Mathematical Models of Computation Using Magnetic Bubble Interactions

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Abstract
This paper considers the computational capabilities of different mathematical models of magnetic bubble interactions. A specific model was studied earlier by R. L. Graham, who showed that there exist combinational functions of 11 or more variables that cannot be computed by this model. This paper extends his results by introducing different types of interactions which seem to be practical and enable the computation of all combinational functions. The problem of efficient computation from the points of view of time and space requirements and the geometrical requirements imposed by the fact that interactions can occur only between physically adjacent locations are also examined. Finally, a model in which computations are carried out by applying uniform magnetic fields to the entire platelet, with individual access limited to locations along the periphery, is presented.

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