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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 discuss combining physical experiments with machine computations and introduce a form of analogue-digital Turing machine. We examine in detail a case study where an experimental procedure based on Newtonian kinematics is combined with a class of Turing machines. Three forms of analogue-digital machine are studied, in which physical parameters can be set… (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)

- Edwin Beggs, José Fé, Lix Costa, Bruno Loff, J V Tucker
- 2009

Earlier, to explore the idea of combining physical experiments with algorithms, we introduced a new form of analogue–digital (AD) Turing machine. We examined in detail a case study where an experimental procedure, based on Newtonian kinematics, is used as an oracle with classes of Turing machines. The physical cost of oracle calls was counted and three… (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 Beggs, Shahn Majid
- 1996

Let X = GM be a finite group factorisation. It is shown that the quantum double D(H) of the associated bicrossproduct Hopf algebra H = kM ⊲◭k(G) is itself a bicrossproduct kX⊲◭k(Y) associated to a group Y X, where Y = G × M op. This provides a class of bicrossproduct Hopf algebras which are qua-sitriangular. We also construct a subgroup Y θ X θ associated… (More)

- Edwin Beggs
- 2000

The paper begins by giving an algebraic structure on a set of coset representatives for the left action of a subgroup on a group. From this we construct a non-trivially associated tensor category. Also a double construction is given, and this allows the construction of a non-trivially associated braided tensor category. In this category we explicitly… (More)