Hash Families and Covering Arrays
نویسنده
چکیده
Let N , k, t, and v be positive integers. Let C be an N × k array with entries from an alphabet Σ of size v; we typically take Σ = {0, . . . , v − 1}. When (ν1, . . . , νt) is a t-tuple with νi ∈ Σ for 1 ≤ i ≤ t, (c1, . . . , ct) is a tuple of t column indices (ci ∈ {1, . . . , k}), and ci 6= cj whenever νi 6= νj , the t-tuple {(ci, νi) : 1 ≤ i ≤ t} is a t-way interaction. The array covers the t-way interaction {(ci, νi) : 1 ≤ i ≤ t} if, in at least one row ρ of C, the entry in row ρ and column ci is νi for 1 ≤ i ≤ t. Array C is a covering array CA(N ; t, k, v) of strength t when every tway interaction is covered. Figure 1 gives an example of a covering array with N = 12 rows, ten factors having two symbols, and strength three. Consider, for example, the 3-way interaction {(2, 0), (5, 1), (6, 1)}; it is covered in the fifth and eighth rows.
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