{"id":"https://openalex.org/W2267350596","doi":"https://doi.org/10.1145/2897518.2897567","title":"A polynomial lower bound for testing monotonicity","display_name":"A polynomial lower bound for testing monotonicity","publication_year":2016,"publication_date":"2016-06-10","ids":{"openalex":"https://openalex.org/W2267350596","doi":"https://doi.org/10.1145/2897518.2897567","mag":"2267350596"},"language":"en","primary_location":{"id":"doi:10.1145/2897518.2897567","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2897518.2897567","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-eighth annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ir.cwi.nl/pub/25079/25079.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033491812","display_name":"Aleksandrs Belovs","orcid":null},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832","https://openalex.org/I4405262988"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Aleksandrs Belovs","raw_affiliation_strings":["CWI, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CWI, Netherlands","institution_ids":["https://openalex.org/I1341640284"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000042413","display_name":"Eric Blais","orcid":"https://orcid.org/0009-0000-5824-9034"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Eric Blais","raw_affiliation_strings":["University of Waterloo, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":42,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1021","last_page":"1032"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9995999932289124,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9947999715805054,"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/monotonic-function","display_name":"Monotonic function","score":0.8122289180755615},{"id":"https://openalex.org/keywords/property-testing","display_name":"Property testing","score":0.6457414627075195},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6115742921829224},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5359467267990112},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5085152387619019},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4904925227165222},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.4711624085903168},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4568707346916199},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44061946868896484},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.43885353207588196},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.431851863861084},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38174164295196533},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36457207798957825},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.33702027797698975}],"concepts":[{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.8122289180755615},{"id":"https://openalex.org/C123842658","wikidata":"https://www.wikidata.org/wiki/Q2918980","display_name":"Property testing","level":2,"score":0.6457414627075195},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6115742921829224},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5359467267990112},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5085152387619019},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4904925227165222},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.4711624085903168},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4568707346916199},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44061946868896484},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.43885353207588196},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.431851863861084},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38174164295196533},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36457207798957825},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33702027797698975},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2897518.2897567","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2897518.2897567","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-eighth annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:cwi.nl:25079","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/25079","pdf_url":"https://ir.cwi.nl/pub/25079/25079.pdf","source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:cwi.nl:25079","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/25079","pdf_url":"https://ir.cwi.nl/pub/25079/25079.pdf","source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323297","display_name":"Latvijas Universitate","ror":"https://ror.org/05g3mes96"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2267350596.pdf","grobid_xml":"https://content.openalex.org/works/W2267350596.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W104148001","https://openalex.org/W199049232","https://openalex.org/W1564713837","https://openalex.org/W1565608045","https://openalex.org/W1586809440","https://openalex.org/W1786299627","https://openalex.org/W1988511047","https://openalex.org/W2001141376","https://openalex.org/W2038521541","https://openalex.org/W2053267965","https://openalex.org/W2063836706","https://openalex.org/W2070486524","https://openalex.org/W2074734756","https://openalex.org/W2079520411","https://openalex.org/W2085693797","https://openalex.org/W2100732817","https://openalex.org/W2105984887","https://openalex.org/W2106623697","https://openalex.org/W2172810949","https://openalex.org/W2212352090","https://openalex.org/W2296570267","https://openalex.org/W2400386569","https://openalex.org/W2914539165","https://openalex.org/W2949466244","https://openalex.org/W2962825398","https://openalex.org/W4235805661","https://openalex.org/W6633713826","https://openalex.org/W6635006221"],"related_works":["https://openalex.org/W2077314575","https://openalex.org/W4315701745","https://openalex.org/W1990290471","https://openalex.org/W4380682190","https://openalex.org/W2005710836","https://openalex.org/W2102386043","https://openalex.org/W621782861","https://openalex.org/W2951610245","https://openalex.org/W3037410748","https://openalex.org/W961142965"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,66],"every":[3],"algorithm":[4],"for":[5,10,19,24,36,80],"testing":[6,81],"n-variate":[7],"Boolean":[8],"functions":[9],"monotonicityhas":[11],"query":[12,48,78],"complexity":[13,49,79],"\u03a9(n1/4).":[14],"All":[15],"previous":[16,33],"lower":[17,34,63],"bounds":[18],"this":[20],"problem":[21],"were":[22],"designed":[23],"non-adaptive":[25,52],"algorithms":[26],"and,":[27],"as":[28],"a":[29,73],"result,":[30],"the":[31,47,51,77],"best":[32],"bound":[35,64],"general":[37],"(possibly":[38],"adaptive)":[39],"monotonicity":[40,53],"testers":[41],"was":[42],"only":[43],"\u03a9(logn).":[44],"Combined":[45],"with":[46],"of":[50,55],"tester":[54],"Khot,":[56],"Minzer,":[57],"and":[58],"Safra":[59],"(FOCS":[60],"2015),":[61],"our":[62],"shows":[65],"adaptivity":[67],"can":[68],"result":[69],"in":[70,76],"at":[71],"most":[72],"quadratic":[74],"reduction":[75],"monotonicity.":[82]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":3}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
