Kolmogorov complexity, which is also called algorithmic (descriptive) complexity is an object, such as a piece of text, to measure the computational resources needed, which are mostly the length of the shortest binary program to specify an object. Strings whose Kolmogorov complexity is small relative to the string’s size are not considered to be complex and easy to use a short program to specif...

We compare the elementary theories of Shannon information and Kolmogorov complexity, the extent to which they have a common purpose, and where they are fundamentally different. We discuss and relate the basic notions of both theories: Shannon entropy versus Kolmogorov complexity, the relation of both to universal coding, Shannon mutual information versus Kolmogorov (‘algorithmic’) mutual inform...

Kolmogorov complexity is a measure of the information contained in a binary string. We investigate here the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state ...

In this article, we analyze the fundamental global and local symmetries involved in action for free relativistic point particle. Moreover, identify a hidden symmetry, whose explicit consideration factorization utilizing of Fujikawa prescription, leads to construction propagators that satisfy Chapman-Kolmogorov identity. By means detailed topological analysis, find three different (orthochronous...

Identification of programs for computable functions from their graphs by algorithmic devices is a well studied problem in learning theory. Freivalds and Chen consider identification of ‘minimal’ and ‘nearly minimal’ programs for functions from their graphs. Freivalds showed that there exists a Gödel numbering in which only finite classes of functions can be identified using minimal programs. To...

A novel topological and computational method for ‘motion’ is described. Motion is constrained by inequalities in terms of Kolmogorov Complexity. Causality is obtained as the output of a high-pass filter, passing through only high values of Kolmogorov Complexity. Motion under the electromagnetic field described with immediate relationship with G2 Holonomy group and its corresponding dense free 2...

Several researchers, including M. Gell-Mann, argue that the notion of Kolmogorov complexity, developed in the algorithmic information theory, is useful in physics (i.e., in the description of the physical world). Their arguments are rather convincing, but there seems to be a gap between traditional physical equations and Kolmogorov complexity: namely, it is not clear how the standard equations ...