{"id":"https://openalex.org/W2296570267","doi":"https://doi.org/10.1007/s004930070011","title":"Testing Monotonicity","display_name":"Testing Monotonicity","publication_year":2000,"publication_date":"2000-03-01","ids":{"openalex":"https://openalex.org/W2296570267","doi":"https://doi.org/10.1007/s004930070011","mag":"2296570267"},"language":"en","primary_location":{"id":"doi:10.1007/s004930070011","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s004930070011","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013698877","display_name":"Oded Goldreich","orcid":"https://orcid.org/0000-0002-4329-135X"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Oded Goldreich","raw_affiliation_strings":["Department of Computer Science and Applied Mathematics, Weizmann Institute of Science; Rehovot, Israel;","[Dept. of Comput. Sci. & Appl. Math., Weizmann Inst. of Sci., Rehovot, Israel]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Applied Mathematics, Weizmann Institute of Science; Rehovot, Israel;","institution_ids":["https://openalex.org/I53964585"]},{"raw_affiliation_string":"[Dept. of Comput. Sci. & Appl. Math., Weizmann Inst. of Sci., Rehovot, Israel]","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062504833","display_name":"S. Goldwassert","orcid":null},"institutions":[{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shafi Goldwasser","raw_affiliation_strings":["Laboratory for Computer Science, MIT; 545 Technology Sq., Cambridge, MA 02139, USA;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Computer Science, MIT; 545 Technology Sq., Cambridge, MA 02139, USA;","institution_ids":["https://openalex.org/I4210110987","https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041227602","display_name":"Eric Lehman","orcid":null},"institutions":[{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eric Lehman","raw_affiliation_strings":["Laboratory for Computer Science, MIT; 545 Technology Sq., Cambridge, MA 02139, USA;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Computer Science, MIT; 545 Technology Sq., Cambridge, MA 02139, USA;","institution_ids":["https://openalex.org/I4210110987","https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Dana Ron","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Dana Ron","raw_affiliation_strings":["Department of EE \u2013 Systems, Tel Aviv University; Ramat Aviv, Israel;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of EE \u2013 Systems, Tel Aviv University; Ramat Aviv, Israel;","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":null,"display_name":"Alex Samorodnitsky","orcid":null},"institutions":[{"id":"https://openalex.org/I40036882","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463","country_code":"US","type":"facility","lineage":["https://openalex.org/I40036882"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alex Samorodnitsky","raw_affiliation_strings":["School of Mathematics, Institute for Advanced Study; Olden Lane, Princeton, NJ 08540, USA;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Institute for Advanced Study; Olden Lane, Princeton, NJ 08540, USA;","institution_ids":["https://openalex.org/I40036882"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.3093,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.95725894,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"20","issue":"3","first_page":"301","last_page":"337"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":1.0,"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":1.0,"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":0.9976000189781189,"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/T11567","display_name":"semigroups and automata theory","score":0.994700014591217,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/property-testing","display_name":"Property testing","score":0.839309811592102},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.8383195996284485},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.7352697849273682},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6946675181388855},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6089358925819397},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5961658954620361},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5709128975868225},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.558165431022644},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5299055576324463},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5142583250999451},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.4250541925430298},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11664876341819763}],"concepts":[{"id":"https://openalex.org/C123842658","wikidata":"https://www.wikidata.org/wiki/Q2918980","display_name":"Property testing","level":2,"score":0.839309811592102},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.8383195996284485},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.7352697849273682},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6946675181388855},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6089358925819397},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5961658954620361},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5709128975868225},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.558165431022644},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5299055576324463},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5142583250999451},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.4250541925430298},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11664876341819763},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1007/s004930070011","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s004930070011","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"doi:10.1109/sfcs.1998.743493","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sfcs.1998.743493","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.17.2393","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.2393","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.wisdom.weizmann.ac.il/~oded/PS/mon1.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.207.7867","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.207.7867","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://theory.lcs.mit.edu/%7Ecis/pubs/shafi/1998-focs.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.31.1111","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.1111","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eng.tau.ac.il/~danar/Public/mon-comb.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.48.3133","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.3133","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://theory.lcs.mit.edu/pub/people/danar/mon-long.ps.gz","raw_type":"text"},{"id":"mag:2296570267","is_oa":false,"landing_page_url":"http://ieeexplore.ieee.org/iel4/5965/15971/00743493.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306418447","display_name":"Foundations of Computer Science","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":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Foundations of Computer Science","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1971801736","https://openalex.org/W1978916077","https://openalex.org/W1983593474","https://openalex.org/W1991006936","https://openalex.org/W2002864099","https://openalex.org/W2003159902","https://openalex.org/W2018925011","https://openalex.org/W2019578639","https://openalex.org/W2053086236","https://openalex.org/W2056168287","https://openalex.org/W2094878497","https://openalex.org/W2097206148","https://openalex.org/W2100654536","https://openalex.org/W2111385661","https://openalex.org/W2139709458","https://openalex.org/W2141815340","https://openalex.org/W2142399242","https://openalex.org/W2144579822","https://openalex.org/W2148352980","https://openalex.org/W2152221184","https://openalex.org/W2156516121","https://openalex.org/W2165100639","https://openalex.org/W2294022756","https://openalex.org/W3004537778","https://openalex.org/W4230174951","https://openalex.org/W4252861488","https://openalex.org/W4256317935"],"related_works":["https://openalex.org/W2018925011","https://openalex.org/W1970630090","https://openalex.org/W1586809440","https://openalex.org/W2038521541","https://openalex.org/W2056168287","https://openalex.org/W2100732817","https://openalex.org/W2294022756","https://openalex.org/W2105984887","https://openalex.org/W2016443407","https://openalex.org/W2949466244","https://openalex.org/W2061468234","https://openalex.org/W3004537778","https://openalex.org/W2963845289","https://openalex.org/W2129311580","https://openalex.org/W2127090196","https://openalex.org/W1909155726","https://openalex.org/W3023302315","https://openalex.org/W2914539165","https://openalex.org/W1997855358","https://openalex.org/W1986542077"],"abstract_inverted_index":{"We":[0,108,125],"present":[1],"a":[2,33,92,143],"(randomized)":[3],"test":[4,30,71],"for":[5],"monotonicity":[6,115],"of":[7,26,64,69,77,113,138],"Boolean":[8,93],"functions.":[9],"Namely,":[10],"given":[11],"the":[12,29,65,70,99,102,111,123,136],"ability":[13],"to":[14,91,98,106],"query":[15],"an":[16,60,127,148],"unknown":[17],"function":[18,53,100],"f:":[19],"{0,":[20],"1}/sup":[21],"n/-{0,":[22],"1}":[23],"at":[24],"arguments":[25],"its":[27],"choice,":[28],"always":[31],"accepts":[32],"monotone":[34,49,52],"f,":[35],"and":[36,101,141],"rejects":[37],"f":[38,56],"with":[39,89],"high":[40],"probability":[41],"if":[42],"it":[43],"is":[44,72],"/spl":[45,61,128],"epsiv/-far":[46],"from":[47,55],"being":[48,96,104],"(i.e.,":[50],"every":[51],"differs":[54],"on":[57,118,135],"more":[58],"than":[59],"epsiv/":[62],"fraction":[63],"domain).":[66],"The":[67,75],"complexity":[68],"poly(n//spl":[73],"epsiv/).":[74],"analysis":[76],"our":[78],"algorithm":[79],"relates":[80],"two":[81],"natural":[82],"combinatorial":[83],"quantities":[84],"that":[85],"can":[86],"be":[87],"measured":[88],"respect":[90],"function;":[94],"one":[95],"global":[97],"other":[103],"local":[105],"it.":[107],"also":[109],"consider":[110],"problem":[112],"testing":[114],"based":[116],"only":[117],"random":[119],"examples":[120],"labeled":[121],"by":[122],"function.":[124],"show":[126],"Omega/(/spl":[129],"radic/2/sup":[130],"n///spl":[131],"epsiv/)":[132],"lower":[133],"bound":[134,146],"number":[137],"required":[139],"examples,":[140],"provide":[142],"matching":[144],"upper":[145],"(via":[147],"algorithm).":[149]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}