Deterministic simulation of probabilistic BSS machines with polynomial slowdown

Determine whether any probabilistic Blum–Shub–Smale (BSS) machine can be simulated by a deterministic BSS machine with the same machine constants and with at most a polynomial slowdown.

Background

The authors discuss randomized algorithms within both Turing and BSS computational models to emphasize that their lower bounds are model-independent. They point out a specific unresolved question in the BSS model concerning deterministic simulation of probabilistic computation with comparable resources.

Resolving this would clarify foundational aspects of randomized computation over the reals, which is relevant for analyzing learning algorithms that operate with real-number inputs.