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 ...

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...

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. To address certain problems in minimal identification for Gödel numberings, Freivalds later considered minimal identification in Kolmogorov...

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 ...

We prove a Kolmogorov complexity variant of the birthday paradox. Sufficiently large random subsets strings are guaranteed to have two members x and y with low K(x/y). To this, we first show that minimum conditional between finite sets is very if they not exotic. Exotic high mutual information halting sequence.

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 representation of integers that we suitably effectivize in order to develop an associated Kolmogorov theory. Such effectivizations are particular instances of a ge...

Methods for discerning and measuring Kolmogorov Complexity are discussed and their relationships explored. A computationally efficient method of using Lempel Ziv 78 Universal compression algorithm to estimate complexity is introduced. 1 Abstract—Methods for discerning and measuring Kolmogorov Complexity are discussed and their relationships explored. A computationally efficient method of using ...

The utility of a Kolmogorov complexity method in combinatorial theory is demonstrated by several examples.

We study partitions of Fra¨ıssé limits of classes of finite relational structures where the partitions are encoded by infinite binary strings which are random in the sense of Kolmogorov-Chaitin.