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- W3113017116 abstract "We establish nearly tight bounds on the expected shrinkage of decision lists and DNF formulas under the $p$-random restriction $mathbf R_p$ for all values of $p in [0,1]$. For a function $f$ with domain ${0,1}^n$, let $mathrm{DL}(f)$ denote the minimum size of a decision list that computes $f$. We show that [ mathbb E[ mathrm{DL}(f{upharpoonright}mathbf R_p) ] le mathrm{DL}(f)^{log_{2/(1-p)}(frac{1+p}{1-p})}. ] For example, this bound is $sqrt{mathrm{DL}(f)}$ when $p = sqrt{5}-2 approx 0.24$. For Boolean functions $f$, we obtain the same shrinkage bound with respect to DNF formula size plus $1$ (i.e., replacing $mathrm{DL}(cdot)$ with $mathrm{DNF}(cdot)+1$ on both sides of the inequality)." @default.
- W3113017116 created "2020-12-21" @default.
- W3113017116 creator A5007686466 @default.
- W3113017116 date "2020-12-09" @default.
- W3113017116 modified "2023-09-27" @default.
- W3113017116 title "Shrinkage of Decision Lists and DNF Formulas." @default.
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