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- W4295772061 abstract "Suppose we have randomized decision trees for an outer function $f$ and an inner function $g$. The natural approach for obtaining a randomized decision tree for the composed function $(fcirc g^n)(x^1,ldots,x^n)=f(g(x^1),ldots,g(x^n))$ involves amplifying the success probability of the decision tree for $g$, so that a union bound can be used to bound the error probability over all the coordinates. The amplification introduces a logarithmic factor cost overhead. We study the question: When is this log factor necessary? We show that when the outer function is parity or majority, the log factor can be necessary, even for models that are more powerful than plain randomized decision trees. Our results are related to, but qualitatively strengthen in various ways, known results about decision trees with noisy inputs." @default.
- W4295772061 created "2022-09-15" @default.
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- W4295772061 date "2020-06-19" @default.
- W4295772061 modified "2023-09-26" @default.
- W4295772061 title "When Is Amplification Necessary for Composition in Randomized Query Complexity?" @default.
- W4295772061 doi "https://doi.org/10.48550/arxiv.2006.10957" @default.
- W4295772061 hasPublicationYear "2020" @default.
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