Boolean Matrices and their Applications to Covering Reductions

This paper proposes two different covering reduction algorithms by means of Boolean matrices. We define a dual notion of product on Boolean matrices and establish the relationship between characteristic matrix of a covering and relational matrices of two covering-induced relations, i.e. the minimum and the maximum relations in a covering. This paper shows that relational matrices of minimum and maximum relations in a covering can be written as intersection and union of many “elementary” matrices and each “elementary” matrix is corresponding to one element in the covering, respectively. Finally, as an application of this result, we propose two types of covering reduction algorithms.