Related papers: Around Kolmogorov complexity: basic notions and re…
The Kolmogorov complexity of a string is the length of its shortest description. We define a second quantised Kolmogorov complexity where the length of a description is defined to be the average length of its superposition. We discuss this…
This paper contains some results of An.A.Muchnik (1958-2007) reported in his talks at the Kolmogorov seminar (Moscow State Lomonosov University, Math. Department, Logic and Algorithms theory division, March 11, 2003 and April 8, 2003) but…
Solomonoff unified Occam's razor and Epicurus' principle of multiple explanations to one elegant, formal, universal theory of inductive inference, which initiated the field of algorithmic information theory. His central result is that the…
An a priori semimeasure (also known as "algorithmic probability" or "the Solomonoff prior" in the context of inductive inference) is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the…
This article is a brief guide to the field of algorithmic information theory (AIT), its underlying philosophy, and the most important concepts. AIT arises by mixing information theory and computation theory to obtain an objective and…
Research into active networking has provided the incentive to re-visit what has traditionally been classified as distinct properties and characteristics of information transfer such as protocol versus service; at a more fundamental level…
The ability to precisely quantify similarity between various entities has been a fundamental complication in various problem spaces specifically in the classification of cellular images. Contemporary similarity measures applied in the…
In this paper, we present a theoretical effort to connect the theory of program size to psychology by implementing a concrete language of thought with Turing-computable Kolmogorov complexity (LT^2C^2) satisfying the following requirements:…
In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have…
This work presents a study of Kolmogorov complexity for general quantum states from the perspective of deterministic-control quantum Turing Machines (dcq-TM). We extend the dcq-TM model to incorporate mixed state inputs and outputs, and…
Symmetry of information states that $C(x) + C(y|x) = C(x,y) + O(\log C(x))$. We show that a similar relation for online Kolmogorov complexity does not hold. Let the even (online Kolmogorov) complexity of an n-bitstring $x_1x_2... x_n$ be…
Drawing on various notions from theoretical computer science, we present a novel numerical approach, motivated by the notion of algorithmic probability, to the problem of approximating the Kolmogorov-Chaitin complexity of short strings. The…
We reconsider some classical natural semantics of integers (namely iterators of functions, cardinals of sets, index of equivalence relations), in the perspective of Kolmogorov complexity. To each such semantics one can attach a simple…
The Coding Theorem of L.A. Levin connects unconditional prefix Kolmogorov complexity with the discrete universal distribution. There are conditional versions referred to in several publications but as yet there exist no written proofs in…
The probability distribution P from which the history of our universe is sampled represents a theory of everything or TOE. We assume P is formally describable. Since most (uncountably many) distributions are not, this imposes a strong…
We reminisce and discuss applications of algorithmic probability to a wide range of problems in artificial intelligence, philosophy and technological society. We propose that Solomonoff has effectively axiomatized the field of artificial…
The crucial but very confidential fact is brought into evidence that, as Kolmogorov himself repeatedly claimed, the mathematical theory of probabilities cannot be applied to physical, factual probabilistic situations because the factual…
Algorithmic information theory translates statements about classes of objects into statements about individual objects; it defines individual random sequences, effective Hausdorff dimension of individual points, amount of information in…
The Kolmogorov complexity of x, denoted C(x), is the length of the shortest program that generates x. For such a simple definition, Kolmogorov complexity has a rich and deep theory, as well as applications to a wide variety of topics…
Markov random fields area popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for…