Name
Abstract | ||
|---|---|---|
Shpilka and Wigderson [22] had posed the problem of proving exponential lower bounds for (nonhomogeneous) depth three arithmetic circuits with bounded bottom fanin over a field F of characteristic zero. We resolve this problem by proving a [EQUATION] lower bound for (nonhomogeneous) depth three arithmetic circuits with bottom fanin at most τ computing an explicit N-variate polynomial of degree d over F. Meanwhile, Nisan and Wigderson [18] had posed the problem of proving superpolynomial lower bounds for homogeneous depth five arithmetic circuits. Over fields of characteristic zero, we show a lower bound of [EQUATION] for homogeneous depth five circuits (resp. also for depth three circuits) with bottom fanin at most Nμ, for any fixed μ < 1. This resolves the problem posed by Nisan and Wigderson only partially because of the added restriction on the bottom fanin (a general homogeneous depth five circuit has bottom fanin at most N). |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1007/s00037-016-0132-0 | Computational Complexity |
Keywords | DocType | Volume |
Arithmetic circuits, depth three, lower bounds, 68Q15, 68Q17 | Conference | 25 |
Issue | ISSN | Citations |
2 | 1420-8954 | 4 |
PageRank | References | Authors |
0.41 | 18 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Neeraj Kayal | 1 | 263 | 19.39 |
| Chandan Saha | 2 | 227 | 16.91 |