A Behavioural Foundation for Natural Computing and a Programmability Test

What does it mean to claim that a physical or natural system computes? One answer, endorsed here, is that computing is about programming a system to behave in different ways. This paper offers an account of what it means for a physical system to compute based on this notion. It proposes a behavioural characterisation of computing in terms of a measure of programmability, which reflects a system's ability to react to external stimuli. The proposed measure of programmability is useful for classifying computers in terms of the apparent algorithmic complexity of their evolution in time. I make some specific proposals in this connection and discuss this approach in the context of other behavioural approaches, notably Turing's test of machine intelligence. I also anticipate possible objections and consider the applicability of these proposals to the task of relating abstract computation to nature-like computation.Comment: 37 pages, 4 figures. Based on an invited Talk at the Symposium on Natural/Unconventional Computing and its Philosophical Significance, Alan Turing World Congress 2012, Birmingham, UK. http://link.springer.com/article/10.1007/s13347-012-0095-2 Ref. glitch fixed in 2nd. version; Philosophy & Technology (special issue on History and Philosophy of Computing), Springer, 201

Computational Processes, Observers and Turing Incompleteness

We propose a formal definition of Wolfram’s notion of computational process based on iterated transducers together with a weak observer, a model of computation that captures some aspects of physics-like computation. These processes admit a natural classification into decidable, intermediate and complete, where intermediate processes correspond to recursively enumerable sets of intermediate degree in the classical setting. It is shown that a standard finite injury priority argument will not suffice to establish the existence of an intermediate computational process