Related papers: Increasing Consecutive Patterns in Words
We give an algorithm to enumerate the results on trees of monadic second-order (MSO) queries represented by nondeterministic tree automata. After linear time preprocessing (in the input tree), we can enumerate answers with linear delay (in…
Serial pattern mining consists in extracting the frequent sequential patterns from a unique sequence of itemsets. This paper explores the ability of a declarative language, such as Answer Set Programming (ASP), to solve this issue…
A subsequence of a word $w$ is a word $u$ such that $u = w[i_1] w[i_2] , \dots w[i_{|u|}]$, for some set of indices $1 \leq i_1 < i_2 < \dots < i_k \leq |w|$. A word $w$ is $k$-subsequence universal over an alphabet $\Sigma$ if every word…
In many data analysis pipelines, a basic and time-consuming process is to produce join results and feed them into downstream tasks. Numerous enumeration algorithms have been developed for this purpose. To be a statistically meaningful…
Let $w$ be an infinite word on an alphabet $A$. We denote by $(n_i)_{i \geq 1}$ the increasing sequence (assumed to be infinite) of all lengths of palindrome prefixes of $w$. In this text, we give an explicit construction of all words $w$…
We study the longest increasing subsequence problem for random permutations avoiding the pattern $312$ and another pattern $\tau$ under the uniform probability distribution. We determine the exact and asymptotic formulas for the average…
This paper explores linear methods for combining several word embedding models into an ensemble. We construct the combined models using an iterative method based on either ordinary least squares regression or the solution to the orthogonal…
A statistical model for segmentation and word discovery in continuous speech is presented. An incremental unsupervised learning algorithm to infer word boundaries based on this model is described. Results of empirical tests showing that the…
Recent work has explored methods for learning continuous vector space word representations reflecting the underlying semantics of words. Simple vector space arithmetic using cosine distances has been shown to capture certain types of…
Let $w$ be a finite word over the alphabet $\{0,1\}$. For any natural number $n$, let $s_w(n)$ denote the number of occurrence of $w$ in the binary expansion of $n$ as a scattered subsequence. We study the behavior of the partial sum…
The sequence of partial sums of Fibonacci numbers, beginning with $2$, $4$, $7$, $12$, $20$, $33,\dots$, has several combinatorial interpretations (OEIS A000071). For instance, the $n$-th term in this sequence is the number of length-$n$…
The deviation of the observed frequency of a word $w$ from its expected frequency in a given sequence $x$ is used to determine whether or not the word is avoided. This concept is particularly useful in DNA linguistic analysis. The value of…
Statistics about n-grams (i.e., sequences of contiguous words or other tokens in text documents or other string data) are an important building block in information retrieval and natural language processing. In this work, we study how…
We present a new approach to encourage neural machine translation to satisfy lexical constraints. Our method acts at the training step and thereby avoiding the introduction of any extra computational overhead at inference step. The proposed…
Given a pattern x of length m and a text y of length n, both over an ordered alphabet, the order-preserving pattern matching problem consists in finding all substrings of the text with the same relative order as the pattern. It is an…
For a fixed integer $m\ge 1$, let $\mathcal{A}_n^{(m)}$ be the set of permutations $\pi\in S_n$ that avoid the pattern $132$ and satisfy the adjacency bound $|\pi_{i+1}-\pi_i|\le m$ for all $i$. Here, a pattern $132$ means three indices…
We propose a sentence-incremental neural coreference resolution system which incrementally builds clusters after marking mention boundaries in a shift-reduce method. The system is aimed at bridging two recent approaches at coreference…
A \Def{composition} of a positive integer $n$ is a $k$-tuple $(\l_1, \l_2, \dots, \l_k) \in \Z_{> 0}^k$ such that $n = \l_1 + \l_2 + \dots + \l_k$. Our goal is to enumerate those compositions whose parts $\l_1, \l_2, \dots, \l_k$ avoid a…
Inversion sequences are integer sequences $(\sigma_1, \dots, \sigma_n)$ such that $0 \leqslant \sigma_i < i$ for all $1 \leqslant i \leqslant n$. The study of pattern-avoiding inversion sequences began in two independent articles by…
It is shown that for finding rational approximates to m'th root of any integer to any accuracy one only needs the ability to count and to distinguish between m different classes of objects. To every integer N can be associated a…