Syndrome-Testability Can be Achieved by Circuit Modification

In [1] and [2] Savir developed many facets of syndrome-testing (checking the number of minterms realized by a circuit against the number realized by a fault-free version of that circuit) and presented evidence showing that syndrome-testing can be used in many practical circuits to detect all single faults. In some cases, where syndrome-testing did not detect all single stuck-at-faults, Savir showed that by the addition of a small number of additional "control" inputs and gates one would get a function which is syndrome-testable for all single stuck-at faults, and yet which realizes the original function when the "control" inputs are fed appropriate values. However, he left open the question of whether one could always modify a circuit to achieve syndrome-testability. In this correspondence we show that a combinatorial circuit can always be modified to produce a single-fault, syndrome-testable circuit.