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Quasi-polynomial hitting-set for set-depth-Δ formulas
2013
Proceedings of the 45th annual ACM symposium on Symposium on theory of computing - STOC '13
We call a depth-4 formula C set-depth-4 if there exists a (unknown) partition X1 • • • X d of the variable indices [n] that the top product layer respects, i.e. C(x) = k i=1 d j=1 fi,j(xX j ), where fi,j is a sparse polynomial in F[xX j ]. Extending this definition to any depth -we call a depth-∆ formula C (consisting of alternating layers of Σ and Π gates, with a Σ-gate on top) a set-depth-∆ formula if every Π-layer in C respects a (unknown) partition on the variables; if ∆ is even then the
doi:10.1145/2488608.2488649
dblp:conf/stoc/AgrawalSS13
fatcat:5ajt6l7etneghgq2kqxyssukmu