On the Power of Threshold Measurements as Oracles

We consider the measurement of physical quantities that are thresholds. We use hybrid computing systems modelled by Turing machines having as an oracle physical equipment that measures thresholds. The Turing machines compute with the help of qualitative information provided by the oracle. The queries are governed by timing protocols and provide the equipment with numerical data with (a) infinite precision, (b) unbounded precision, or (c) finite precision. We classify the computational power in polynomial time of a canonical example of a threshold oracle using non-uniform complexity classes.