Related papers: Sorting and generating reduced words
The lattice of partitions of a set and its d-divisible generalization have been much studied for their combinatorial, topological, and representation-theoretic properties. An ordered set partition is a set partition where the subsets are…
We present an algorithm to generate positive braids of a given length as words in Artin generators with a uniform probability. The complexity of this algorithm is polynomial in the number of strands and in the length of the generated…
We consider a discrete-time Markov chain, called fragmentation process, that describes a specific way of successively removing objects from a linear arrangement. The process arises in population genetics and describes the ancestry of the…
Stemming is the process of reducing related words to a standard form by removing affixes from them. Existing algorithms vary with respect to their complexity, configurability, handling of unknown words, and ability to avoid under- and…
One approach for reducing run time and improving efficiency of machine learning is to reduce the convergence rate of the optimization algorithm used. Shuffling is an algorithm technique that is widely used in machine learning, but it only…
We compare the performance of different clustering algorithms applied to the task of unsupervised text categorization. We consider agglomerative clustering algorithms, principal direction divisive partitioning and (for the first time)…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
Every semigroup which is a finite disjoint union of copies of the free mono- genic semigroup (natural numbers under addition) has soluble word prob- lem and soluble membership problem. Efficient algorithms are given for both problems.
Various grammar compression algorithms have been proposed in the last decade. A grammar compression is a restricted CFG deriving the string deterministically. An efficient grammar compression develops a smaller CFG by finding duplicated…
A generalized lexicographic order on words is a lexicographic order where the total order of the alphabet depends on the position of the comparison. A generalized Lyndon word is a finite word which is strictly smallest among its class of…
Word embeddings allow natural language processing systems to share statistical information across related words. These embeddings are typically based on distributional statistics, making it difficult for them to generalize to rare or unseen…
A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive…
In the present paper we consider biologically motivated reduction operations on double occurrence words. Then we define the nesting index of a double occurrence word to be the least number of reduction operations it takes for a word to be…
We survey several methods of generating large random lambda-terms, focusing on their closed and simply-typed variants. We discuss methods of exact- and approximate-size generation, as well as methods of achieving size-uniform and…
Algorithm design is a laborious process and often requires many iterations of ideation and validation. In this paper, we explore automating algorithm design and present a method to learn an optimization algorithm, which we believe to be the…
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…
Let P be a poset and let P* be the set of all finite length words over P. Generalized subword order is the partial order on P* obtained by letting u \leq w if and only if there is a subword u' of w having the same length as u such that each…
Our goal in this paper is to automatically extract a set of decision rules (rule set) that best explains a classification data set. First, a large set of decision rules is extracted from a set of decision trees trained on the data set. The…
The theorem of factorisation forests shows the existence of nested factorisations -- a la Ramsey -- for finite words. This theorem has important applications in semigroup theory, and beyond. The purpose of this paper is to illustrate the…
As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type…