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Existing diagnostic test generation procedures are output-independent, i.e., they attempt to distinguish faults on any output. We show that an output-dependent approach can facilitate diagnostic test generation and produce smaller diagnostic test sets for stuck-at faults in full-scan circuits. In the proposed output-dependent approach, the outputs of the circuit are considered one at a time. Faults in the logic cone of an output z under consideration are distinguished from other faults by detecting some faults but not others on z. Diagnostic test generation is facilitated by the need to consider only the inputs driving the output under consideration. Furthermore, we demonstrate that an output typically has a small number of input vectors that differ in their subsets of detected faults and are thus effective for diagnosis.