Time Bounds on Space Computations

A physicomathematical basis is used to establish bounds TD(n) on the time needed to compute n-argument functions by spatially distributed primitive devices or composite systems D. The axioms used concern the speed, packing density, and noise threshold of the energy with which any computing device detects or alters the physical representation of information. The principal result is that TD(n) grows at least as n^1/2. Composite systems consisting of spatially distributed identical components are examined in light of this bound. Inherent bounds on the computing time of n-argument functions are then combined with TD(n), resulting in a measure of computational efficiency which bounds computing time to processor size.