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We present a general approach to the problem of determining the asymptotic order of the variance of the optimal score between two independent random sequences defined over an arbitrary finite alphabet. Our general approach is based on…
This note is an attempt to unconditionally prove the existence of weak one way functions (OWF). Starting from a provably intractable decision problem $L_D$ (whose existence is nonconstructively assured from the well-known discrete…
We present new results on the relation between purely symbolic context-free parsing strategies and their probabilistic counter-parts. Such parsing strategies are seen as constructions of push-down devices from grammars. We show that…
We consider the problem of reconstructing a function given its values on a set of points with finite density. We prove that with probability one, the values of an almost periodic function on a random array of points (with finite density)…
If p is the probability of a letter of a memoryless source, the length l of the corresponding binary Huffman codeword can be very different from the value -log p. We show that, nevertheless, for a typical letter, l is approximately equal to…
The output of Large Language Models (LLMs) are a function of the internal model's parameters and the input provided into the context window. The hypothesis presented here is that under a greedy sampling strategy the variance in the LLM's…
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…
A common technique to speed up shortest path queries in graphs is to use a bidirectional search, i.e., performing a forward search from the start and a backward search from the destination until a common vertex on a shortest path is found.…
A reformulation of the path length of binary search trees is given in terms of permutations, allowing to extend the definition to the instance of words, where the letters are obtained by independent geometric random variables (with…
The rate of occurrence of words is not uniform but varies from document to document. Despite this observation, parameters for conventional n-gram language models are usually derived using the assumption of a constant word rate. In this…
The analysis of randomized search heuristics on classes of functions is fundamental for the understanding of the underlying stochastic process and the development of suitable proof techniques. Recently, remarkable progress has been made in…
Tree search is a fundamental tool for planning, as many sequential decision-making problems can be framed as searching over tree-structured spaces. We propose an uncertainty-guided tree search algorithm for settings where the reward…
By periodically returning a search process to a known or random state, random resetting possesses the potential to unveil new trajectories, sidestep potential obstacles, and consequently enhance the efficiency of locating desired targets.…
The main object of investigation in this paper is a very general regression model in optional setting - when an observed process is an optional semimartingale depending on an unknown parameter. It is well-known that statistical data may…
In this paper, we explore and evaluate the use of ranking-based objective functions for learning simultaneously a word string and a word image encoder. We consider retrieval frameworks in which the user expects a retrieval list ranked…
We obtain the posterior distribution of a random process conditioned on observing the empirical frequencies of a finite sample path. We find under a rather broad assumption on the "dependence structure" of the process, {\em c.f.}…
Word maps provide a wealth of information about finite groups. We examine the connection between the probability distribution induced by a word map and the underlying structure of a finite group. We show that a finite group is nilpotent if…
In the paper I study properties of random polynomials with respect to a general system of functions. Some lower bounds for the mathematical expectation of the uniform and recently introduced integral-uniform norms of random polynomials are…
Strings in the real world are often encoded with some level of uncertainty. In the character-level uncertainty model, an uncertain string $X$ of length $n$ on an alphabet $\Sigma$ is a sequence of $n$ probability distributions over…
We present a general approach to the problem of determining tight asymptotic lower bounds for generalized central moments of the optimal alignment score of two independent sequences of i.i.d. random variables. At first, these are obtained…