2026-07-24T22:06:31Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16365 2024-03-06T10:57:17Z ddc:004 open_access

Reconstructing Decision Trees Blanc, Guy Lange, Jane Tan, Li-Yang Property reconstruction property testing tolerant testing decision trees We give the first reconstruction algorithm for decision trees: given queries to a function f that is opt-close to a size-s decision tree, our algorithm provides query access to a decision tree T where: - T has size S := s^O((log s)²/ε³); - dist(f,T) ≤ O(opt)+ε; - Every query to T is answered with poly((log s)/ε)⋅ log n queries to f and in poly((log s)/ε)⋅ n log n time. This yields a tolerant tester that distinguishes functions that are close to size-s decision trees from those that are far from size-S decision trees. The polylogarithmic dependence on s in the efficiency of our tester is exponentially smaller than that of existing testers. Since decision tree complexity is well known to be related to numerous other boolean function properties, our results also provide a new algorithm for reconstructing and testing these properties. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Guy Blanc and Jane Lange and Li-Yang Tan 2022 Is Part Of LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2022.24 urn:nbn:de:0030-drops-163653 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.24 eng https://creativecommons.org/licenses/by/4.0/legalcode