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Testing Submodularity and Other Properties of Valuation Functions Blais, Eric Bommireddi, Abhinav Property testing Testing by implicit learning Self-bounding functions We show that for any constant \epsilon > 0 and p \ge 1, it is possible to distinguish functions f : \{0,1\}^n \to [0,1] that are submodular from those that are \epsilon-far from every submodular function in \ell_p distance with a constant number of queries. More generally, we extend the testing-by-implicit-learning framework of Diakonikolas et al.(2007) to show that every property of real-valued functions that is well-approximated in \ell_2 distance by a class of k-juntas for some k = O(1) can be tested in the \ell_p-testing model with a constant number of queries. This result, combined with a recent junta theorem of Feldman and \Vondrak (2016), yields the constant-query testability of submodularity. It also yields constant-query testing algorithms for a variety of other natural properties of valuation functions, including fractionally additive (XOS) functions, OXS functions, unit demand functions, coverage functions, and self-bounding functions. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Eric Blais and Abhinav Bommireddi 2017 Is Part Of LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2017.33 urn:nbn:de:0030-drops-81619 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.33 eng https://creativecommons.org/licenses/by/3.0/legalcode