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In this article, we have presented a novel constrained broadside transition ATPG algorithm to avoid overtesting functionally (sequentially) untestable transition faults. In some circuits, significantly more functionally untestable transition faults were identified. At the same time, more faults could be detected without incidental detection of functionally untestable transition faults. With a test set that reduces launching of transitions that are functionally impossible, we believe our method offers a practical solution to avoid overtesting these functionally impossible transitions, thus reducing yield loss. However, the runtime for our constrained ATPG is much longer than the conventional ATPG as a result of the constraint learning and construction process. Our future work concentrates on more-efficient constraint learning algorithms to reduce the over all ATPG runtime.