Subcomputable Schnorr Randomness

TL;DR

This paper introduces a new concept of Schnorr randomness applicable to subcomputable classes, extending the classical notion and providing multiple characterizations such as Martin Löf tests, martingales, and measure computable machines.

Contribution

It extends Schnorr randomness to subcomputable classes and offers various characterizations, broadening the understanding of randomness in computational complexity.

Findings

Defines subcomputable Schnorr randomness

Provides characterizations via Martin Löf tests, martingales, and measure computable machines

Enhances the theoretical framework of algorithmic randomness

Abstract

The notion of Schnorr randomness refers to computable reals or computable functions. We propose a version of Schnorr randomness for subcomputable classes and characterize it in different ways: by Martin L\"of tests, martingales or measure computable machines.