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- W3001787625 abstract "We present a deterministic algorithm for reconstructing multilinear ΣΠΣΠ(k) circuits, i.e. multilinear depth-4 circuits with fan-in k at the top + gate. For any fixed k, given black-box access to a polynomial f ∈ F[x1, x2, ..., xn] computable by a multilinear ΣΠΣΠ(k) circuit of size s, the algorithm runs in time quasi-poly(n, s, |F|) and outputs a multilinear ΣΠΣΠ(k) circuit of size quasi-poly(n, s) that computes f. Our result solves an open problem posed in [15] (STOC, 2012). Indeed, prior to our work, efficient reconstruction algorithms for multilinear ΣΠΣΠ(k) circuits were known only for the case of k = 2 [15, 52]." @default.
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- W3001787625 date "2019-01-01" @default.
- W3001787625 modified "2023-09-24" @default.
- W3001787625 title "Reconstruction of Depth-$4$ Multilinear Circuits." @default.
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