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- E J Beggs, J V Tucker
- 2006

Following a methodology we have proposed for analysing the nature of experimental computation, we prove that there is a 3-dimensional Newtonian machine which given any point x ∈ [0, 1] can generate an infinite sequence [pn, qn], for n = 1, 2, . . ., of rational number interval approximations that converges to x as n → ∞. The machine is a system for… (More)

- E. J. Beggs
- 2004

Consider the idea of computing functions using experiments with kinematic systems. We prove that for any set A of natural numbers there exists a 2-dimensional kinematic system BA with a single particle P whose observable behaviour decides n ∈ A for all n ∈ N. The system is a bagatelle and can be designed to operate under (a) Newtonian mechanics or (b)… (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)

- Edwin J. Beggs, J. V. Tucker
- Applied Mathematics and Computation
- 2006

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)

- Edwin Beggs
- 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×Mop. This provides a class of bicrossproduct Hopf algebras which are quasitriangular. We also construct a subgroup Y X associated to every… (More)

- E. J. Beggs
- 1994

We compute the quantum double, braiding and other canonical Hopf algebra constructions for the bicrossproduct Hopf algebra H associated to the factorization of a finite group into two subgroups. The representations of the quantum double are described by a notion of bicrossed bimodules, generalising the cross modules of Whitehead. We also show that… (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)

- E. J. Beggs
- 2006

We introduce the notion of ‘bar category’ by which we mean a monoidal category equipped with additional structure induced by complex conjugation. Examples of our theory include bimodules over a ∗-algebra, modules over a conventional Hopf ∗-algebra and modules over a more general object which call a ‘quasi-∗-Hopf algebra’ and for which examples include the… (More)

- Edwin J. Beggs, J. V. Tucker
- Theor. Comput. Sci.
- 2007

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)

- Edwin J. Beggs, José Félix Costa, Bruno Loff, J. V. Tucker
- TAMC
- 2008

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)