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First, we reflect on computing sets and functions using measurements from experiments with a class of physical systems. We call this experimental computation. We outline a programme to analyse theoretically experimental computation in which a central problem is: Given a physical theory T , explore and classify the computational models that can be embedded… (More)

In the theoretical analysis of the physical basis of computation there is a great deal of confusion and controversy (e.g., on the existence of hyper-computers). First, we present a methodology for making a theoretical analysis of computation by physical systems. We focus on the construction and analysis of simple examples that are models of simple… (More)

We pose the following question: If a physical experiment were to be completely controlled by an algorithm, what effect would the algorithm have on the physical measurements made possible by the experiment? In a programme to study the nature of computation possible by physical systems, and by algorithms coupled with physical systems, we have begun to analyse… (More)

If we measure the position of a point particle, then we will come up with an interval [an, bn] into which the point falls. We make use of a Gedankenexperiment to find better and better values of an and bn, by reducing their separation, in a succession of intervals [a1, b1] ⊃ [a2, b2] ⊃. .. ⊃ [an, bn] that contain the point. We then use such a point as an… (More)

In this paper we will try to understand how oracles and advice functions, which are mathematical abstractions in the theory of computability and complexity, can be seen as physical measurements in Classical Physics. First, we consider how physical measurements are a natural external source of information to an algorithmic computation. We argue that oracles… (More)

- Edwin J Beggs, Peter R Johnson
- 1996

We implement the inverse scattering method in the case of the A n affine Toda field theories, by studying the space-time evolution of simple poles in the underlying loop group. We find the known single and multi-soliton solutions, as well as additional solutions with non-linear modes of oscillation around the standard solution, by studying the particularly… (More)

We developed earlier a theory of combining algorithms with physical systems, on the basis of using physical experiments as oracles to algorithms. Although our concepts and methods are general, each physical oracle requires its own analysis, on the basis of some fragment of physical theory that specifies the equipment and its behaviour. For specific examples… (More)