相关论文: String Comparison in $V$-Order: New Lexicographic …

The problem of storing a set of strings --- a string dictionary --- in compact form appears naturally in many cases. While classically it has represented a small part of the whole data to be processed (e.g., for Natural Language processing…

This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one…

The suffix array is a fundamental data structure for many applications that involve string searching and data compression. Designing time/space-efficient suffix array construction algorithms has attracted significant attention and…

There is inherent information captured in the order in which we write words in a list. The orderings of binomials --- lists of two words separated by `and' or `or' --- has been studied for more than a century. These binomials are common…

Classification is a common AI problem, and vector search is a typical solution. This transforms a given body of text into a numerical representation, known as an embedding, and modern improvements to vector search focus on optimising speed…

A string is said to be closed if its length is one, or if it has a non-empty factor that occurs both as a prefix and as a suffix of the string, but does not occur elsewhere. The notion of closed words was introduced by [Fici, WORDS 2011].…

Sorting an array is a fundamental routine in machine learning, one that is used to compute rank-based statistics, cumulative distribution functions (CDFs), quantiles, or to select closest neighbors and labels. The sorting function is…

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…

Most popular word embedding techniques involve implicit or explicit factorization of a word co-occurrence based matrix into low rank factors. In this paper, we aim to generalize this trend by using numerical methods to factor higher-order…

We consider the set of finite random words $\mathcal A^\star$, with independent letters drawn from a finite or infinite totally ordered alphabet according to a general probability distribution. On a specific subset of $\mathcal A^\star$,…

In this paper, we explore applications of combinatorics on words across various domains, including data compression, error detection, cryptographic protocols, and pseudorandom number generation. The examination of the theoretical…

There has been surprisingly little work on algorithms for sorting strings on distributed-memory parallel machines. We develop efficient algorithms for this problem based on the multi-way merging principle. These algorithms inspect only…

In this work, we present the \texttt{LLM ORDER BY} semantic operator as a logical abstraction and conduct a systematic study of its physical implementations. First, we propose several improvements to existing semantic sorting algorithms and…

The world's languages exhibit certain so-called typological or implicational universals; for example, Subject-Object-Verb (SOV) languages typically use postpositions. Explaining the source of such biases is a key goal of linguistics. We…

String matching is the problem of finding all the substrings of a text which match a given pattern. It is one of the most investigated problems in computer science, mainly due to its very diverse applications in several fields. Recently,…

Online string matching is a computational problem involving the search for patterns or substrings in a large text dataset, with the pattern and text being processed sequentially, without prior access to the entire text. Its relevance stems…

We show that the existence of string order in a given quantum state is intimately related to the presence of a local symmetry by proving that both concepts are equivalent within the framework of finitely correlated states. Once this…

The \emph{generalized sorting problem} is a restricted version of standard comparison sorting where we wish to sort $n$ elements but only a subset of pairs are allowed to be compared. Formally, there is some known graph $G = (V, E)$ on the…

In his 1987 paper entitled "Generalized String Matching", Abrahamson introduced {\em pattern matching with character classes} and provided the first efficient algorithm to solve it. The best known solution to date is due to Linhart and…

Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…