Related papers: Reduction ratio of the IS-algorithm: worst and ran…
An occurrence of a repeated substring $u$ in a string $S$ is called a net occurrence if extending the occurrence to the left or to the right decreases the number of occurrences to 1. The net frequency (NF) of a repeated substring $u$ in a…
Combining the representations of the words that make up a sentence into a cohesive whole is difficult, since it needs to account for the order of words, and to establish how the words present relate to each other. The solution we propose…
The Subset Sum Problem is a fundamental NP-complete problem in cryptography and combinatorial optimization, with many real-world applications. The Random Subset Sum Problem (RSSP) is a more applicable version of subset sum, where numbers…
We consider the problem of finding repetitive structures and inherent patterns in a given string $\s{s}$ of length $n$ over a finite totally ordered alphabet. A border $\s{u}$ of a string $\s{s}$ is both a prefix and a suffix of $\s{s}$…
The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…
Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…
Inverse Probability Weighting (IPW) is widely used in empirical work in economics and other disciplines. As Gaussian approximations perform poorly in the presence of "small denominators," trimming is routinely employed as a regularization…
The theory of reinforcement learning has focused on two fundamental problems: achieving low regret, and identifying $\epsilon$-optimal policies. While a simple reduction allows one to apply a low-regret algorithm to obtain an…
A string is said to be closed if its length is one, or if it has a non-empty factor that occurs both as a prefix and as a suffix of the string, but does not occur elsewhere. The notion of closed words was introduced by [Fici, WORDS 2011].…
Retrieval-Augmented Generation (RAG) has recently emerged as a method to extend beyond the pre-trained knowledge of Large Language Models by augmenting the original prompt with relevant passages or documents retrieved by an Information…
We construct fast algorithms for evaluating transforms associated with families of functions which satisfy recurrence relations. These include algorithms both for computing the coefficients in linear combinations of the functions, given the…
In the problem of online unweighted interval selection, the objective is to maximize the number of non-conflicting intervals accepted by the algorithm. In the conventional online model of irrevocable decisions, there is an Omega(n) lower…
Importance sampling (IS) is a common reweighting strategy for off-policy prediction in reinforcement learning. While it is consistent and unbiased, it can result in high variance updates to the weights for the value function. In this work,…
The problem of word sense disambiguation (WSD) is considered in the article. Given a set of synonyms (synsets) and sentences with these synonyms. It is necessary to select the meaning of the word in the sentence automatically. 1285…
In real-time speech recognition applications, the latency is an important issue. We have developed a character-level incremental speech recognition (ISR) system that responds quickly even during the speech, where the hypotheses are…
In this paper, we explore worst-case solutions for the problems of single and multiple matching on strings in the word RAM model with word length w. In the first problem, we have to build a data structure based on a pattern p of length m…
Estimating the expectations of functionals applied to sums of random variables (RVs) is a well-known problem encountered in many challenging applications. Generally, closed-form expressions of these quantities are out of reach. A naive…
We study the problems of finding a shortest synchronizing word and its length for a given prefix code. This is done in two different settings: when the code is defined by an arbitrary decoder recognizing its star and when the code is…
We study a variation of the classical Shortest Common Superstring (SCS) problem in which a shortest superstring of a finite set of strings $S$ is sought containing as a factor every string of $S$ or its reversal. We call this problem…
Polynomial time reductions between problems have long been used to delineate problem classes. Simulation reductions also exist, where an oracle for simulation from some probability distribution can be employed together with an oracle for…