The equivalence between optimal detecting arrays and super-simple OAs
The notion of a detecting array (DTA) was proposed, recently, by Colbourn and McClary in their research on software interaction tests. Roughly speaking, testing with a (d, t)-DTA(N, k, v) can locate d interaction faults and detect whether there are more than d interaction faults. In this paper, we establish a general lower bound on sizes of DTAs and explore an equivalence between optimal DTAs and super-simple orthogonal arrays (OAs). Taking advantage of this equivalence, a great number of DTAs are constructed, which are all optimal in the sense of their sizes. In particular, an optimal (2, t)-DTA(N, 5, v) of strength t = 2 or 3 is shown to exist whenever v >= 3 excepting (t, v) is an element of {(2, 3), (2, 6), (3, 4), (3, 6)}. .
equivalence detecting arrays super-simple orthogonal arrays error locating arrays