Functionally Complete Machines

This paper defines a functionally complete machine as a machine which is capable of evaluating every two place function over its data space. Necessary conditions on memory size for completeness are developed. These conditions are applied to System/360 as modelled by the space of bytes, the space of halfwords, and the space of words. Sufficiently large (> 64K bytes) models of System/360 are shown to be complete for the space of bytes. No models of System/360 are complete for the spaces of halfwords or words. The inequalities developed and known examples of universal decision elements suggest structures for complete machines.