Randomization benefits for Turing machines in complexity theory

Ascertain whether randomization confers additional computational power for Turing machines in the complexity-theoretic sense, i.e., determine whether randomized computation is more powerful than deterministic computation (for example, whether BPP equals P).

Background

In motivating probabilistic learning algorithms (e.g., stochastic training and Monte Carlo sampling), the authors place their results within broader computational models. They note that while randomization is widely used in practice, its theoretical advantage for Turing machines remains unsettled in complexity theory.

This context underpins their use of probabilistic general algorithms and the strength of their lower bounds, which hold even for randomized models.