Related papers: String Attractors and Infinite Words
The minimizers sampling mechanism is a popular mechanism for string sampling introduced independently by Schleimer et al. [SIGMOD 2003] and by Roberts et al. [Bioinf. 2004]. Given two positive integers $w$ and $k$, it selects the…
An integer array y = y[1..n] is said to be feasible if and only if y[1] = n and, for every i \in 2..n, i \le i+y[i] \le n+1. A string is said to be indeterminate if and only if at least one of its elements is a subset of cardinality greater…
In this paper we propose a new, more appropriate definition of regular and indeterminate strings. A regular string is one that is "isomorphic" to a string whose entries all consist of a single letter, but which nevertheless may itself…
In this paper we introduce and study a new complexity measure for finite words. For positive integer $d$ special scattered subwords, called super-$d$-subwords, in which the gaps are of length at least $(d-1)$, are defined. We give methods…
In this paper we are interested in studying concise representations of concepts and dependencies, i.e., implications and association rules. Such representations are based on equivalence classes and their elements, i.e., minimal generators,…
We consider document listing on string collections, that is, finding in which strings a given pattern appears. In particular, we focus on repetitive collections: a collection of size $N$ over alphabet $[1,\sigma]$ is composed of $D$ copies…
This study aims to publish a novel similarity metric to increase the speed of comparison operations. Also the new metric is suitable for distance-based operations among strings. Most of the simple calculation methods, such as string length…
A compressed self-index stores a string in compressed form while supporting locate queries without decompression. For highly repetitive strings (arising in web crawls, versioned documents, and genomic collections), static self-indexes can…
Modern NLP models rely heavily on engineered features, which often combine word and contextual information into complex lexical features. Such combination results in large numbers of features, which can lead to over-fitting. We present a…
We present results from numerical studies of supervised learning operations in recurrent networks considered as graphs, leading from a given set of input conditions to predetermined outputs. Graphs that have optimized their output for…
Large language models (LLMs) have been applied in various applications due to their astonishing capabilities. With advancements in technologies such as chain-of-thought (CoT) prompting and in-context learning (ICL), the prompts fed to LLMs…
The subword complexity of a word $w$ over a finite alphabet $\mathcal{A}$ is a function that assigns for each positive integer $n$, the number of distinct subwords of length $n$ in $w$. The subword complexity of a word is a good measure of…
We present a new graph compressor that works by recursively detecting repeated substructures and representing them through grammar rules. We show that for a large number of graphs the compressor obtains smaller representations than other…
Ambitwistor-strings are chiral strings whose targets are spaces of complex massless particles, and whose correlation functions directly lead to simple, compact formulae for scattering amplitudes and loop integrands for massless gauge and…
Recent methods for learning vector space representations of words have succeeded in capturing fine-grained semantic and syntactic regularities using vector arithmetic. However, these vector space representations (created through large-scale…
The automatic complexity of a finite word (string) is an analogue for finite automata of Sipser's distinguishing complexity (1983) and was introduced by Shallit and Wang (2001). For a finite alphabet $\Sigma$ of at least two elements, we…
We present an algorithm that takes an unannotated corpus as its input, and returns a ranked list of probable morphologically related pairs as its output. The algorithm tries to discover morphologically related pairs by looking for pairs…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
We study the complexity of the problem of searching for a set of patterns that separate two given sets of strings. This problem has applications in a wide variety of areas, most notably in data mining, computational biology, and in…
Grammar based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. In this paper, we present a novel…