There arose two successful formalisations of the quantitative aspect of information over the course of the twentieth century: Shannon information and Kolmogorov complexity. Both afore mentioned definitions are rooted in mostly separate parts of mathematics. Shannon's information came to existence as an application of the elementary theory of probability and statistics. It is defined as a function in probability, with it being a lower bound on binary compression. Kolmogorov complexity, on the other hand, springs from formal logic and theory of computability. Kolmogrov defined it as the length of a minimal algorithmic description of a message. It is a beautiful result that when certain conditions do apply then those two functions behave asymp...
There are (at least) three approaches to quantifying information. The first, algorithmic information...
In contrast to statistical entropy which measures the quantity of information in an average object ...
The notion of algorithmic complexity (also sometimes called \algorithmic en-tropy") appeared in...
We compare the elementary theories of Shannon information and Kolmogorov complexity, the extent to w...
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We e...
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We e...
Information theory is a branch of mathematics that attempts to quantify information. To quantify inf...
Information theory is a well developed field, but does not capture the essence of what information ...
AbstractKolmogorov's very first paper on algorithmic information theory (Kolmogorov, Problemy pereda...
This document contains lecture notes of an introductory course on Kolmogorov complexity. They cover ...
This document contains lecture notes of an introductory course on Kolmogorov complexity. They cover ...
There are (at least) three approaches to quantifying information. The first, algorithmic information...
There are (at least) three approaches to quantifying information. The first, algorithmic information...
There are (at least) three approaches to quantifying information. The first, algorithmic information...
There are (at least) three approaches to quantifying information. The first, algorithmic information...
There are (at least) three approaches to quantifying information. The first, algorithmic information...
In contrast to statistical entropy which measures the quantity of information in an average object ...
The notion of algorithmic complexity (also sometimes called \algorithmic en-tropy") appeared in...
We compare the elementary theories of Shannon information and Kolmogorov complexity, the extent to w...
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We e...
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We e...
Information theory is a branch of mathematics that attempts to quantify information. To quantify inf...
Information theory is a well developed field, but does not capture the essence of what information ...
AbstractKolmogorov's very first paper on algorithmic information theory (Kolmogorov, Problemy pereda...
This document contains lecture notes of an introductory course on Kolmogorov complexity. They cover ...
This document contains lecture notes of an introductory course on Kolmogorov complexity. They cover ...
There are (at least) three approaches to quantifying information. The first, algorithmic information...
There are (at least) three approaches to quantifying information. The first, algorithmic information...
There are (at least) three approaches to quantifying information. The first, algorithmic information...
There are (at least) three approaches to quantifying information. The first, algorithmic information...
There are (at least) three approaches to quantifying information. The first, algorithmic information...
In contrast to statistical entropy which measures the quantity of information in an average object ...
The notion of algorithmic complexity (also sometimes called \algorithmic en-tropy") appeared in...