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DOI: 10.4230/LIPIcs.ITCS.2021.70
URN: urn:nbn:de:0030-drops-136098
URL: https://drops.dagstuhl.de/opus/volltexte/2021/13609/
Rossman, Benjamin
Shrinkage of Decision Lists and DNF Formulas
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Abstract
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).
BibTeX - Entry
@InProceedings{rossman:LIPIcs.ITCS.2021.70,
author = {Benjamin Rossman},
title = {{Shrinkage of Decision Lists and DNF Formulas}},
booktitle = {12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
pages = {70:1--70:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-177-1},
ISSN = {1868-8969},
year = {2021},
volume = {185},
editor = {James R. Lee},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/13609},
URN = {urn:nbn:de:0030-drops-136098},
doi = {10.4230/LIPIcs.ITCS.2021.70},
annote = {Keywords: shrinkage, decision lists, DNF formulas}
}
| Keywords: | shrinkage, decision lists, DNF formulas | |
| Seminar: | 12th Innovations in Theoretical Computer Science Conference (ITCS 2021) | |
| Issue date: | 2021 | |
| Date of publication: | 04.02.2021 |
