Direct Sums for Parity Decision Trees

Tyler Besselman; Mika Göös; Siyao Guo; Gilbert Maystre; Weiqiang Yuan

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arXiv · 2412.06552

Direct Sums for Parity Decision Trees

Tyler Besselman·Mika Göös·Siyao Guo·Gilbert Maystre·Weiqiang Yuan

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Abstract

Direct sum theorems state that the cost of solving $k$ instances of a problem is at least $\Omega(k)$ times the cost of solving a single instance. We prove the first such results in the randomised parity decision tree model. We show that a direct sum theorem holds whenever (1) the lower bound for parity decision trees is proved using the discrepancy method; or (2) the lower bound is proved relative to a product distribution.

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Tyler Besselman, Mika Göös, Siyao Guo, Gilbert Maystre, Weiqiang Yuan. 2024-12-09. Direct Sums for Parity Decision Trees. https://arxiv.org/abs/2412.06552

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