Stephen Warshall presents a theorem on boolean matrices. He defines the boolean product A ∧ B and boolean sum A ∨ B. The paper discusses the use of boolean matrices to represent program topology and the transformation of a d×d boolean matrix M to another matrix M'. The transformation is defined as the boolean sum of boolean products of M's powers. Warshall proves an algorithm that computes M* which equals M'. The algorithm involves initializing M* as M, then iteratively updating entries based on previous values. The proof shows that if an entry in M* is 1, then the corresponding entry in M' is also 1. The reverse implication is also proven, showing that if an entry in M' is 1, then the corresponding entry in M* must be 1. The algorithm's running time is slightly faster than the square of d. The paper references two prior works on boolean matrices.Stephen Warshall presents a theorem on boolean matrices. He defines the boolean product A ∧ B and boolean sum A ∨ B. The paper discusses the use of boolean matrices to represent program topology and the transformation of a d×d boolean matrix M to another matrix M'. The transformation is defined as the boolean sum of boolean products of M's powers. Warshall proves an algorithm that computes M* which equals M'. The algorithm involves initializing M* as M, then iteratively updating entries based on previous values. The proof shows that if an entry in M* is 1, then the corresponding entry in M' is also 1. The reverse implication is also proven, showing that if an entry in M' is 1, then the corresponding entry in M* must be 1. The algorithm's running time is slightly faster than the square of d. The paper references two prior works on boolean matrices.