Related papers: Algorithmic Information Theory and Foundations of …
We discuss views about whether the universe can be rationally comprehended, starting with Plato, then Leibniz, and then the views of some distinguished scientists of the previous century. Based on this, we defend the thesis that…
Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown that the parameters of a specific model…
John organized a state lottery and his wife won the main prize. You may feel that the event of her winning wasn't particularly random, but how would you argue that in a fair court of law? Traditional probability theory does not even have…
Link prediction in graphs is an important task in the fields of network science and machine learning. We investigate a flexible means of regularization for link prediction based on an approximation of the Kolmogorov complexity of graphs…
Shannon based his information theory on the notion of probability measures as it we developed by Kolmogorov. In this paper we study some fundamental problems in information theory based on expectation measures. In the theory of expectation…
I will survey some matters of relevance to a philosophical discussion of information, taking into account developments in algorithmic information theory (AIT). I will propose that meaning is deep in the sense of Bennett's logical depth, and…
In computability theory and computable analysis, finite programs can compute infinite objects. Presenting a computable object via any program for it, provides at least as much information as presenting the object itself, written on an…
Randomness extraction is the process of constructing a source of randomness of high quality from one or several sources of randomness of lower quality. The problem can be modeled using probability distributions and min-entropy to measure…
The normalized information distance is a universal distance measure for objects of all kinds. It is based on Kolmogorov complexity and thus uncomputable, but there are ways to utilize it. First, compression algorithms can be used to…
This is a 1971 dissertation. Only its extended abstract was published at the time. While some results appeared in other publications, a number of details remained unpublished and may still have relevance.
For the most of my life, I have earned my living as a computer vision professional busy with image processing tasks and problems. In the computer vision community there is a widespread belief that artificial vision systems faithfully…
The probabilistic prediction of quantum theory is mystery. I solved the mystery by a geometrical interpretation of a wave function. This suggests the unification between quantum theory and the theory of relativity. This suggests Many-Worlds…
In the last decades, several objects such as grammars, economical agents, laws of physics... have been defined as algorithms. In particular, after Brouwer, Heyting, and Kolomogorov, mathematical proofs have been defined as algorithms. In…
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…
In this paper we prove estimates on the behaviour of the Kolmogorov-Sinai entropy relative to a partition for randomly perturbed dynamical systems. Our estimates use the entropy for the unperturbed system and are obtained using the notion…
Increasing amounts of available data have led to a heightened need for representing large-scale probabilistic knowledge bases. One approach is to use a probabilistic database, a model with strong assumptions that allow for efficiently…
Forecasting techniques for assessing the power of future experiments to discriminate between theories or discover new laws of nature are of great interest in many areas of science. In this paper, we introduce a Bayesian forecasting method…
Historically, probability theory has been studied for a long time, and Kolmogorov, Levy Ito Kiyoshi, and others have mathematically developed modern probability in conjunction with measurement theory. On the other hand, commutative algebra…
Although procedural generation is popular among game developers, academic research on the topic has primarily focused on new applications, with some research into empirical analysis. In this paper we relate theoretical work in information…
While Kolmogorov complexity is the accepted absolute measure of information content in an individual finite object, a similarly absolute notion is needed for the information distance between two individual objects, for example, two…