2026-07-22T05:23:20Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:7484 2024-03-06T10:40:15Z ddc:004 open_access

Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps Baleshzar, Roksana Chakrabarty, Deeparnab Pallavoor, Ramesh Krishnan S. Raskhodnikova, Sofya Seshadhri, C. Property testing unate and monotone functions We study the problem of testing unateness of functions f:{0,1}^d -> R. We give an O(d/\epsilon . log(d/\epsilon))-query nonadaptive tester and an O(d/\epsilon)-query adaptive tester and show that both testers are optimal for a fixed distance parameter \epsilon. Previously known unateness testers worked only for Boolean functions, and their query complexity had worse dependence on the dimension both for the adaptive and the nonadaptive case. Moreover, no lower bounds for testing unateness were known. We generalize our results to obtain optimal unateness testers for functions f:[n]^d -> R. Our results establish that adaptivity helps with testing unateness of real-valued functions on domains of the form {0,1}^d and, more generally, [n]^d. This stands in contrast to the situation for monotonicity testing where there is no adaptivity gap for functions f:[n]^d -> R. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Roksana Baleshzar and Deeparnab Chakrabarty and Ramesh Krishnan S. Pallavoor and Sofya Raskhodnikova and C. Seshadhri 2017 Is Part Of LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2017.5 urn:nbn:de:0030-drops-74844 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.5 eng https://creativecommons.org/licenses/by/3.0/legalcode