We study the randomness necessary for the simulation of a random process with given distributions, in terms of the finite-precision resolvability of the process. Finite-precision resolvability is defined as the minimal random-bit rate required by the simulator as a function of the accuracy with which the distributions are replicated. The accuracy is quantified by means of various measures: vari...

A space X is said to be κ-resolvable (resp. almost κ-resolvable) if it contains κ dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets). X is maximally resolvable iff it is ∆(X)-resolvable, where ∆(X) = min{|G| : G 6= ∅ open}. We show that every crowded monotonically normal (in short: MN) space is ω-resolvable and almost μ-resolvable, where μ = mi...

This paper proposes an extension of the ML module system with recursion that keeps a flexible use of nested structures and functors. For the purpose of formal study, we design a calculus, called PathCal, which has a module system with nested structures and simple functors along with recursion. It is important for this calculus to guarantee resolvability of recursive references between modules. ...

The achievable rate region and degrees of freedom are studied for interference channels with confidential messages under strong secrecy constraints. The problem is studied based on the framework of Han and Verdú’s channel resolvability theory. It is shown that if the random binning rate for securing a confidential message is slightly above the resolution of its corresponding wiretapped channel,...

We characterize the resolvability region for a large class of point-to-point channels with continuous alphabets. In our direct result, we prove not only the existence of good resolvability codebooks, but adapt an approach based on the Chernoff-Hoeffding bound to the continuous case showing that the probability of drawing an unsuitable codebook is doubly exponentially small. For the converse par...

This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length resolvability. Previous study has derived the general formula of the -variable-length resolvability. We derive the general formula of the -variable-length intri...