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The complexity of deterministic sequential test generation for a target fault in a circuit with n primary inputs is determined by the need to explore a search space that consists of 2n primary input vectors at every time unit. This paper studies the possibility of reducing the complexity of deterministic sequential test generation by using subsets of primary input vectors of limited sizes during test generation for target faults. It considers a test generation procedure that uses subsets of primary input vectors of size N, for increasing values of N starting with N=1 . The subsets consist of primary input vectors from the test sequence already generated, and of random primary input vectors. The results indicate that all or most of the detectable single stuck-at faults in benchmark circuits can be detected using small subsets of primary input vectors.