Randomness Conservation over Algorithms

TL;DR

This paper extends the concept of randomness conservation from deterministic functions to algorithms and enumerable transformations, establishing tight bounds and showing conservation under broader computational models.

Contribution

It proves tight bounds for randomness and information conservation under recursively enumerable transformations, broadening the scope beyond total recursive functions.

Findings

Randomness conservation holds for enumerable transformations.

Tight bounds are established for randomness and information conservation.

Conservation of randomness is shown for finite strings and enumerable distributions.

Abstract

Current discrete randomness and information conservation inequalities are over total recursive functions, i.e. restricted to deterministic processing. This restriction implies that an algorithm can break algorithmic randomness conservation inequalities. We address this issue by proving tight bounds of randomness and information conservation with respect to recursively enumerable transformations, i.e. processing by algorithms. We also show conservation of randomness of finite strings with respect to enumerable distributions, i.e. semicomputable semi-measures.