In the system level fault diagnosis area, the fundamental problem of characterizing sequentially t-diagnosable systems in the PMC model has remained open for more than two decades. We resolve this problem by providing a complete characterization of such systems. Our solution to the characterization problem leads to the correct identification of optimal sequentially t-diagnosable D/sub /spl delta/,k/ systems. Given a set of n units where n=2t+1, an optimal D/sub /spl delta/,k/ system can be constructed with just n([(t+2)/3]) tests, rather than n([t/2]+1) tests-a previously misjudged bound. An efficient algorithm for identifying the set of faulty units in a sequentially t-diagnosable D/sub /spl delta/,k/ system is given along the line of the proposed characterization, which is linear with respect to the number of tests in the system.>