Ming Li Paul Vitányi Fourth Edition Page 1 An Introduction to Kolmogorov Complexity and Its
Applications Ming Li Paul Vitányi Fourth Edition Texts in Computer Science Page 2 Texts in …

We show that the mutual information, in the sense of Kolmogorov complexity, of any pair of
strings x and y is equal, up to logarithmic precision, to the length of the longest shared secret …

We propose a linear algebraic method, rooted in the spectral properties of graphs, that can
be used to prove lower bounds in communication complexity. Our proof technique effectively …

We discuss research developments on the complexity of shortest programs since the turn of
the millennium. In particular, we will delve into the phenomenon of list approximation: while …

In a lossless compression system with target lengths, a compressor ${\cal C} $ maps an
integer $ m $ and a binary string $ x $ to an $ m $-bit code $ p $, and if $ m $ is sufficiently …

This formula can be informally read as follows: the ith messagemi brings us log (1= pi)" bits
of information"(whatever this means), and appears with frequency pi, so H is the expected …

Many statements from the classic information theory (the theory of Shannon's entropy) have
natural counterparts in the algorithmic information theory (in the framework of Kolmogorov …

We give simplify the proofs of the 2 results in Marius Zimand's paper" Kolmogorov
complexity version of Slepian-Wolf coding, proceedings of STOC 2017, p22--32". The first is …

We put forth new models for universal channel coding. Unlike standard codes which are
designed for a specific type of channel, our most general universal code makes …

In a lossless compression system with target lengths, a compressor 𝒞 maps an integer m
and a binary string x to an m-bit code p, and if m is sufficiently large, a decompressor 𝒟 …