Physical oracles: Measurement, complexity and cyber-physical systems

Edwin Beggs, Swansea University. Part of the algebra, logic and algorithms seminar series.

Turing's mythological 1939 idea of oracle postulated a device that was not a Turing machine and lay outside the formal idea of algorithms. The oracle is a source of information for an algorithm. Suppose that the oracle is a physical process or experiment - a 'physical oracle'. This oracle is subject to errors and delays, and further it is subject to one or more physical theories that allow us to understand its behaviour.

We can look at interactions between algorithms and the physical world in two ways: A physical oracle assists a computation (e.g. an analogue computer), or we can have a computer controlling an experiment, so we can have consequences for both the theory of measurement and complexity theory. Reasonable assumptions suggest a limit of the non-uniform complexity class BPP//log* for an algorithm assisted by a physical oracle. Cyber-physical systems consist of algorithms communicating with a mixture of other algorithms and physical oracles. We consider the consequences of the limitations on physical oracles on cyber-physical systems, and in particular the idea of splitting physical systems into modes for the purposes of control theory.

Edwin Beggs, Swansea University