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- W2592941363 abstract "We show tight upper and lower bounds for switching lemmas obtained by the action of random $p$-restrictions on boolean functions that can be expressed as decision trees in which every vertex is at a distance of at most $t$ from some leaf, also called $t$-clipped decision trees. More specifically, we show the following: $bullet$ If a boolean function $f$ can be expressed as a $t$-clipped decision tree, then under the action of a random $p$-restriction $rho$, the probability that the smallest depth decision tree for $f|_{rho}$ has depth greater than $d$ is upper bounded by $(4p2^{t})^{d}$. $bullet$ For every $t$, there exists a function $g_{t}$ that can be expressed as a $t$-clipped decision tree, such that under the action of a random $p$-restriction $rho$, the probability that the smallest depth decision tree for $g_{t}|_{rho}$ has depth greater than $d$ is lower bounded by $(c_{0}p2^{t})^{d}$, for $0leq pleq c_{p}2^{-t}$ and $0leq dleq c_{d}frac{log n}{2^{t}log t}$, where $c_{0},c_{p},c_{d}$ are universal constants." @default.
- W2592941363 created "2017-03-16" @default.
- W2592941363 creator A5010651923 @default.
- W2592941363 date "2017-02-28" @default.
- W2592941363 modified "2023-09-27" @default.
- W2592941363 title "Tree tribes and lower bounds for switching lemmas" @default.
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