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- W2998669040 abstract "We show that any Algebraic Branching Program (ABP) computing the [MATH HERE] has at least Ω(n2) vertices. This improves upon the lower bound of Ω(n log n), which follows from the classical result of Baur and Strassen [24, 1], and extends the results of Kumar [13], which showed a quadratic lower bound for homogeneous ABPs computing the same polynomial.Our proof relies on a notion of depth reduction which is reminiscent of similar statements in the context of matrix rigidity, and shows that any small enough ABP computing the [MATH HERE] can be depth reduced to essentially a homogeneous ABP of the same size which computes the [MATH HERE], for a structured error polynomial e(x). To complete the proof, we then observe that the lower bound in [13] is robust enough and continues to hold for all polynomials [MATH HERE], where e(x) has the appropriate structure." @default.
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- W2998669040 date "2020-07-28" @default.
- W2998669040 modified "2023-09-23" @default.
- W2998669040 title "A quadratic lower bound for algebraic branching programs" @default.
- W2998669040 doi "https://doi.org/10.4230/lipics.ccc.2020.2" @default.
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