Abstract :
The introduction to this paper motivates a simple mathematical model for catastrophic failure, based on solid state diodes (or vacuum tube grids, relay solenoids) shorting or opening permanently at some time after gate operation has commenced. Based on the assumption that a given copy can fail only in a manner within the scope of this model, it is unnecessary to check each output for every input in order to establish with certainty that the copy is in fact providing the intended combinational logic. A small subset of inputs is in general sufficient to provide "go, no-go" information with 100% confidence; and after such a subset or checkup is determined, the problem of which inputs to administer for check out of a given copy of the prototype, is solved once and for all. The main results of this paper center around a shortcut procedure to obtain a "reasonably small" checkup for any given prototype, with considerably less effort than by exhaustive analysis. The penalty for this computational efficiency is that checkups so obtained will occasionally not be absolutely minimal. The shortcut is applicable to any switching function: however it is sensible to obtain checkups only with those functions that are realizable in hardware for which this particular failure model is intended. On the basis of the shortcut it is shown that: considering all M-place switching functions over all M ¿ 1, there is no minimum checkup containing more than 2M of the possible 2M inputs.
