{"id":"https://openalex.org/W2071283394","doi":"https://doi.org/10.1142/s0218196704001980","title":"THE GROUPS OF RICHARD THOMPSON AND COMPLEXITY","display_name":"THE GROUPS OF RICHARD THOMPSON AND COMPLEXITY","publication_year":2004,"publication_date":"2004-10-01","ids":{"openalex":"https://openalex.org/W2071283394","doi":"https://doi.org/10.1142/s0218196704001980","mag":"2071283394"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196704001980","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196704001980","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5109973858","display_name":"Jean-Camille Birget","orcid":null},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"JEAN-CAMILLE BIRGET","raw_affiliation_strings":["Department of Computer Science, Rutgers University at Camden, Camden, NJ 08102, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Rutgers University at Camden, Camden, NJ 08102, USA","institution_ids":["https://openalex.org/I102322142"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109973858"],"corresponding_institution_ids":["https://openalex.org/I102322142"],"apc_list":null,"apc_paid":null,"fwci":5.0305,"has_fulltext":false,"cited_by_count":88,"citation_normalized_percentile":{"value":0.95804774,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"14","issue":"05n06","first_page":"569","last_page":"626"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8971019387245178},{"id":"https://openalex.org/keywords/word-problem","display_name":"Word problem (mathematics education)","score":0.6550678014755249},{"id":"https://openalex.org/keywords/undecidable-problem","display_name":"Undecidable problem","score":0.6137261390686035},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.518497109413147},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5054588317871094},{"id":"https://openalex.org/keywords/nondeterministic-algorithm","display_name":"Nondeterministic algorithm","score":0.4661712944507599},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.45746666193008423},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.45509597659111023},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.4507952034473419},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4504294991493225},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.43132686614990234},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.3383401334285736},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.2548636198043823},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.18834498524665833}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8971019387245178},{"id":"https://openalex.org/C90988201","wikidata":"https://www.wikidata.org/wiki/Q255912","display_name":"Word problem (mathematics education)","level":2,"score":0.6550678014755249},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.6137261390686035},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.518497109413147},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5054588317871094},{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.4661712944507599},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.45746666193008423},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.45509597659111023},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.4507952034473419},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4504294991493225},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.43132686614990234},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3383401334285736},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.2548636198043823},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.18834498524665833},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218196704001980","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196704001980","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.234.5467","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.5467","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0204292v1.pdf","raw_type":"text"},{"id":"pmh:oai:alma.01RUT_INST:11664909340004646","is_oa":false,"landing_page_url":"https://scholarship.libraries.rutgers.edu/esploro/outputs/journalArticle/THE-GROUPS-OF-RICHARD-THOMPSON-AND/991031665305004646","pdf_url":null,"source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W12630071","https://openalex.org/W41330591","https://openalex.org/W134176662","https://openalex.org/W196919032","https://openalex.org/W254146484","https://openalex.org/W650848797","https://openalex.org/W1505284964","https://openalex.org/W1516116134","https://openalex.org/W1517585663","https://openalex.org/W1520357511","https://openalex.org/W1541824250","https://openalex.org/W1546322230","https://openalex.org/W1556167844","https://openalex.org/W1572982068","https://openalex.org/W1594985246","https://openalex.org/W1606202023","https://openalex.org/W1834284857","https://openalex.org/W1967222652","https://openalex.org/W1968436506","https://openalex.org/W1973933705","https://openalex.org/W1977665851","https://openalex.org/W1986593186","https://openalex.org/W1996511490","https://openalex.org/W2001227217","https://openalex.org/W2009571139","https://openalex.org/W2026119659","https://openalex.org/W2033463487","https://openalex.org/W2041073233","https://openalex.org/W2045817093","https://openalex.org/W2066477598","https://openalex.org/W2070866382","https://openalex.org/W2072880081","https://openalex.org/W2092354902","https://openalex.org/W2131739013","https://openalex.org/W2132750992","https://openalex.org/W2158324864","https://openalex.org/W2312844687","https://openalex.org/W2322599043","https://openalex.org/W2326666498","https://openalex.org/W2576128646","https://openalex.org/W4206794571","https://openalex.org/W4230191592","https://openalex.org/W4251535942","https://openalex.org/W4292101339"],"related_works":["https://openalex.org/W2158086683","https://openalex.org/W1492906489","https://openalex.org/W1511851241","https://openalex.org/W2618109676","https://openalex.org/W2282186771","https://openalex.org/W1515007745","https://openalex.org/W2049964808","https://openalex.org/W2038666277","https://openalex.org/W1995628728","https://openalex.org/W3102739368"],"abstract_inverted_index":{"We":[0,17,50,79],"prove":[1],"new":[2],"results":[3],"about":[4],"the":[5,15,23,29,38,41,53,60,71,81,114,119,121,127,137],"remarkable":[6],"infinite":[7],"simple":[8,32],"groups":[9,99],"introduced":[10],"by":[11],"Richard":[12],"Thompson":[13],"in":[14,22],"1960s.":[16],"give":[18],"a":[19,106],"faithful":[20],"representation":[21],"Cuntz":[24],"C":[25],"\u22c6":[26],"-algebra.":[27],"For":[28],"finitely":[30,96,133],"presented":[31,134],"group":[33],"V":[34,57,76,85,89],"we":[35],"show":[36,51,87],"that":[37,52,88],"word-length":[39],"and":[40,86,136],"table":[42],"size":[43],"satisfy":[44],"an":[45],"n":[46,48],"log":[47],"relation.":[49],"word":[54,73],"problem":[55,74],"of":[56,68,75,84,95,112,123,125,129,132,139,143],"belongs":[58],"to":[59,109],"parallel":[61],"complexity":[62,141],"class":[63],"AC":[64],"1":[65],"(a":[66],"subclass":[67],"P),":[69],"whereas":[70],"generalized":[72],"is":[77],"undecidable.":[78],"study":[80],"distortion":[82],"functions":[83,131,142],"contains":[90],"all":[91],"finite":[92],"direct":[93],"products":[94],"generated":[97],"free":[98],"as":[100],"subgroups":[101],"with":[102],"linear":[103],"distortion.":[104],"As":[105],"consequence,":[107],"up":[108],"polynomial":[110],"equivalence":[111],"functions,":[113],"following":[115],"three":[116],"sets":[117],"are":[118],"same:":[120],"set":[122,128,138],"distortions":[124],"V,":[126],"Dehn":[130],"groups,":[135],"time":[140],"nondeterministic":[144],"Turing":[145],"machines.":[146]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}