contexts to handle matching fragments of a string consistently. String synchronizing sets [Kempa, Kociumaka; STOC 2019] are an influential instantiation of this…
Recently, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. One application of this novel methodology is the separation of data, which is composed of two (or more)…
We propose novel algorithms for sequence prediction based on ideas from stringology. These algorithms are time and space efficient and satisfy mistake bounds related to particular stringological complexity measures of the sequence. In this…
The Shortest Superstring Problem (SSP) consists, for a set of strings S = {s_1,...,s_n}, to find a minimum length string that contains all s_i, 1 <= i <= k, as substrings. This problem is proved to be NP-Complete and APX-hard. Guaranteed…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
The goal of compressed sensing is to learn a structured signal $x$ from a limited number of noisy linear measurements $y \approx Ax$. In traditional compressed sensing, "structure" is represented by sparsity in some known basis. Inspired by…
We consider compact representations of collections of similar strings that support random access queries. The collection of strings is given by a rooted tree where edges are labeled by an edit operation (inserting, deleting, or replacing a…
Given a set of $k$ strings $I$, their longest common subsequence (LCS) is the string with the maximum length that is a subset of all the strings in $I$. A data-structure for this problem preprocesses $I$ into a data-structure such that the…