When does a physical system compute? (1309.7979v3)

Abstract: Computing is a high-level process of a physical system. Recent interest in non-standard computing systems, including quantum and biological computers, has brought this physical basis of computing to the forefront. There has been, however, no consensus on how to tell if a given physical system is acting as a computer or not; leading to confusion over novel computational devices, and even claims that every physical event is a computation. In this paper we introduce a formal framework that can be used to determine whether or not a physical system is performing a computation. We demonstrate how the abstract computational level interacts with the physical device level, drawing the comparison with the use of mathematical models to represent physical objects in experimental science. This powerful formulation allows a precise description of the similarities between experiments, computation, simulation, and technology, leading to our central conclusion: physical computing is the use of a physical system to predict the outcome of an abstract evolution. We give conditions that must be satisfied in order for computation to be occurring, and illustrate these with a range of non-standard computing scenarios. The framework also covers broader computing contexts, where there is no obvious human computer user. We define the critical notion of a 'computational entity', and show the role this plays in defining when computing is taking place in physical systems.