Related papers: Net Occurrences in Fibonacci and Thue-Morse Words
An occurrence of a repeated substring $u$ in a string $S$ is called a net occurrence if extending the occurrence to the left or to the right decreases the number of occurrences to 1. The net frequency (NF) of a repeated substring $u$ in a…
The net frequency (NF) of a string, of length $m$, in a text, of length $n$, is the number of occurrences of the string in the text with unique left and right extensions. Recently, Guo et al. [CPM 2024] showed that NF is combinatorially…
A substring $u$ of a string $T$ is said to be a repeat if $u$ occurs at least twice in $T$. An occurrence $[i..j]$ of a repeat $u$ in $T$ is said to be a net occurrence if each of the substrings $aub = T[i-1..j+1]$, $au = T[i-1..j+1]$, and…
Knowing which strings in a massive text are significant -- that is, which strings are common and distinct from other strings -- is valuable for several applications, including text compression and tokenization. Frequency in itself is not…
Nishimoto and Tabei [CPM, 2021] proposed r-enum, an algorithm to enumerate various characteristic substrings, including maximal repeats, in a string $T$ of length $n$ in $O(r)$ words of compressed working space, where $r \le n$ is the…
In this paper we present two algorithms for the following problem: given a string and a rational $e > 1$, detect in the online fashion the earliest occurrence of a repetition of exponent $\ge e$ in the string. 1. The first algorithm…
Recent studies have explored the addition of virtual edges to word co-occurrence networks using word embeddings to enhance graph representations, particularly for short texts. While these enriched networks have demonstrated some success,…
In this work we explore the ability of the Google search engine to find results for random N-letter strings. These random strings, dense over the set of possible N-letter words, address the existence of typos, acronyms, and other words…
Word co-occurrence networks have been employed to analyze texts both in the practical and theoretical scenarios. Despite the relative success in several applications, traditional co-occurrence networks fail in establishing links between…
The Thue--Morse sequence is a prototypical automatic sequence found in diverse areas of mathematics, and in computer science. We study occurrences of factors $w$ within this sequence, more precisely, the sequence of gaps between consecutive…
Given a text $T$ of length $n$ and a pattern $P$ of length $m$, the string matching problem is a task to find all occurrences of $P$ in $T$. In this study, we propose an algorithm that solves this problem in $O((n + m)q)$ time considering…
Methods from statistical physics, such as those involving complex networks, have been increasingly used in quantitative analysis of linguistic phenomena. In this paper, we represented pieces of text with different levels of simplification…
The paper explores combinatorial properties of Fibonacci words and their generalizations within the framework of combinatorics on words. These infinite sequences, measures the diversity of subwords in Fibonacci words, showing non-decreasing…
Well-established automatic analyses of texts mainly consider frequencies of linguistic units, e.g. letters, words and bigrams, while methods based on co-occurrence networks consider the structure of texts regardless of the nodes label (i.e.…
We consider the number of occurrences of subwords (non-consecutive sub-sequences) in a given word. We first define the notion of subword entropy of a given word that measures the maximal number of occurrences among all possible subwords. We…
Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…
In this short note we present a comprehensive bibliography for the online exact string matching problem. The problem consists in finding all occurrences of a given pattern in a text. It is an extensively studied problem in computer science,…
Many words in documents recur very frequently but are essentially meaningless as they are used to join words together in a sentence. It is commonly understood that stop words do not contribute to the context or content of textual documents.…
This paper addresses the online exact string matching problem which consists in finding all occurrences of a given pattern p in a text t. It is an extensively studied problem in computer science, mainly due to its direct applications to…
With the increasing number of texts made available on the Internet, many applications have relied on text mining tools to tackle a diversity of problems. A relevant model to represent texts is the so-called word adjacency (co-occurrence)…