Size-depth trade-offs for monotone arithmetic circuits

Marc Snir

doi:10.1016/0304-3975(91)90173-Y

Size-depth trade-offs for monotone arithmetic circuits

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Abstract

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.

Original language	English (US)
Pages (from-to)	85-93
Number of pages	9
Journal	Theoretical Computer Science
Volume	82
Issue number	1
DOIs	https://doi.org/10.1016/0304-3975(91)90173-Y
State	Published - May 22 1991
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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AB - 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.

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Size-depth trade-offs for monotone arithmetic circuits

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