Some Exact Complexity Results for Straight-Line Computations over Semirings

The problem of computing polynomials in certain semmngs is considered. Precise bounds are obtained on the number of multiplications required by straight-hne algorithms which compute such functions as iterated matrix multiplication, iterated convolution, and permanent Usmg these bounds, tt is shown that the use of branching can exponentially speed up computations using the min, + operations, and that subtraction can exponentially speed up arithmetic computations These results can be interpreted as denying the existence of fast "universal" algorithms for computing certain polynomials K~V wol~os AND prmASES artthmeuc complexity, convexity theory, Farkas Lemma, minimax algebra, straight-hne algorithm

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