Size-depth trade-offs for monotone arithmetic circuits

Marc Snir
1991 Theoretical Computer Science  
Snir, M., Size-depth trade-offs for monotone arithmetic circuits, Theoretical Computer Science 82 (1991) 85-93. Consider the problem of computing the product u'A"' -* -A"'6, where A"', . . . , A"' are n x n matrices, u and 6 are vectors. We show that the size s and depth d of monotone arithmetic circuits for this problem are related as s + n3d = R( tn.') Thus, a reduction to depth d similar trade-off is shown for = o( t ) requires an increase from (opt imal) size n't to size n"t. A the evaluation of linear recurrences.
doi:10.1016/0304-3975(91)90173-y fatcat:nn52764ewjaknaawxnau47z64i