Math @ Duke

Publications [#359224] of Benjamin Rossman
Papers Published
 Rossman, B, Shrinkage of decision lists and DNF formulas,
Leibniz International Proceedings in Informatics, Lipics, vol. 185
(February, 2021), ISBN 9783959771771 [doi]
(last updated on 2022/01/23)
Abstract: We establish nearly tight bounds on the expected shrinkage of decision lists and DNF formulas under the prandom restriction Rp 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(fRp) ] ≤ DL(f)log2/(1p)(1 1+  p p) . For example, this bound is pDL(f) when p = √52 ≈ 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).


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