eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-02-04
70:1
70:14
10.4230/LIPIcs.ITCS.2021.70
article
Shrinkage of Decision Lists and DNF Formulas
Rossman, Benjamin
1
Duke University, Durham, NC, USA
We establish nearly tight bounds on the expected shrinkage of decision lists and DNF formulas under the p-random restriction R_p for all values of p ∈ [0,1]. For a function f with domain {0,1}ⁿ, let DL(f) denote the minimum size of a decision list that computes f. We show that E[DL(f ↾ R_p)] ≤ DL(f)^log_{2/(1-p)}((1+p)/(1-p)). For example, this bound is √{DL(f)} when p = √5-2 ≈ 0.24. For Boolean functions f, we obtain the same shrinkage bound with respect to DNF formula size plus 1 (i.e., replacing DL(⋅) with DNF(⋅)+1 on both sides of the inequality).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol185-itcs2021/LIPIcs.ITCS.2021.70/LIPIcs.ITCS.2021.70.pdf
shrinkage
decision lists
DNF formulas