{"id":"https://openalex.org/W2152293882","doi":"https://doi.org/10.4086/toc.2010.v006a012","title":"","display_name":"","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2152293882","doi":"https://doi.org/10.4086/toc.2010.v006a012","mag":"2152293882"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2010.v006a012","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2010.v006a012","pdf_url":"https://theoryofcomputing.org/articles/v006a012/v006a012.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/v006a012/v006a012.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013053155","display_name":"Zeev Dvir","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zeev Dvir","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039043184","display_name":"Avi Wigderson","orcid":"https://orcid.org/0000-0002-1539-1417"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Avi Wigderson","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013053155"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3316,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.90122295,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"6","issue":"1","first_page":"291","last_page":"308"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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/T11567","display_name":"semigroups and automata theory","score":0.9988999962806702,"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/monotone-polygon","display_name":"Monotone polygon","score":0.7428485751152039},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.7103116512298584},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.662704348564148},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6073320508003235},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.58371901512146},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5526490807533264},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5119284391403198},{"id":"https://openalex.org/keywords/pseudorandomness","display_name":"Pseudorandomness","score":0.5073296427726746},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49416473507881165},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.47431278228759766},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38586926460266113},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3161463737487793},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16261273622512817}],"concepts":[{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7428485751152039},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.7103116512298584},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.662704348564148},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6073320508003235},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.58371901512146},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5526490807533264},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5119284391403198},{"id":"https://openalex.org/C19086982","wikidata":"https://www.wikidata.org/wiki/Q2115856","display_name":"Pseudorandomness","level":3,"score":0.5073296427726746},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49416473507881165},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.47431278228759766},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38586926460266113},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3161463737487793},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16261273622512817},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2010.v006a012","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2010.v006a012","pdf_url":"https://theoryofcomputing.org/articles/v006a012/v006a012.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.2010.v006a012","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2010.v006a012","pdf_url":"https://theoryofcomputing.org/articles/v006a012/v006a012.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/G4117300866","display_name":null,"funder_award_id":"832797","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4289525447","display_name":null,"funder_award_id":"CCF-0832797","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G630445715","display_name":null,"funder_award_id":"DMS-0835373","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6651341434","display_name":"CDI Type II:  Pseudorandomness","funder_award_id":"0835373","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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2152293882.pdf","grobid_xml":"https://content.openalex.org/works/W2152293882.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W189296720","https://openalex.org/W1485507727","https://openalex.org/W1660438011","https://openalex.org/W1966779504","https://openalex.org/W1967125711","https://openalex.org/W1982180670","https://openalex.org/W1998294201","https://openalex.org/W2006575126","https://openalex.org/W2018047324","https://openalex.org/W2026797659","https://openalex.org/W2031808668","https://openalex.org/W2038643780","https://openalex.org/W2045377861","https://openalex.org/W2045876200","https://openalex.org/W2051758697","https://openalex.org/W2062934582","https://openalex.org/W2077571023","https://openalex.org/W2086156863","https://openalex.org/W2094783167","https://openalex.org/W2130229205","https://openalex.org/W2132890668","https://openalex.org/W2134311784","https://openalex.org/W2136172021","https://openalex.org/W2156569826","https://openalex.org/W2158177004","https://openalex.org/W2402372368","https://openalex.org/W2952371212","https://openalex.org/W4213098650","https://openalex.org/W4235946010"],"related_works":["https://openalex.org/W1489292980","https://openalex.org/W2951610245","https://openalex.org/W2795079910","https://openalex.org/W1430963189","https://openalex.org/W2052430123","https://openalex.org/W3037410748","https://openalex.org/W4319835971","https://openalex.org/W2049901819","https://openalex.org/W1983437306","https://openalex.org/W1974262772"],"abstract_inverted_index":{"The":[0],"main":[1],"purpose":[2],"of":[3,38],"this":[4],"work":[5],"is":[6],"to":[7,21,25],"formally":[8],"define":[9],"monotone":[10,36],"expanders":[11,37],"and":[12,18,24,28],"motivate":[13],"their":[14],"study":[15],"with":[16],"(known":[17],"new)":[19],"connections":[20],"other":[22],"graphs":[23],"several":[26],"computational":[27],"pseudorandomness":[29],"problems.":[30],"In":[31],"particular":[32],"we":[33],"explain":[34],"how":[35],"constant":[39],"degree":[40],"lead":[41],"to:":[42]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2016-06-24T00:00:00"}
