The Power of Machines That Control Experiments

We consider the experimenter (e.g. the experimental physicist) as a Turing machine — the digital component — and the experiment of measurement — the analog component — as an oracle to the Turing machine. The algorithm running in the machine abstracts the experimental method of measurement (encoding the recursive structure of experimental actions) chosen by the experimenter. In this paper we prove that the central analogue-digital complexity classes [Formula: see text], [Formula: see text] and [Formula: see text] can be characterized in terms of protocols to perform measurements controlled by standard Turing machines.