Matrix Boolean multiplication

This modification for Boolean matrix multiplication permits use of the Boolean union operation (logical OR operation or logical sum) instead of regular multiplication and union operations. The Boolean union operation can be executed much faster on a digital computer. Experience has shown that performing the Boolean union of rows instead of the standard Boolean multiplication of matrices can reduce the computation time by as much as a factor of four. 

Boolean matrix multiplication is carried out according to the usual matrix rules, expressed in terms of the logical product and logical sum as defined above. 

One method of partitioning the system equations is to compute the maximal loops using powers of the adjacency matrix as discussed in Section II. Certain modifications to the methods of Section II are needed in order to reduce the computation time. The first modification is to obtain the product of the matrices using Boolean unions of rows instead of the multiplication technique previously demonstrated to obtain a power of an adjacency matrix. To show how the Boolean union of rows can replace the standard matrix multiplication, consider the definition of Boolean matrix multiplication, Eq. (2), which can be expanded to... 

T. Akutsu, S. Miyano, and S. Kuhara, Algorithms for identifying Boolean networks and related biological networks based on matrix multiplication and fingerprint fnnction. / Comput Biol 7(3 ) 331-343 (2000). 

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