{"id":"https://openalex.org/W2180664492","doi":"https://doi.org/10.1007/s00037-012-0055-3","title":"2-Transitivity is Insufficient for Local Testability","display_name":"2-Transitivity is Insufficient for Local Testability","publication_year":2012,"publication_date":"2012-12-17","ids":{"openalex":"https://openalex.org/W2180664492","doi":"https://doi.org/10.1007/s00037-012-0055-3","mag":"2180664492"},"language":"en","primary_location":{"id":"doi:10.1007/s00037-012-0055-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00037-012-0055-3","pdf_url":null,"source":{"id":"https://openalex.org/S193995496","display_name":"Computational Complexity","issn_l":"1016-3328","issn":["1016-3328","1420-8954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"computational complexity","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/A5090091569","display_name":"Elena Grigorescu","orcid":"https://orcid.org/0000-0001-9673-4313"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Elena Grigorescu","raw_affiliation_strings":["Department of Computer Science, Purdue University, West Lafayette, USA","Department of Computer Science, Purdue University, West Lafayette, IN, 47907, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Purdue University, West Lafayette, USA","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Department of Computer Science, Purdue University, West Lafayette, IN, 47907, USA","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109110331","display_name":"Tali Kaufman","orcid":null},"institutions":[{"id":"https://openalex.org/I13955877","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495","country_code":"IL","type":"education","lineage":["https://openalex.org/I13955877"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Tali Kaufman","raw_affiliation_strings":["Computer Science, Bar-Ilan University, Ramat Gan, Israel","Computer Science, Bar-Ilan University, Ramat Gan, 52900, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science, Bar-Ilan University, Ramat Gan, Israel","institution_ids":["https://openalex.org/I13955877"]},{"raw_affiliation_string":"Computer Science, Bar-Ilan University, Ramat Gan, 52900, Israel","institution_ids":["https://openalex.org/I13955877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101519422","display_name":"Madhu Sudan","orcid":"https://orcid.org/0000-0003-3718-6489"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I4400600948","display_name":"Microsoft Research New England (United States)","ror":"https://ror.org/010wkqn50","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4400600948"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Madhu Sudan","raw_affiliation_strings":["Microsoft Research New England, One Memorial Drive, Cambridge, USA","Microsoft Research New England, One Memorial Drive, Cambridge, MA, 02142, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research New England, One Memorial Drive, Cambridge, USA","institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I4400600948"]},{"raw_affiliation_string":"Microsoft Research New England, One Memorial Drive, Cambridge, MA, 02142, USA","institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I4400600948"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5090091569","https://openalex.org/A5101519422","https://openalex.org/A5109110331"],"corresponding_institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I13955877","https://openalex.org/I219193219","https://openalex.org/I4400600948"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":2.2699,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.8906636,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"22","issue":"1","first_page":"137","last_page":"158"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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":0.9995999932289124,"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/T10237","display_name":"Cryptography and Data Security","score":0.9965999722480774,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9912999868392944,"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/transitive-relation","display_name":"Transitive relation","score":0.6887900829315186},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.647493302822113},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6304349899291992},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5343522429466248},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4950534403324127},{"id":"https://openalex.org/keywords/cyclic-code","display_name":"Cyclic code","score":0.480035662651062},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4687770903110504},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4408321976661682},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.43285900354385376},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.41898638010025024},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40032002329826355},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.33784347772598267},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22604167461395264},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.22018113732337952},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21075740456581116},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.11745128035545349}],"concepts":[{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.6887900829315186},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.647493302822113},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6304349899291992},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5343522429466248},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4950534403324127},{"id":"https://openalex.org/C2096984","wikidata":"https://www.wikidata.org/wiki/Q245464","display_name":"Cyclic code","level":5,"score":0.480035662651062},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4687770903110504},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4408321976661682},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.43285900354385376},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.41898638010025024},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40032002329826355},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.33784347772598267},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22604167461395264},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.22018113732337952},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21075740456581116},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.11745128035545349},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00037-012-0055-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00037-012-0055-3","pdf_url":null,"source":{"id":"https://openalex.org/S193995496","display_name":"Computational Complexity","issn_l":"1016-3328","issn":["1016-3328","1420-8954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"computational complexity","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.550000011920929,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1606480398","https://openalex.org/W1970630090","https://openalex.org/W2016987856","https://openalex.org/W2018925011","https://openalex.org/W2019578639","https://openalex.org/W2027040874","https://openalex.org/W2051880745","https://openalex.org/W2053086236","https://openalex.org/W2065465262","https://openalex.org/W2086653003","https://openalex.org/W2097206148","https://openalex.org/W2101060997","https://openalex.org/W2113719649","https://openalex.org/W2126296671","https://openalex.org/W2146453677","https://openalex.org/W2148352980","https://openalex.org/W2151095335","https://openalex.org/W2151626804","https://openalex.org/W2171684223","https://openalex.org/W2912644552","https://openalex.org/W3004537778","https://openalex.org/W3125166132","https://openalex.org/W4256317935"],"related_works":["https://openalex.org/W4248511311","https://openalex.org/W4312970405","https://openalex.org/W2144730981","https://openalex.org/W4312394523","https://openalex.org/W2111330432","https://openalex.org/W2181551151","https://openalex.org/W2157171589","https://openalex.org/W1995198297","https://openalex.org/W3097204850","https://openalex.org/W2290229330"],"abstract_inverted_index":null,"counts_by_year":[{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}