The very first Kolmogorov's paper on algorithmic
information theory was entitled `Three approaches to the
definition of the quantity of information'. These three
approaches were called combinatorial, probabilistic and
algorithmic. Trying to establish formal connections
between combinatorial and algorithmic approaches, we
prove that any ...
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Multisource information theory in Shannon setting is well known. In this article we try to develop its algorithmic information theory counterpart and use it as the general framework for many interesting questions about Kolmogorov complexity.
more >>>In a sampling problem, we are given an input $x\in\left\{0,1\right\} ^{n}$, and asked to sample approximately from a probability
distribution $D_{x}$ over poly(n)-bit strings. In a search problem, we are given an input
$x\in\left\{ 0,1\right\} ^{n}$, and asked to find a member of a nonempty set
$A_{x}$ with high probability. ...
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We show that given a quantum measurement, for an overwhelming majority of pure states, no meaningful information is produced. This is independent of the number of outcomes of the quantum measurement. Due to conservation inequalities, such random noise cannot be processed into coherent data.
more >>>We provide another proof to the EL Theorem. We show the tradeoff between compressibility of codebooks and their communication capacity. A resource bounded version of the EL Theorem is proven. This is used to prove three instances of resource bounded derandomization.
