A Behavioural Foundation for Natural Computing and a Programmability Test
This work addresses a foundational issue in natural computing, offering a conceptual framework that could influence how computation is understood in physical systems, though it appears incremental relative to existing behavioral approaches.
The paper tackles the problem of defining what it means for a physical or natural system to compute by proposing a behavioral characterization based on programmability, which measures a system's ability to react to external stimuli and classify computers by their algorithmic complexity.
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.