Related papers: String Attractors and Infinite Words
Pattern matching is the most central task for text indices. Most recent indices leverage compression techniques to make pattern matching feasible for massive but highly-compressible datasets. Within this kind of indices, we propose a new…
Given a static reference string $R$ and a source string $S$, a relative compression of $S$ with respect to $R$ is an encoding of $S$ as a sequence of references to substrings of $R$. Relative compression schemes are a classic model of…
The process of meaning composition, wherein smaller units like morphemes or words combine to form the meaning of phrases and sentences, is essential for human sentence comprehension. Despite extensive neurolinguistic research into the brain…
This paper is an extended abstract of the dissertation presented by the author for the doctoral degree in physics and mathematics (in Russia). The main characteristic studied in the dissertation is combinatorial complexity, which is a…
Kolmogorov complexity of a finite binary word reflects both algorithmic structure and the empirical distribution of symbols appearing in the word. Words with symbol frequencies far from one half have smaller combinatorial richness and…
Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However,…
Minimizers are sampling schemes with numerous applications in computational biology. Assuming a fixed alphabet of size $\sigma$, a minimizer is defined by two integers $k,w\ge2$ and a linear order $\rho$ on strings of length $k$ (also…
There have been multiple attempts to resolve various inflection matching problems in information retrieval. Stemming is a common approach to this end. Among many techniques for stemming, statistical stemming has been shown to be effective…
Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…
The compressed indexing problem is to preprocess a string $S$ of length $n$ into a compressed representation that supports pattern matching queries. That is, given a string $P$ of length $m$ report all occurrences of $P$ in $S$. We present…
In the era of deep learning, word embeddings are essential when dealing with text tasks. However, storing and accessing these embeddings requires a large amount of space. This is not conducive to the deployment of these models on…
We show how to compress string dictionaries using the Lempel-Ziv (LZ78) data compression algorithm. Our approach is validated experimentally on dictionaries of up to 1.5 GB of uncompressed text. We achieve compression ratios often…
An infinite permutation is a linear ordering of the set of non-negative integers. Generally, the properties of infinite permutations analogous to those of infinite words show some resemblances and some differences between permutations and…
We address the satisfiability problem for string constraints that combine relational constraints represented by transducers, word equations, and string length constraints. This problem is undecidable in general. Therefore, we propose a new…
Entropy quantifies the number of bits required to store objects under certain given assumptions. While this is a well established concept for strings, in the context of tries the state-of-the-art regarding entropies is less developed. The…
Zimin words are very special finite words which are closely related to the pattern-avoidability problem. This problem consists in testing if an instance of a given pattern with variables occurs in almost all words over any finite alphabet.…
We study the framework of abductive logic programming extended with integrity constraints. For this framework, we introduce a new measure of the simplicity of an explanation based on its degree of \emph{arbitrariness}: the more arbitrary…
We introduce a new family of compressed data structures to efficiently store and query large string dictionaries in main memory. Our main technique is a combination of hierarchical Front-coding with ideas from longest-common-prefix…
We consider questions related to the structure of infinite words (over an integer alphabet) with bounded additive complexity, i.e., words with the property that the number of distinct sums exhibited by factors of the same length is bounded…
Most of the fastest-growing string collections today are repetitive, that is, most of the constituent documents are similar to many others. As these collections keep growing, a key approach to handling them is to exploit their…