Algebraic Models for Arbitrary Strength Covering Arrays over v-ary Alphabets

摘要

Extending our previous work [7], we introduce a novel technique to model and compute arbitrary strength covering arrays over v-ary alphabets, using methods arising from linear algebra commutative algebra and symbolic computation. Concrete instances of covering arrays for given parameters then appear as points in varieties as they occur in solutions of multivariate polynomial equation systems. To solve these systems we apply polynomial solvers based on the theory of Grobner bases and exhaustive search using serial and parallel programming techniques.