{"id":"https://openalex.org/W2942259633","doi":"https://doi.org/10.4086/toc.2019.v015a001","title":"","display_name":"","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2942259633","doi":"https://doi.org/10.4086/toc.2019.v015a001","mag":"2942259633"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2019.v015a001","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2019.v015a001","pdf_url":"http://www.theoryofcomputing.org/articles/v015a001/v015a001.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://www.theoryofcomputing.org/articles/v015a001/v015a001.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071869723","display_name":"Cl\u00e9ment L. Canonne","orcid":"https://orcid.org/0000-0001-7153-5211"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Clement L. Canonne","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090091569","display_name":"Elena Grigorescu","orcid":"https://orcid.org/0000-0001-9673-4313"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Elena Grigorescu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103160306","display_name":"Siyao Guo","orcid":"https://orcid.org/0000-0002-8402-1866"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Siyao Guo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100755285","display_name":"Akash Kumar","orcid":"https://orcid.org/0000-0001-7125-1737"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Akash Kumar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5042196132","display_name":"Karl Wimmer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Karl Wimmer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4755,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.73320187,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"15","issue":"1","first_page":"1","last_page":"55"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12535","display_name":"Machine Learning and Data Classification","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/property-testing","display_name":"Property testing","score":0.8108511567115784},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.7853953838348389},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.7814708948135376},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6806197166442871},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.664243221282959},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6111551523208618},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5341770648956299},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5205053687095642},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.5135600566864014},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.48264700174331665},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4688704311847687},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.46783649921417236},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4357106685638428},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09782835841178894},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07553866505622864}],"concepts":[{"id":"https://openalex.org/C123842658","wikidata":"https://www.wikidata.org/wiki/Q2918980","display_name":"Property testing","level":2,"score":0.8108511567115784},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7853953838348389},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.7814708948135376},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6806197166442871},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.664243221282959},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6111551523208618},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5341770648956299},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5205053687095642},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.5135600566864014},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.48264700174331665},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4688704311847687},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.46783649921417236},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4357106685638428},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09782835841178894},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07553866505622864},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2019.v015a001","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2019.v015a001","pdf_url":"http://www.theoryofcomputing.org/articles/v015a001/v015a001.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4086/toc.2019.v015a001","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2019.v015a001","pdf_url":"http://www.theoryofcomputing.org/articles/v015a001/v015a001.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1498875312","display_name":"AF: Small:  Learning and Testing Classes of Distributions","funder_award_id":"1319788","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4802441260","display_name":null,"funder_award_id":"CCF-1319788","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5465299154","display_name":null,"funder_award_id":"NSF CCF-1649515","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6093009578","display_name":null,"funder_award_id":"CCF-1115703","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G697731757","display_name":"EAGER:   Complexity of Computation on Codes and Lattices","funder_award_id":"1649515","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G80611279","display_name":null,"funder_award_id":"CCF-1649515","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320319918","display_name":"York University","ror":"https://ror.org/05fq50484"},{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2942259633.pdf","grobid_xml":"https://content.openalex.org/works/W2942259633.grobid-xml"},"referenced_works_count":61,"referenced_works":["https://openalex.org/W74032123","https://openalex.org/W1528180898","https://openalex.org/W1557882449","https://openalex.org/W1586809440","https://openalex.org/W1786299627","https://openalex.org/W1891181203","https://openalex.org/W1964775192","https://openalex.org/W1966278576","https://openalex.org/W1983415430","https://openalex.org/W1986542077","https://openalex.org/W1988511047","https://openalex.org/W1992650621","https://openalex.org/W2001141376","https://openalex.org/W2011717937","https://openalex.org/W2016443407","https://openalex.org/W2019363670","https://openalex.org/W2024435371","https://openalex.org/W2029370139","https://openalex.org/W2029876610","https://openalex.org/W2038521541","https://openalex.org/W2071769989","https://openalex.org/W2073966617","https://openalex.org/W2085693797","https://openalex.org/W2092614531","https://openalex.org/W2094878497","https://openalex.org/W2100732817","https://openalex.org/W2105984887","https://openalex.org/W2106458073","https://openalex.org/W2116455242","https://openalex.org/W2119024968","https://openalex.org/W2121615984","https://openalex.org/W2132467825","https://openalex.org/W2139709458","https://openalex.org/W2142399242","https://openalex.org/W2168115971","https://openalex.org/W2212352090","https://openalex.org/W2265337971","https://openalex.org/W2267350596","https://openalex.org/W2278426376","https://openalex.org/W2296292655","https://openalex.org/W2400386569","https://openalex.org/W2490907619","https://openalex.org/W2514222156","https://openalex.org/W2515694000","https://openalex.org/W2553932890","https://openalex.org/W2593853527","https://openalex.org/W2952208743","https://openalex.org/W2962917999","https://openalex.org/W2963754417","https://openalex.org/W2963845289","https://openalex.org/W3023302315","https://openalex.org/W3102754027","https://openalex.org/W4226347946","https://openalex.org/W4235805661","https://openalex.org/W4238893454","https://openalex.org/W4249956697","https://openalex.org/W4252861488","https://openalex.org/W4254911307","https://openalex.org/W6910507753","https://openalex.org/W6929182515","https://openalex.org/W6966394780"],"related_works":["https://openalex.org/W4221165195","https://openalex.org/W4247687185","https://openalex.org/W2569682947","https://openalex.org/W2396049940","https://openalex.org/W170121841","https://openalex.org/W3012217727","https://openalex.org/W2091126969","https://openalex.org/W2963396042","https://openalex.org/W2951610245","https://openalex.org/W2717711556"],"abstract_inverted_index":{"$":[0,3],"\\newcommand{\\ensuremath}[1]{#1}":[1],"\\newcommand{\\eps}{\\ensuremath{\\varepsilon}}":[2],"A":[4],"Boolean":[5],"$k$-monotone":[6,33,54,86,104,170],"function":[7],"defined":[8],"over":[9],"a":[10,82,126,144,184,201,217],"finite":[11],"poset":[12],"domain":[13,137],"$\\mathcal{D}$":[14],"alternates":[15],"between":[16,128,146],"the":[17,39,45,50,57,67,75,89,96,122,135,230,240,259,262],"values":[18],"$0$":[19],"and":[20,62,65,131,148,243],"$1$":[21],"at":[22],"most":[23],"$k$":[24],"times":[25],"on":[26,134,150,216,239],"any":[27],"ascending":[28],"chain":[29],"in":[30,53,56,74,88,210,258,265],"$\\mathcal{D}$.":[31],"Therefore,":[32],"functions":[34,55,101,112,171,190,207],"are":[35,44,103,106,114],"natural":[36],"generalizations":[37],"of":[38,59,77,85,189,196,206,236,254,261],"classical":[40],"monotone":[41],"functions,":[42,87],"which":[43,213],"$1$-monotone":[46],"functions.":[47],"Motivated":[48],"by":[49,66,221],"recent":[51],"interest":[52],"context":[58,76],"circuit":[60],"complexity":[61,194],"learning":[63,149,169],"theory,":[64],"central":[68],"role":[69],"that":[70,102,113],"monotonicity":[71,205],"testing":[72,91,129,132,147,155,248],"plays":[73],"property":[78,90],"testing,":[79],"we":[80],"initiate":[81],"systematic":[83],"study":[84],"model.":[92],"In":[93],"this":[94,255],"model,":[95],"goal":[97],"is":[98],"to":[99,108,246],"distinguish":[100],"(or":[105],"close":[107],"being":[109,117],"$k$-monotone)":[110],"from":[111,116],"far":[115],"$k$-monotone.":[118],"Our":[119,227],"results":[120],"include":[121],"following.":[123],"We":[124,142,182],"demonstrate":[125,143],"separation":[127,145],"$k$-monotonicity":[130,156,188],"monotonicity,":[133],"hypercube":[136],"$\\{0,1\\}^d$,":[138,151],"for":[139,152,187,204],"$k\\geq":[140],"3$;":[141],"$k=\\omega(\\log":[153],"d)$:":[154],"can":[157],"be":[158],"performed":[159],"with":[160,193],"$\\exp(O(\\sqrt":[161],"d":[162],"\\cdot":[163],"\\log":[164],"d\\cdot":[165],"\\log(1/\\eps)))$":[166],"queries,":[167],"while":[168],"requires":[172],"$\\exp(\\Omega(k\\cdot":[173],"\\sqrt":[174],"d\\cdot{1/\\eps}))$":[175],"queries":[176],"(Blais":[177],"et":[178,223],"al.":[179,224],"(RANDOM":[180],"2015));":[181],"present":[183],"tolerant":[185,202],"test":[186,199,203],"$f\\colon[n]^d\\to":[191,208],"\\{0,1\\}$":[192],"independent":[195],"$n$.":[197],"The":[198],"implies":[200],"[0,1]$":[209],"$\\ell_1$":[211],"distance,":[212],"makes":[214],"progress":[215],"problem":[218],"left":[219],"open":[220],"Berman":[222],"(STOC":[225],"2014).":[226],"techniques":[228],"exploit":[229],"testing-by-learning":[231],"paradigm,":[232],"use":[233],"novel":[234],"applications":[235],"Fourier":[237],"analysis":[238],"grid":[241],"$[n]^d$,":[242],"draw":[244],"connections":[245],"distribution":[247],"techniques.":[249],"----------":[250],"An":[251],"extended":[252],"abstract":[253],"paper":[256],"appeared":[257],"Proceedings":[260],"8th":[263],"Innovations":[264],"Theoretical":[266],"Computer":[267],"Science":[268],"conference,":[269],"2017.":[270]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2019-05-03T00:00:00"}
