Related papers: The Inverse Lyndon Array: Definition, Properties, …
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…
Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…
The suffix array is arguably one of the most important data structures in sequence analysis and consequently there is a multitude of suffix sorting algorithms. However, to this date the GSACA algorithm introduced in 2015 is the only known…
In highly repetitive strings, like collections of genomes from the same species, distinct measures of repetition all grow sublinearly in the length of the text, and indexes targeted to such strings typically depend only on one of these…
Let $\widetilde{\alpha}$ be a length-$L$ cyclic sequence of characters from a size-$K$ alphabet $\mathcal{A}$ such that the number of occurrences of any length-$m$ string on $\mathcal{A}$ as a substring of $\widetilde{\alpha}$ is $\lfloor L…
Large Language Models are transformer neural networks which are trained to produce a probability distribution on the possible next words to given texts in a corpus, in such a way that the most likely word predicted is the actual word in the…
Longest common extension queries (often called longest common prefix queries) constitute a fundamental building block in multiple string algorithms, for example computing runs and approximate pattern matching. We show that a sequence of $q$…
Tasks that model the relation between pairs of tokens in a string are a vital part of understanding natural language. Such tasks, in general, require exhaustive pair-wise comparisons of tokens, thus having a quadratic runtime complexity in…
The class of input-output systems representable as Chen-Fliess series arises often in control theory. One well known drawback of this representation, however, is that the iterated integrals which appear in these series are algebraically…
Sequential word order is important when processing text. Currently, neural networks (NNs) address this by modeling word position using position embeddings. The problem is that position embeddings capture the position of individual words,…
We revisit the classic combinatorial pattern matching problem of finding a longest common subsequence (LCS). For strings $x$ and $y$ of length $n$, a textbook algorithm solves LCS in time $O(n^2)$, but although much effort has been spent,…
We prove several combinatorial properties of suffix arrays, including a characterization of suffix arrays through a bijection with a certain well-defined class of permutations. Our approach is based on the characterization of…
The circular dictionary matching problem is an extension of the classical dictionary matching problem where every string in the dictionary is interpreted as a circular string: after reading the last character of a string, we can move back…
We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…
We prove that longest common prefix (LCP) information can be stored in much less space than previously known. More precisely, we show that in the presence of the text and the suffix array, o(n) additional bits are sufficient to answer…
In this note, we establish the periodicity of chains of affine standard Lyndon words in all types and determine tight bounds on that periodicity, greatly generalizing the $A$-type results of arXiv:2305.16299. Our approach crucially utilizes…
The nature of the alignment with gaps corresponding to a longest common subsequence (LCS) of two independent iid random sequences drawn from a finite alphabet is investigated. It is shown that such an optimal alignment typically matches…
We show that the compressed suffix array and the compressed suffix tree of a string $T$ can be built in $O(n)$ deterministic time using $O(n\log\sigma)$ bits of space, where $n$ is the string length and $\sigma$ is the alphabet size.…
In the last decades, the necessity to process massive amounts of textual data fueled the development of compressed text indexes: data structures efficiently answering queries on a given text while occupying space proportional to the…
Searches for phrases and word sets in large text arrays by means of additional indexes are considered. Their use may reduce the query-processing time by an order of magnitude in comparison with standard inverted files.