Related papers: Sorting and generating reduced words
Sorting is a foundational problem in computer science that is typically employed on sequences or total orders. More recently, a more general form of sorting on partially ordered sets (or posets), where some pairs of elements are…
Let $(W,S)$ be an arbitrary Coxeter system. For each word $\omega$ in the generators we define a partial order--called the {\sf $\omega$-sorting order}--on the set of group elements $W_\omega\subseteq W$ that occur as subwords of $\omega$.…
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors…
We discuss the theory of certain partially ordered sets that capture the structure of commutation classes of words in monoids. As a first application, it follows readily that counting words in commutation classes is #P-complete. We then…
We study the following rearrangement problem: Given $n$ words, rearrange and concatenate them so that the obtained string is lexicographically smallest (or largest, respectively). We show that this problem reduces to sorting the given words…
The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…
The article focuses on word (or string) attractors, which are sets of positions related to the text compression efficiency of the underlying word. The article presents two combinatorial algorithms based on Suffix automata or Directed…
We generalize a well-known algorithm for the generation of all subsets of a set in lexicographic order with respect to the sets as lists of elements (subset-lex order). We obtain algorithms for various combinatorial objects such as the…
We describe an implementation of a genetic algorithm on partially commutative groups and apply it to the double coset search problem on a subclass of groups. This transforms a combinatorial group theory problem to a problem of combinatorial…
Word sense disambiguation algorithms, with few exceptions, have made use of only one lexical knowledge source. We describe a system which performs unrestricted word sense disambiguation (on all content words in free text) by combining…
A family of partial orders in the free monoid of words, induced from a partial order in alphabet, is presented. The induced orders generalize the chronological posets that have been defined for the two-letter alphabet only, and the…
Most natural languages have a predominant or fixed word order. For example in English the word order is usually Subject-Verb-Object. This work attempts to explain this phenomenon as well as other typological findings regarding word order…
We extend the left-to-right Lyndon factorisation of a word to the left Lyndon tree construction of a Lyndon word. It yields an algorithm to sort the prefixes of a Lyndon word according to the infinite ordering defined by Dolce et al.…
We introduce an algorithm for the uniform generation of infinite traces, i.e., infinite words up to commutation of some letters. The algorithm outputs on-the-fly approximations of a theoretical infinite trace, the latter being distributed…
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…
We explore the fundamental problem of sorting through the lens of learning-augmented algorithms, where algorithms can leverage possibly erroneous predictions to improve their efficiency. We consider two different settings: In the first…
This paper presents a machine learning approach to discourse planning in natural language generation. More specifically, we address the problem of learning the most natural ordering of facts in discourse plans for a specific domain. We…
Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study a more general setting, in which some pairs of objects are incomparable. This generalization is relevant…
We continue to consider the ordered lexicographic sequence, which is constructed according to the formal characteristics of a series of natural numbers. For analysis, we selected balanced parentheses with zeros, Motzkin words. As you know,…
Sentence ordering is the task of arranging the sentences of a given text in the correct order. Recent work using deep neural networks for this task has framed it as a sequence prediction problem. In this paper, we propose a new framing of…