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Given a test sequence and a list of faults detected by the sequence, vector restoration techniques extract a minimal subsequence that detects a chosen subset of modeled faults. Vector restoration techniques are useful in static compaction of test sequences and in fault diagnosis. We propose a new vector restoration technique that is a significant improvement over the state of the art in several ways: (1) a sequence of length n can be restored with only O(n log^sub 2^ n) simulations while known approaches require simulation of O(n^sup 2^) vectors, (2) a two-step restoration process is used that makes vector restoration practical for large designs, and (3) restoration process for several faults is overlapped to provide significant acceleration in vector restoration. Our new ideas can be used to improve run-times of known static compaction and fault diagnosis methods. We integrated the proposed vector restoration technique into a static test sequence compaction system. Our experiments show that the new restoration technique, as compared to known techniques (Proceedings of Int. Conf. on Computer Design, University of Iowa, Aug. 1997, pp. 360-365.), is (1) about 2 times faster for the ISCAS benchmark circuits, and (2) 3 to 5 times faster on large, industrial designs. Using the new restoration technique, we successfully processed large industrial designs that could not be handled by earlier techniques (Proceedings of Int. Conf. on Computer Design, University of Iowa, Aug. 1997, pp. 360-365.) in 2 CPU days.[PUBLICATION ABSTRACT]