Kolmogorov Theorem Revisited

Resour e-Bounded Kolmogorov Complexity Revisited

Resource bounded symmetry of information revisited

The information contained in a string x about a string y is the difference between the Kolmogorov complexity of y and the conditional Kolmogorov complexity of y given x, i.e., I(x : y) = C(y) − C(y |x). The Kolmogorov–Levin Theorem says that I(x : y) is symmetric up to a small additive term. We investigate if this property also holds for several versions of polynomial time bounded Kolmogorov co...

Individual ergodic theorem for intuitionistic fuzzy observables using intuitionistic fuzzy state

The classical ergodic theory hasbeen built on σ-algebras. Later the Individual ergodictheorem was studied on more general structures like MV-algebrasand quantum structures. The aim of this paper is to formulate theIndividual ergodic theorem for intuitionistic fuzzy observablesusing  m-almost everywhere convergence, where  m...

The Kolmogorov–riesz Compactness Theorem

We show that the Arzelà–Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly’s theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.

Kolmogorov complexity and the second incompleteness theorem

We shall prove the second incompleteness theorem via Kolmogorov complexity.