The paper is concerned with analyzing and comparing two exact algorithms from the viewpoint of computational complexity. They are: composite justification and the D-algorithm. Both serve for calculating fault-detection tests of digital circuits. As a result, it is pointed out that the composite justification requires significantly less computational step than the D-algorithm. From this fact it has been conjectured that possibly no other algorithm is available in this field with fewer computational steps. If the claim holds, then it follows directly that the test-generation problem is of exponential time, and so are all the other NP-complete problems in the field of computation theory. © 2011 IEEE.