Noise stability and complexity classification of noisy variants of undecidable physical problems

Ascertain which undecidable physical decision problems retain undecidability in the presence of natural sources of noise in their corresponding models, and, for those that do not remain undecidable, determine the exact computational complexity class of the resulting noisy decision problems.

Background

The paper notes that most undecidability constructions neglect noise, whereas real physical systems invariably include it. Recent work shows that certain undecidable non-local game problems become decidable (in NEXP) when noise is present, raising broader questions about the robustness of undecidability.

The authors call for a systematic understanding of which undecidable results are stable under realistic noise models and, when undecidability is lost, the precise complexity classification of the noisy problems—key for practical implications and algorithmic boundaries.