Using cellular automata as models of parallel machines we investigate constraints for the energy consumption of r-dimensional machines which are motivated by physical limitations for the case r = 3. Depending on the operations which must be considered to dissipate energy, some relations between the relative performance of 2-dimensional and 3-dimensional machines are derived. In the light of these results it seems imperative that for feasible models of computation energy consumption has to be considered as an additional complexity measure.
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