We give two theorems for identifying untestable faults in sequential circuits. The first, the single-fault theorem, states that if a single fault in a combinational array is untestable then that fault is untestable in the sequential circuit. The array replicates the combinational logic and can have any finite length. We assume that the present state inputs of the left-most block are completely controllable. The next state outputs of the right-most block are considered observable. A combinational test pattern generator determines the detectability of single faults in the right-most block. The second theorem, called the multifault theorem, uses the array model with a multifault consisting of a single fault in every block. The theorem states that an untestable multifault in the array corresponds to an untestable single fault in the sequential circuit. For the array with a single block both theorems identify combinational redundancies. Experiments on ISCAS benchmarks show that using a small array size (typically, two to four blocks) we can identify a large number of sequentially untestable faults.
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