{"id":"https://openalex.org/W2067149955","doi":"https://doi.org/10.1142/s0129054104002297","title":"WORD COMPLEXITY AND REPETITIONS IN WORDS","display_name":"WORD COMPLEXITY AND REPETITIONS IN WORDS","publication_year":2004,"publication_date":"2004-02-01","ids":{"openalex":"https://openalex.org/W2067149955","doi":"https://doi.org/10.1142/s0129054104002297","mag":"2067149955"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054104002297","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054104002297","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"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 Foundations of Computer Science","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/A5048178906","display_name":"Lucian Ilie","orcid":"https://orcid.org/0000-0003-1856-3509"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"LUCIAN ILIE","raw_affiliation_strings":["Department of Computer Science, University of Western Ontario, N6A 5B7, London, Ontario, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Western Ontario, N6A 5B7, London, Ontario, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111766129","display_name":"Sheng Y\u00fc","orcid":"https://orcid.org/0000-0002-5189-7140"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"SHENG YU","raw_affiliation_strings":["Department of Computer Science, University of Western Ontario, N6A 5B7, London, Ontario, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Western Ontario, N6A 5B7, London, Ontario, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081729547","display_name":"Kaizhong Zhang","orcid":"https://orcid.org/0000-0003-1734-5921"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"KAIZHONG ZHANG","raw_affiliation_strings":["Department of Computer Science, University of Western Ontario, N6A 5B7, London, Ontario, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Western Ontario, N6A 5B7, London, Ontario, Canada","institution_ids":["https://openalex.org/I125749732"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I125749732"],"apc_list":null,"apc_paid":null,"fwci":1.374,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.85035273,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"15","issue":"01","first_page":"41","last_page":"55"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","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/T11269","display_name":"Algorithms and Data Compression","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/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"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/T11130","display_name":"Coding theory and cryptography","score":0.9962999820709229,"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/repetition","display_name":"Repetition (rhetorical device)","score":0.7683311104774475},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.6819441914558411},{"id":"https://openalex.org/keywords/de-bruijn-sequence","display_name":"De Bruijn sequence","score":0.6514471173286438},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5787788033485413},{"id":"https://openalex.org/keywords/combinatorics-on-words","display_name":"Combinatorics on words","score":0.5577704906463623},{"id":"https://openalex.org/keywords/prefix","display_name":"Prefix","score":0.5537600517272949},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.541172981262207},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5334427952766418},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.5195205807685852},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5071868896484375},{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.4972582161426544},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4819490611553192},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47913071513175964},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4748264253139496},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3513703942298889},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22215184569358826}],"concepts":[{"id":"https://openalex.org/C2776141515","wikidata":"https://www.wikidata.org/wiki/Q1274479","display_name":"Repetition (rhetorical device)","level":2,"score":0.7683311104774475},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.6819441914558411},{"id":"https://openalex.org/C170320093","wikidata":"https://www.wikidata.org/wiki/Q1953457","display_name":"De Bruijn sequence","level":2,"score":0.6514471173286438},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5787788033485413},{"id":"https://openalex.org/C164804908","wikidata":"https://www.wikidata.org/wiki/Q2985058","display_name":"Combinatorics on words","level":3,"score":0.5577704906463623},{"id":"https://openalex.org/C141603448","wikidata":"https://www.wikidata.org/wiki/Q134830","display_name":"Prefix","level":2,"score":0.5537600517272949},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.541172981262207},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5334427952766418},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.5195205807685852},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5071868896484375},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.4972582161426544},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4819490611553192},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47913071513175964},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4748264253139496},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3513703942298889},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22215184569358826},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0129054104002297","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054104002297","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"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 Foundations of Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.69.4570","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.69.4570","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.csd.uwo.ca/faculty/ilie/IJFCS04.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W137071685","https://openalex.org/W1514324498","https://openalex.org/W1551117435","https://openalex.org/W1586417893","https://openalex.org/W1882010690","https://openalex.org/W1968517468","https://openalex.org/W1973456884","https://openalex.org/W2005097301","https://openalex.org/W2006431506","https://openalex.org/W2007378578","https://openalex.org/W2011039300","https://openalex.org/W2024145045","https://openalex.org/W2034339630","https://openalex.org/W2061829075","https://openalex.org/W2067580807","https://openalex.org/W2067787802","https://openalex.org/W2077770566","https://openalex.org/W2086390954","https://openalex.org/W2107745473","https://openalex.org/W2122962290","https://openalex.org/W2156169026","https://openalex.org/W2592570088","https://openalex.org/W2611477341","https://openalex.org/W4244795967","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2499949544","https://openalex.org/W1566890150","https://openalex.org/W2035407289","https://openalex.org/W2121658477","https://openalex.org/W4256081955","https://openalex.org/W4298247746","https://openalex.org/W2913002857","https://openalex.org/W2025348860","https://openalex.org/W2512610949","https://openalex.org/W1491300721"],"abstract_inverted_index":{"With":[0],"ideas":[1],"from":[2],"data":[3],"compression":[4],"and":[5,86,98,144,182,186],"combinatorics":[6],"on":[7],"words,":[8,15,151],"we":[9],"introduce":[10],"a":[11,26],"complexity":[12,30,72,78,169],"measure":[13],"for":[14,116,154],"called":[16],"repetition":[17,24,29,71,165],"complexity,":[18,83,88,158],"which":[19],"quantifies":[20],"the":[21,38,52,60,103,108,167],"amount":[22,40],"of":[23,31,41,59,64,118],"in":[25,177],"word.":[27],"The":[28,70],"w,":[32],"R":[33,94,172],"(w),":[34],"is":[35,105,110,133,184],"defined":[36],"as":[37,68,81],"smallest":[39],"space":[42],"needed":[43],"to":[44,161,190],"store":[45],"w":[46,65],"when":[47],"reduced":[48],"by":[49,123],"repeatedly":[50],"applying":[51],"following":[53],"procedure:":[54],"n":[55],"consecutive":[56],"occurrences":[57],"uu\u2026u":[58],"same":[61],"subword":[62,82,157],"u":[63],"are":[66,159],"stored":[67],"(u,n).":[69],"has":[73],"interesting":[74],"relations":[75],"with":[76],"well-known":[77],"measures,":[79],"such":[80],"SUB":[84],",":[85],"Lempel-Ziv":[87],"LZ":[89,96],".":[90],"We":[91],"have":[92,162],"always":[93],"(w)\u2265":[95],"(w)":[97,173],"could":[99],"even":[100],"be":[101,175],"that":[102],"former":[104],"linear":[106],"while":[107],"latter":[109],"only":[111],"logarithmic;":[112],"e.g.,":[113],"this":[114],"happens":[115],"prefixes":[117],"certain":[119],"infinite":[120,127],"words":[121],"obtained":[122],"iterated":[124],"morphisms.":[125],"An":[126],"word":[128],"\u03b1":[129],"being":[130],"ultimately":[131],"periodic":[132],"equivalent":[134],"to:":[135],"(i)":[136],"[Formula:":[137,141,146,179],"see":[138,142,147,180],"text],":[139,143],"(ii)":[140],"(iii)":[145],"text].":[148],"De":[149],"Bruijn":[150],"well":[152],"known":[153],"their":[155],"high":[156],"shown":[160],"almost":[163],"highest":[164],"complexity;":[166],"precise":[168],"remains":[170],"open.":[171],"can":[174],"computed":[176],"time":[178],"text]":[181],"it":[183],"open,":[185],"probably":[187],"very":[188],"difficult,":[189],"find":[191],"fast":[192],"algorithms.":[193]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}