Lowness for the class of Schnorr random reals

TL;DR

This paper proves that if a real is low for Schnorr randomness, then it is also low for Schnorr tests, confirming a conjecture in the field of algorithmic randomness.

Contribution

It establishes that lowness for Schnorr randomness implies lowness for Schnorr tests, resolving an open question.

Findings

Confirmed that lowness for Schnorr randomness implies lowness for Schnorr tests.

Answered an open question posed by Ambos-Spies and Kucera.

Strengthened understanding of the relationship between different notions of lowness in algorithmic randomness.

Abstract

We answer a question of Ambos-Spies and Ku\v{c}era in the affirmative. They asked whether, when a real is low for Schnorr randomness, it is already low for Schnorr tests.