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This paper introduces a new class of finite memory compaction schemes called convolutional compactors (CCs). They provide compaction ratios of test responses in excess of 100×, even for a very small number of outputs. This is combined with the capability to detect multiple errors, handling of unknown states, and the ability to diagnose failing scan cells directly from compacted responses. The CCs can also be used to significantly enhance conventional multiple input signature registers. Experimental results presented in the paper demonstrate the efficiency of convolutional compaction for several industrial circuits.