Complexity of monotone networks for Boolean matrix product

Any computation of Boolean matrix product by an acyclic network using only the operations of binary conjunction and disjunction requires at least IJK conjunctions and IJ(K?1) disjunctions for the product of matrices of sizes I×K and K×J. Furthermore any two such networks having these minimum numbers of operations are equivalent using only the commutativity of both operations and the associativity of disjunction.