2026-07-23T06:32:45Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:15827 2024-03-06T10:56:17Z ddc:004 open_access

On Testing Decision Tree Bshouty, Nader H. Haddad-Zaknoon, Catherine A. Testing decision trees In this paper, we study testing decision tree of size and depth that are significantly smaller than the number of attributes n. Our main result addresses the problem of poly(n,1/ε) time algorithms with poly(s,1/ε) query complexity (independent of n) that distinguish between functions that are decision trees of size s from functions that are ε-far from any decision tree of size ϕ(s,1/ε), for some function ϕ > s. The best known result is the recent one that follows from Blanc, Lange and Tan, [Guy Blanc et al., 2020], that gives ϕ(s,1/ε) = 2^{O((log³s)/ε³)}. In this paper, we give a new algorithm that achieves ϕ(s,1/ε) = 2^{O(log² (s/ε))}. Moreover, we study the testability of depth-d decision tree and give a distribution free tester that distinguishes between depth-d decision tree and functions that are ε-far from depth-d² decision tree. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Nader H. Bshouty and Catherine A. Haddad-Zaknoon 2022 Is Part Of LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2022.17 urn:nbn:de:0030-drops-158273 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.17 eng https://creativecommons.org/licenses/by/4.0/legalcode