Lifting with Inner Functions of Polynomial Discrepancy

Yahel Manor; Or Meir

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arXiv · 2404.07606

Lifting with Inner Functions of Polynomial Discrepancy

Yahel Manor·Or Meir

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Abstract

Lifting theorems are theorems that bound the communication complexity of a composed function $f\circ g^{n}$ in terms of the query complexity of $f$ and the communication complexity of $g$. Such theorems constitute a powerful generalization of direct-sum theorems for $g$, and have seen numerous applications in recent years. We prove a new lifting theorem that works for every two functions $f,g$ such that the discrepancy of $g$ is at most inverse polynomial in the input length of $f$. Our result is a significant generalization of the known direct-sum theorem for discrepancy, and extends the range of inner functions $g$ for which lifting theorems hold.

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Yahel Manor, Or Meir. 2024-04-11. Lifting with Inner Functions of Polynomial Discrepancy. https://arxiv.org/abs/2404.07606

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