Related papers: Gray code orders for $q$-ary words avoiding a give…
Finding an Andrews--Gordon type generating function identity for a linked partition ideal is difficult in most cases. In this paper, we will handle this problem in the setting of graph theory. With the generating function of directed graphs…
Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes,…
Recently Kubica et al. (Inf. Process. Let., 2013) and Kim et al. (submitted to Theor. Comp. Sci.) introduced order-preserving pattern matching. In this problem we are looking for consecutive substrings of the text that have the same "shape"…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
As a generalization of cyclic codes, quasi-cyclic (QC) codes contain many good linear codes. But quasi-cyclic codes studied so far are mainly limited to one generator (1-generator) QC codes. In this correspondence, 2-generator and…
Existing works have studied the impacts of the order of words within natural text. They usually analyze it by destroying the original order of words to create a scrambled sequence, and then comparing the models' performance between the…
A generate and test algorithm is described which parses a surface form into one or more lexical entries using linearly ordered phonological rules. This algorithm avoids the exponential expansion of search space which a naive parsing…
We present an encoding and decoding scheme for constant weight sequences, that is, given an information sequence, the construction results in a sequence of specific weight within a certain range. The scheme uses a prefix design that is…
Universal cycles are generalizations of de Bruijn cycles and Gray codes that were introduced originally by Chung, Diaconis, and Graham in 1990. They have been developed by many authors since, for various combinatorial objects such as…
It is natural for probabilistic programs to use conditionals to express alternative substructures in models, and loops (recursion) to express repeated substructures in models. Thus, probabilistic programs with conditionals and recursion…
Granular operator spaces and variants had been introduced and used in theoretical investigations on the foundations of general rough sets by the present author over the last few years. In this research, higher order versions of these are…
Over the recent years, the theory of rewriting has been used and extended in order to provide systematic techniques to show coherence results for strict higher categories. Here, we investigate a further generalization to Gray categories,…
In this paper we propose an algorithm to generate binary words with no more 0's than 1's having a fixed number of 1's and avoiding the pattern $(10)^j1$ for any fixed $j \geq 1$. We will prove that this generation is exhaustive, that is,…
Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain…
For any integer $n\geq 1$ a middle levels Gray code is a cyclic listing of all bitstrings of length $2n+1$ that have either $n$ or $n+1$ entries equal to 1 such that any two consecutive bitstrings in the list differ in exactly one bit. The…
Question Generation (QG) aims to automate the task of composing questions for a passage with a set of chosen answers found within the passage. In recent years, the introduction of neural generation models has resulted in substantial…
Generative sequence models have shown strong results in recommendation. Applying them to search ranking is more challenging. Search behavior is inherently query-driven. Each query switch introduces a sharp topic shift in the user's…
The most well-known Gray code of permutations is plain changes. It was discovered in the 1600s by bell-ringers who wished to order the permutations of [n] by swaps (e.g., 123, 132, 312, 321, 231, 213 for n = 3). In other words, plain…
We say that a word $w$ on a totally ordered alphabet avoids the word $v$ if there are no subsequences in $w$ order-equivalent to $v$. In this paper we suggest a new approach to the enumeration of words on at most $k$ letters avoiding a…
We engineer an algorithm to solve the approximate dictionary matching problem. Given a list of words $\mathcal{W}$, maximum distance $d$ fixed at preprocessing time and a query word $q$, we would like to retrieve all words from…