相关论文: String Attractors and Combinatorics on Words

A reduced word of a permutation $w$ is a minimal length expression of $w$ as a product of simple transpositions. We examine the computational complexity, formulas and (randomized) algorithms for their enumeration. In particular, we prove…

An injective word over a finite alphabet $V$ is a sequence $w=v_1v_2\cdots v_t$ of distinct elements of $V$. The set $\mathrm{inj}(V)$ of injective words on $V$ is partially ordered by inclusion. A complex of injective words is the order…

A finite deterministic (semi)automaton $\mathcal{A} =(Q,\Sigma,\delta)$ is $k$-compressible if there is some word $w\in \Sigma^+$ such that the image of its state set $Q$ under the natural action of $w$ is reduced by at least $k$ states.…

Word embeddings are representations of individual words of a text document in a vector space and they are often use- ful for performing natural language pro- cessing tasks. Current state of the art al- gorithms for learning word embeddings…

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…

Minimizers sampling is one of the most widely-used mechanisms for sampling strings [Roberts et al., Bioinformatics 2004]. Let $S=S[1]\ldots S[n]$ be a string over a totally ordered alphabet $\Sigma$. Further let $w\geq 2$ and $k\geq 1$ be…

A reconstruction problem of words from scattered factors asks for the minimal information, like multisets of scattered factors of a given length or the number of occurrences of scattered factors from a given set, necessary to uniquely…

We survey known results and open problems in abelian combinatorics on words. Abelian combinatorics on words is the extension to the commutative setting of the classical theory of combinatorics on words. The extension is based on…

The combinatorics of reduced words and commutation classes plays an important role in geometric representation theory. A string polytope is a lattice polytope associated to each reduced word of the longest element $w_0$ in the symmetric…

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…

We present a new data structure called the \emph{Compressed Random Access Memory} (CRAM) that can store a dynamic string $T$ of characters, e.g., representing the memory of a computer, in compressed form while achieving asymptotically…

Recently the Fibonacci word $W$ on an infinite alphabet was introduced by [Zhang et al., Electronic J. Combinatorics 24-2 (2017) #P2.52] as a fixed point of the morphism $\phi: (2i) \mapsto (2i)(2i+ 1),\ (2i+ 1) \mapsto (2i+ 2)$ over all $i…

Word complexity is defined in a number of different ways. Psycholinguistic, morphological and lexical proxies are often used. Human ratings are also used. The problem here is that these proxies do not measure complexity directly, and human…

Our current best guess for a unified theory of gravitation and quantum field theory (string theory) generically predicts a set of requirements for a consistently quantized theory, the Swampland criteria. Refined versions of these criteria…

In recent years, word embeddings have been surprisingly effective at capturing intuitive characteristics of the words they represent. These vectors achieve the best results when training corpora are extremely large, sometimes billions of…

A \emph{square} is a word of the form $uu$, where $u$ is a nonempty finite word. Given a finite word $w$ of length $n$, let $[w]$ denote the corresponding \emph{circular word}, i.e., the set of all cyclic rotations of $w$. We study the…

The dictionary matching problem is to locate occurrences of any pattern among a set of patterns in a given text. Massive data sets abound and at the same time, there are many settings in which working space is extremely limited. We…

Conventional word embeddings represent words with fixed vectors, which are usually trained based on co-occurrence patterns among words. In doing so, however, the power of such representations is limited, where the same word might be…

Given a set of pattern strings $\mathcal{P}=\{P_1, P_2,\ldots P_k\}$ and a text string $S$, the classic dictionary matching problem is to report all occurrences of each pattern in $S$. We study the dictionary problem in the compressed…

Word embeddings have become the basic building blocks for several natural language processing and information retrieval tasks. Pre-trained word embeddings are used in several downstream applications as well as for constructing…