A string $p$ is called a program to compute $y$ given $x$
if $U(p,x)=y$, where $U$ denotes universal programming language.
Kolmogorov complexity $K(y|x)$ of $y$ relative to $x$
is defined as minimum length of
a program to compute $y$ given $x$.
Let $K(x)$ denote $K(x|\text{empty string})$
(Kolmogorov complexity of $x$) ... more >>>

We examine the communication required for generating random variables
remotely. One party Alice will be given a distribution D, and she
has to send a message to Bob, who is then required to generate a
value with distribution exactly D. Alice and Bob are allowed
to share random bits generated ... more >>>

This paper provides the first general technique for proving information lower bounds on two-party
unbounded-rounds communication problems. We show that the discrepancy lower bound, which
applies to randomized communication complexity, also applies to information complexity. More
precisely, if the discrepancy of a two-party function $f$ with respect ... more >>>

We define the lower and upper mutual dimensions $mdim(x:y)$ and $Mdim(x:y)$ between any two points $x$ and $y$ in Euclidean space. Intuitively these are the lower and upper densities of the algorithmic information shared by $x$ and $y$. We show that these quantities satisfy the main desiderata for a satisfactory ... more >>>

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 key that
two parties, one having $x$ and the complexity profile of the pair and the ... more >>>