{"id":"https://openalex.org/W2186390088","doi":"https://doi.org/10.4086/toc.2011.v007a011","title":"","display_name":"","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2186390088","doi":"https://doi.org/10.4086/toc.2011.v007a011","mag":"2186390088"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2011.v007a011","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2011.v007a011","pdf_url":"https://theoryofcomputing.org/articles/v007a011/v007a011.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":"https://theoryofcomputing.org/articles/v007a011/v007a011.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001007406","display_name":"Elya Dolev","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Elya Dolev","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5063746987","display_name":"Dana Ron","orcid":"https://orcid.org/0000-0001-6576-7200"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dana Ron","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":0.912,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.83675512,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"7","issue":"1","first_page":"155","last_page":"176"},"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":0.9997000098228455,"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/T12288","display_name":"Optimization and Search Problems","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/monomial","display_name":"Monomial","score":0.9096606969833374},{"id":"https://openalex.org/keywords/property-testing","display_name":"Property testing","score":0.8203099966049194},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6664369702339172},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6517857313156128},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.551059901714325},{"id":"https://openalex.org/keywords/contrast","display_name":"Contrast (vision)","score":0.5348049402236938},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4724205732345581},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.46998679637908936},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4298988878726959},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.42577987909317017},{"id":"https://openalex.org/keywords/uniform-distribution","display_name":"Uniform distribution (continuous)","score":0.42335373163223267},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41916099190711975},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2288835048675537},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10642123222351074},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07474318146705627}],"concepts":[{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.9096606969833374},{"id":"https://openalex.org/C123842658","wikidata":"https://www.wikidata.org/wiki/Q2918980","display_name":"Property testing","level":2,"score":0.8203099966049194},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6664369702339172},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6517857313156128},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.551059901714325},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.5348049402236938},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4724205732345581},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.46998679637908936},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4298988878726959},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.42577987909317017},{"id":"https://openalex.org/C108882938","wikidata":"https://www.wikidata.org/wiki/Q274506","display_name":"Uniform distribution (continuous)","level":2,"score":0.42335373163223267},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41916099190711975},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2288835048675537},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10642123222351074},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07474318146705627},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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":1,"locations":[{"id":"doi:10.4086/toc.2011.v007a011","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2011.v007a011","pdf_url":"https://theoryofcomputing.org/articles/v007a011/v007a011.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.2011.v007a011","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2011.v007a011","pdf_url":"https://theoryofcomputing.org/articles/v007a011/v007a011.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/G3363470889","display_name":null,"funder_award_id":"246/08","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2186390088.pdf","grobid_xml":"https://content.openalex.org/works/W2186390088.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1488030543","https://openalex.org/W1557097080","https://openalex.org/W1586809440","https://openalex.org/W1607834888","https://openalex.org/W1970630090","https://openalex.org/W2012797687","https://openalex.org/W2018925011","https://openalex.org/W2019363670","https://openalex.org/W2042587503","https://openalex.org/W2046654297","https://openalex.org/W2055194501","https://openalex.org/W2061468234","https://openalex.org/W2064609684","https://openalex.org/W2066748671","https://openalex.org/W2073966617","https://openalex.org/W2081192873","https://openalex.org/W2123346810","https://openalex.org/W2140566134","https://openalex.org/W2154224414","https://openalex.org/W2568354864","https://openalex.org/W2914377170","https://openalex.org/W2914539165","https://openalex.org/W3004537778","https://openalex.org/W3023302315","https://openalex.org/W4235805661","https://openalex.org/W4238893454","https://openalex.org/W4249956697","https://openalex.org/W4391285994"],"related_works":["https://openalex.org/W4247687185","https://openalex.org/W1530005306","https://openalex.org/W2569682947","https://openalex.org/W3012217727","https://openalex.org/W2963396042","https://openalex.org/W2951610245","https://openalex.org/W2717711556","https://openalex.org/W2069059622","https://openalex.org/W3037410748","https://openalex.org/W2892448241"],"abstract_inverted_index":{"We":[0,143],"consider":[1],"the":[2,8,14,35,58,89,160,165,189],"problem":[3],"of":[4,7,10,16,30,32,101,176,188],"distribution-free":[5,41,107,134,152],"testing":[6],"class":[9,15],"monotone":[11,110],"monomials":[12,17,76,111,117,177],"and":[13,49,85,98,171],"over":[18],"$n$":[19],"variables.":[20],"While":[21],"there":[22],"are":[23],"very":[24],"efficient":[25],"testers":[26,42,135,155,161],"for":[27,74,109,115,136,151],"a":[28,72,124,185],"variety":[29],"classes":[31,138],"functions":[33,179],"when":[34],"underlying":[36,59],"distribution":[37,60],"is":[38,61,92],"uniform,":[39,62],"designing":[40],"(which":[43],"must":[44,118],"work":[45,163,198],"under":[46,164],"an":[47],"arbitrary":[48],"unknown":[50],"distribution)":[51],"tends":[52],"to":[53,148],"be":[54],"more":[55],"challenging.":[56],"When":[57],"Parnas":[63],"et":[64],"al.":[65],"(SIAM":[66],"J.":[67],"Discr.":[68],"Math.,":[69],"2002)":[70],"give":[71],"tester":[73,108],"(monotone)":[75],"whose":[77,86],"query":[78,120,140],"complexity":[79,121,141],"does":[80],"not":[81,157,194],"depend":[82],"on":[83,88,159,184,199],"$n$,":[84],"dependence":[87],"distance":[90,126],"parameter":[91,127],"(inverse)":[93],"linear.":[94],"In":[95,129],"contrast,":[96],"Glasner":[97],"Servedio":[99],"(Theory":[100],"Computing,":[102],"2009)":[103],"prove":[104],"that":[105,145,162,180],"every":[106],"as":[112,114],"well":[113],"general":[116],"have":[119],"$\\widetilde{\\Omega}(n^{1/5})$":[122],"(for":[123],"constant":[125],"$\\epsilon$).":[128],"this":[130],"paper":[131],"we":[132,169],"present":[133],"these":[137],"whith":[139],"$\\widetilde{O}(n^{1/2}/\\epsilon)$.":[142],"note":[144],"in":[146,196],"contrast":[147],"previous":[149,197],"results":[150],"testing,":[153],"our":[154],"do":[156],"build":[158],"uniform":[166],"distribution.":[167],"Rather,":[168],"define":[170],"exploit":[172],"certain":[173],"structural":[174],"properties":[175],"(and":[178],"differ":[181],"from":[182],"them":[183],"non-negligible":[186],"part":[187],"input":[190],"space),":[191],"which":[192],"were":[193],"used":[195],"property":[200],"testing.":[201]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2016-06-24T00:00:00"}