Algorithmic randomness and monotone complexity on product space

Algorithmic randomness and monotone complexity on product space

We study algorithmic randomness and monotone complexity on product of the set of infinite binary sequences. We explore the following problems: monotone complexity on product space, Lambalgen’s theorem for correlated probability, classification of random sets by likelihood ratio tests, decomposition of complexity and independence, Bayesian statistics for individual random sequences. Formerly Lam...

Algorithmic Randomness and Complexity

Kolmogorov Complexity and Algorithmic Randomness

This paper aims to provide a minimal introduction to algorithmic randomness. In particular, we cover the equivalent 1-randomness and MartinLöf randomness. After a brief review of relevant concepts in computability, we develop the basic theory of Kolmogorov complexity, including the KC theorem and more general notion of information content measures. We then build two natural definitions of rando...

Computability, Algorithmic Randomness and Complexity

I think mathematical ability manifests itself in many different ways. In particular, mathematicians can be drawn to space and geometry, can have strong analytic intuition, can be drawn to formalism, they can be drawn to counting arguments, etc. There is definitely no unique type of mathematician. Maybe those mathematicians who are drawn to algorithmic thinking have found a home in computer scie...

Algorithmic complexity and randomness in elastic solids

A system comprised of an elastic solid and its response to an external random force sequence is shown to behave based on the principles of the theory of algorithmic complexity and randomness. The solid distorts the randomness of an input force sequence in a way proportional to its algorithmic complexity. We demonstrate this by numerical analysis of a one-dimensional vibrating elastic solid (the...