Covering Arrays of Strength Four and Software Testing

Abstract

A covering array $t-\text{ CA }(n,k,g)$, of size n, strength t, degree k, and order g, is a $k\times n$ array on g symbols such that every $t\times n$ subarray contains every $t\times 1$ column on g symbols at least once. Covering arrays have been studied for their applications on software testing, hardware testing, drug screening, and in areas where interactions of multiple parameters are to be tested. We define the coverage measure $\mu _t(A)$ of an array A by the ratio between the number of distinct t-tuples contained in the column vectors of A and the total number of t-tuples given by ${\left( {\begin{array}{c}k\\ t\end{array}}\right) }g^t$. Given fixed values of t, k, g, and n, our objective is to construct an array A of size atmost n having largest possible coverage measure. This problem is called covering arrays with budget constrains. In this article, we present an algebraic construction method for strength four covering arrays with budget constraints.