Automatic reproduction of a genius algorithm: Strassen's algorithm revisited by genetic search
IEEE Transactions on Evolutionary Computation
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This paper develops techniques for establishing a lower bound on the number of arithmetic operations necessary for sets of simple expressions. The techniques are applied to matrix multiplication. A modification of Strassen's algorithm is developed for multiplying n 脳 p matrices by p 脳 q matrices. The techniques are used to prove that this algorithm minimizes the number of multiplications for a few special cases. In so doing we establish that matrix multiplication with elements from a commutative ring requires fewer multiplications than with elements from a non-commutative ring.