Related papers: Possibilities and impossibilities in Kolmogorov co…
Topological measurements are increasingly being accepted as an important tool for quantifying complex structures. In many applications, these structures can be expressed as nodal domains of real-valued functions and are obtained only…
The article is devoted to the resampling approach application to the reliability problems. This approach to reliability problems was first proposed by Ivnitsky (1967). Resampling is intensive statistical computer method, which is…
The ability to find short representations, i.e. to compress data, is crucial for many intelligent systems. We present a theory of incremental compression showing that arbitrary data strings, that can be described by a set of features, can…
We investigate the problem of generating common randomness (CR) from finite compound sources aided by unidirectional communication over rate-limited perfect channels. The two communicating parties, often referred to as terminals, observe…
Large language models (LLMs) are susceptible to memorizing training data, raising concerns about the potential extraction of sensitive information at generation time. Discoverable extraction is the most common method for measuring this…
An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the signal, but also on its structure. This paper is about understanding this phenomenon,…
Neural networks are becoming a popular tool for solving many real-world problems such as object recognition and machine translation, thanks to its exceptional performance as an end-to-end solution. However, neural networks are complex…
We provide a unified method for constructing explicit distributions which are difficult for restricted models of computation to generate. Our constructions are based on a new notion of robust extractors, which are extractors that remain…
Information-efficient approaches for extracting randomness from imperfect sources have been extensively studied, but simpler and faster ones are required in the high-speed applications of random number generation. In this paper, we focus on…
We present a new approach to formal language theory using Kolmogorov complexity. The main results presented here are an alternative for pumping lemma(s), a new characterization for regular languages, and a new method to separate…
We examine the extent to which random samplings from the values of a random set, determine the distribution of the random set itself. We also comment on how, given the statistics of the sampling, to detect the distribution. Several methods…
In many situations, sample data is obtained from a noisy or imperfect source. In order to address such corruptions, this paper introduces the concept of a sampling corrector. Such algorithms use structure that the distribution is purported…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
Computer science theory provides many different measures of complexity of a system including Kolmogorov complexity, logical depth, computational depth, and Levin complexity. However, these measures are all defined only for deterministic…
The use of algorithmic information theory (Kolmogorov complexity theory) to explain the relation between mathematical probability theory and `real world' is discussed.
Invention involves combination, or more precisely, ratios of composition. According to Thomas Edison, "Genius is one percent inspiration and 99 percent perspiration" is an example. In many situations, researchers and inventors already have…
Randomness is viewed through an analogy between a physical quantity, density of gas, and a mathematical construct -- probability density. Boltzmann's deduction of equilibrium distribution of ideal gas placed in an external potential field…
Although information content is invariant up to an additive constant, the range of possible additive constants applicable to programming languages is so large that in practice it plays a major role in the actual evaluation of K(s), the…
The rapid advancement of large language model (LLM) technology has led to diverse applications, many of which inherently require randomness, such as stochastic decision-making, gaming, scheduling, AI agents, and cryptography-related tasks.…
Data generated in the fields of science, technology, business and in many other fields of research are increasing in an exponential rate. The way to extract knowledge from a huge set of data is a challenging task. This paper aims to propose…