Optimal unateness testers for real-valued functions: Adaptivity helps

Roksana Baleshzar, Deeparnab Chakrabarty, Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, C. Seshadhri

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

We study the problem of testing unateness of functions f: {0, 1}d → ℝ. We give an O(d/ϵ · log O(d/ϵ)- query nonadaptive tester and an O(O(d/ϵ)-query adaptive tester and show that both testers are optimal for a fixed distance parameter ϵ. 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.

Original languageEnglish (US)
Title of host publication44th International Colloquium on Automata, Languages, and Programming, ICALP 2017
EditorsAnca Muscholl, Piotr Indyk, Fabian Kuhn, Ioannis Chatzigiannakis
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770415
DOIs
StatePublished - Jul 1 2017
Event44th International Colloquium on Automata, Languages, and Programming, ICALP 2017 - Warsaw, Poland
Duration: Jul 10 2017Jul 14 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume80
ISSN (Print)1868-8969

Other

Other44th International Colloquium on Automata, Languages, and Programming, ICALP 2017
CountryPoland
CityWarsaw
Period7/10/177/14/17

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All Science Journal Classification (ASJC) codes

  • Software

Cite this

Baleshzar, R., Chakrabarty, D., Pallavoor, R. K. S., Raskhodnikova, S., & Seshadhri, C. (2017). Optimal unateness testers for real-valued functions: Adaptivity helps. In A. Muscholl, P. Indyk, F. Kuhn, & I. Chatzigiannakis (Eds.), 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017 [5] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 80). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ICALP.2017.5