Raymond F. Boyce, Donald D. Chamberlin, et al.
CACM
Consider the problem of computing the product a1A(1)⋯A(t)b, where A(1),...,A(t) are n × n matrices, a and b are vectors. We show that the size s and depth d of monotone arithmetic circuits for this problem are related as s + n3d = Ω(tn3) Thus, a reduction to depth d = o(t) requires an increase from (optimal) size n2t to size n3t. A similar trade-off is shown for the evaluation of linear recurrences. © 1991.
Raymond F. Boyce, Donald D. Chamberlin, et al.
CACM
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CONTEXT 2005
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CoNEXT 2006
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ACL 2007