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A Theorem on Boolean Matrices
 JOURNAL OF THE ACM
, 1962
"... Given two boolean matrices A and B, we define the boolean product A AND B as that matrix whose (i, j)th entry is OR_k(a_ik AND b_kj). We define the boolean sum A OR B as that matrix whose (i, j)th entry is a_ij OR b_ij. The use of boolean matrices to represent program topology (Prosser [1], and Mari ..."
Abstract

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Given two boolean matrices A and B, we define the boolean product A AND B as that matrix whose (i, j)th entry is OR_k(a_ik AND b_kj). We define the boolean sum A OR B as that matrix whose (i, j)th entry is a_ij OR b_ij. The use of boolean matrices to represent program topology (Prosser [1], and Marimont [2], for example) has led to interest in algorithms for transforming the d × d boolean matrix M to the d × d boolean matrix M' given by:
M' = OR_i=1^d M^i where we define M^1 = M and M^(i + 1) = M^i AND M.