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Improved Low-Depth Set-Multilinear Circuit Lower Bounds
[article]

2022
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arXiv
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pre-print

We prove strengthened lower bounds for constant-depth set-multilinear formulas. More precisely, we show that over any field, there is an explicit polynomial f in VNP defined over n^2 variables, and of degree n, such that any product-depth Δ set-multilinear formula computing f has size at least n^Ω( n^1/Δ/Δ). The hard polynomial f comes from the class of Nisan-Wigderson (NW) design-based polynomials. Our lower bounds improve upon the recent work of Limaye, Srinivasan and Tavenas (STOC 2022),

arXiv:2205.00611v1
fatcat:76itrp6dj5b3zcfhvwcy5dotje