{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:22:58Z","timestamp":1750306978873,"version":"3.41.0"},"reference-count":40,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2018,9,24]],"date-time":"2018-09-24T00:00:00Z","timestamp":1537747200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF 1703925, 1420349 and 1563155"],"award-info":[{"award-number":["CCF 1703925, 1420349 and 1563155"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2019,1,31]]},"abstract":"<jats:p>\n            We study the problem of testing whether an unknown\n            <jats:italic>n<\/jats:italic>\n            -variable Boolean function is a\n            <jats:italic>k<\/jats:italic>\n            -junta in the\n            <jats:italic>distribution-free<\/jats:italic>\n            property testing model, where the distance between functions is measured with respect to an arbitrary and unknown probability distribution over {0,1}\n            <jats:sup>\n              <jats:italic>n<\/jats:italic>\n            <\/jats:sup>\n            . Our first main result is that distribution-free\n            <jats:italic>k<\/jats:italic>\n            -junta testing can be performed, with one-sided error, by an adaptive algorithm that uses \u00d5(\n            <jats:italic>k<\/jats:italic>\n            <jats:sup>2<\/jats:sup>\n            )\/\u03f5 queries (independent of\n            <jats:italic>n<\/jats:italic>\n            ). Complementing this, our second main result is a lower bound showing that any\n            <jats:italic>non-adaptive<\/jats:italic>\n            distribution-free\n            <jats:italic>k<\/jats:italic>\n            -junta testing algorithm must make \u03a9(2\n            <jats:sup>\n              <jats:italic>k<\/jats:italic>\n              \/3\n            <\/jats:sup>\n            ) queries even to test to accuracy \u03f5 = 1\/3. These bounds establish that while the optimal query complexity of non-adaptive\n            <jats:italic>k<\/jats:italic>\n            -junta testing is 2\n            <jats:sup>\n              \u0398(\n              <jats:italic>k<\/jats:italic>\n              )\n            <\/jats:sup>\n            , for adaptive testing it is poly(\n            <jats:italic>k<\/jats:italic>\n            ), and thus show that adaptivity provides an exponential improvement in the distribution-free query complexity of testing juntas.\n          <\/jats:p>","DOI":"10.1145\/3264434","type":"journal-article","created":{"date-parts":[[2018,9,24]],"date-time":"2018-09-24T12:05:57Z","timestamp":1537790757000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Distribution-free Junta Testing"],"prefix":"10.1145","volume":"15","author":[{"given":"Zhengyang","family":"Liu","sequence":"first","affiliation":[{"name":"Shanghai Jiao Tong University, Minhang District, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xi","family":"Chen","sequence":"additional","affiliation":[{"name":"Columbia University, New York, NY, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rocco A.","family":"Servedio","sequence":"additional","affiliation":[{"name":"Columbia University, New York, NY, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Sheng","sequence":"additional","affiliation":[{"name":"Columbia University, New York, NY, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinyu","family":"Xie","sequence":"additional","affiliation":[{"name":"Columbia University, New York, NY, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2018,9,24]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.856958"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2011.12.005"},{"key":"e_1_2_1_3_1","unstructured":"Roksana Baleshzar Meiram Murzabulatov Ramesh Krishnan S. Pallavoor and Sofya Raskhodnikova. 2016. Testing unateness of real-valued functions. CoRR abs\/1608.07652.  Roksana Baleshzar Meiram Murzabulatov Ramesh Krishnan S. Pallavoor and Sofya Raskhodnikova. 2016. Testing unateness of real-valued functions. CoRR abs\/1608.07652."},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897518.2897567"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2010.54"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-85363-3_26"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1536414.1536437"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1109\/CCC.2011.31"},{"volume-title":"Proceedings of the International Conference on Randomization and Computation (RANDOM\u201912)","author":"Blais Eric","key":"e_1_2_1_9_1","unstructured":"Eric Blais and Daniel M. Kane . 2012. Tight bounds for testing k-linearity . In Proceedings of the International Conference on Randomization and Computation (RANDOM\u201912) . 435--446. Eric Blais and Daniel M. Kane. 2012. Tight bounds for testing k-linearity. In Proceedings of the International Conference on Randomization and Computation (RANDOM\u201912). 435--446."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(93)90044-W"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.4086\/cjtcs.2013.006"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/2488608.2488660"},{"key":"e_1_2_1_13_1","unstructured":"Deeparnab Chakrabarty and C. Seshadhri. 2016. A \u00d5(n) non-adaptive tester for unateness. CoRR abs\/1608.06980.  Deeparnab Chakrabarty and C. Seshadhri. 2016. A \u00d5 ( n ) non-adaptive tester for unateness. CoRR abs\/1608.06980."},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/2746539.2746570"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2014.38"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.5555\/3135595.3135621"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/3055399.3055461"},{"key":"e_1_2_1_18_1","volume-title":"Proceedings of the 58th Annual IEEE Symposium on Foundations of Computer Science (FOCS\u201917)","author":"Chen Xi","year":"2017","unstructured":"Xi Chen , Erik Waingarten , and Jinyu Xie . 2017 c. Boolean unateness testing with \u00d5(n<sup>3\/4<\/sup>) adaptive queries . In Proceedings of the 58th Annual IEEE Symposium on Foundations of Computer Science (FOCS\u201917) . 868--879. Xi Chen, Erik Waingarten, and Jinyu Xie. 2017c. Boolean unateness testing with \u00d5(n<sup>3\/4<\/sup>) adaptive queries. 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An O(n) queries adaptive tester for unateness. In Approximation Randomization and Combinatorial Optimization Algorithms and Techniques. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik.  Subhash Khot and Igor Shinkar. 2016. An O(n) queries adaptive tester for unateness. In Approximation Randomization and Combinatorial Optimization Algorithms and Techniques. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik."},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.5555\/1958016.1958029"},{"volume-title":"Proceedings of the International Conference on Approximation Algorithms for Combinatorial Optimization Problems and the International Conference on Randomization and Computation (APPROX-RANDOM\u201909)","author":"Matulef Kevin","key":"e_1_2_1_34_1","unstructured":"Kevin Matulef , Ryan O\u2019Donnell , Ronitt Rubinfeld , and Rocco A. Servedio . 2009. Testing \u00b11-weight halfspace . 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