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A novel approach to automatic generation of diagnostic memory tests based on fault decomposition and output tracing is described. Fault decomposition allows fault models that precisely describe the fault effects of a specific technology to be considered during test generation; therefore, overtesting of the memory-under-test is avoided. Output tracing of failing memory cells allows for distinguishing of all memory faults of the fault model. An extended greedy-based set-cover algorithm is utilized to generate the march tests that detect all basic fault effects and distinguish among them. The effectiveness of the generated tests is verified using simulation. Test generation time is on the order of a few seconds, while the lengths of the generated tests are only 1N to 3N higher than those of known optimal tests for the same fault models.