{"id":"https://openalex.org/W4403281076","doi":"https://doi.org/10.1007/s00224-024-10197-5","title":"Automatic Abelian Complexities of Parikh-Collinear Fixed Points","display_name":"Automatic Abelian Complexities of Parikh-Collinear Fixed Points","publication_year":2024,"publication_date":"2024-10-10","ids":{"openalex":"https://openalex.org/W4403281076","doi":"https://doi.org/10.1007/s00224-024-10197-5"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-024-10197-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-024-10197-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-024-10197-5.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00224-024-10197-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027485931","display_name":"Michel Rigo","orcid":"https://orcid.org/0000-0001-7463-8507"},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Michel Rigo","raw_affiliation_strings":["Department of Mathematics, ULi\u00e8ge, All\u00e9e de la D\u00e9couverte 12, Li\u00e8ge, 4000, Belgium"],"raw_orcid":"https://orcid.org/0000-0001-7463-8507","affiliations":[{"raw_affiliation_string":"Department of Mathematics, ULi\u00e8ge, All\u00e9e de la D\u00e9couverte 12, Li\u00e8ge, 4000, Belgium","institution_ids":["https://openalex.org/I157674565"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023077959","display_name":"Manon Stipulanti","orcid":"https://orcid.org/0000-0002-2805-2465"},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Manon Stipulanti","raw_affiliation_strings":["Department of Mathematics, ULi\u00e8ge, All\u00e9e de la D\u00e9couverte 12, Li\u00e8ge, 4000, Belgium"],"raw_orcid":"https://orcid.org/0000-0002-2805-2465","affiliations":[{"raw_affiliation_string":"Department of Mathematics, ULi\u00e8ge, All\u00e9e de la D\u00e9couverte 12, Li\u00e8ge, 4000, Belgium","institution_ids":["https://openalex.org/I157674565"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040858119","display_name":"Markus A. Whiteland","orcid":"https://orcid.org/0000-0002-6006-9902"},"institutions":[{"id":"https://openalex.org/I143804889","display_name":"Loughborough University","ror":"https://ror.org/04vg4w365","country_code":"GB","type":"education","lineage":["https://openalex.org/I143804889"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Markus A. Whiteland","raw_affiliation_strings":["Department of Computer Science, Loughborough University, Epinal Way, Loughborough, Leicestershire, LE11 3TU, United Kingdom"],"raw_orcid":"https://orcid.org/0000-0002-6006-9902","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Loughborough University, Epinal Way, Loughborough, Leicestershire, LE11 3TU, United Kingdom","institution_ids":["https://openalex.org/I143804889"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040858119"],"corresponding_institution_ids":["https://openalex.org/I143804889"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20630729,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"68","issue":"6","first_page":"1622","last_page":"1639"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9952999949455261,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9952999949455261,"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":0.9945999979972839,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9926999807357788,"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/abelian-group","display_name":"Abelian group","score":0.7750271558761597},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.6176561117172241},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41619983315467834},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3643249273300171},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3633362054824829},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13513827323913574}],"concepts":[{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7750271558761597},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.6176561117172241},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41619983315467834},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3643249273300171},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3633362054824829},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13513827323913574}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00224-024-10197-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-024-10197-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-024-10197-5.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},{"id":"pmh:oai:orbi.ulg.ac.be:2268/324352","is_oa":true,"landing_page_url":"https://orbi.uliege.be/handle/2268/324352","pdf_url":"https://orbi.uliege.be/bitstream/2268/324352/1/sn-article.pdf","source":{"id":"https://openalex.org/S4306400651","display_name":"Open Repository and Bibliography (University of Li\u00e8ge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I157674565","host_organization_name":"University of Li\u00e8ge","host_organization_lineage":["https://openalex.org/I157674565"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Theory of Computing Systems (2024)","raw_type":"peer reviewed"}],"best_oa_location":{"id":"doi:10.1007/s00224-024-10197-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-024-10197-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-024-10197-5.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403281076.pdf","grobid_xml":"https://content.openalex.org/works/W4403281076.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1722971898","https://openalex.org/W1974406060","https://openalex.org/W2119013637","https://openalex.org/W2305237263","https://openalex.org/W2468104078","https://openalex.org/W2953325968","https://openalex.org/W2963494353","https://openalex.org/W2963731267","https://openalex.org/W2981143402","https://openalex.org/W3205986289","https://openalex.org/W4205178514","https://openalex.org/W4206601558","https://openalex.org/W4223476461","https://openalex.org/W4238159413","https://openalex.org/W4297662269","https://openalex.org/W4307957395","https://openalex.org/W4313316759","https://openalex.org/W4381303960","https://openalex.org/W4391507097"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Abstract":[0],"Parikh-collinear":[1,37,89],"morphisms":[2,38],"have":[3],"the":[4,8,12,19,27,45,69,76,116,124],"property":[5],"that":[6,33,44,75,112],"all":[7],"Parikh":[9],"vectors":[10],"of":[11,14,36,49,54,80,84,118,120],"images":[13],"letters":[15],"are":[16,39],"collinear,":[17],"i.e.,":[18],"associated":[20],"adjacency":[21],"matrix":[22],"has":[23],"rank":[24],"1.":[25],"In":[26,63],"conference":[28],"DLT\u2013WORDS":[29],"2023":[30],"we":[31,66,73,114],"showed":[32,43],"fixed":[34,52,82],"points":[35],"automatic.":[40,92],"We":[41],"also":[42],"abelian":[46,77,102],"complexity":[47,78,103],"function":[48,79,104],"a":[50,56,81,94,121],"binary":[51],"point":[53,83],"such":[55],"morphism":[57,90,122],"is":[58,91,105],"automatic":[59],"under":[60],"some":[61],"assumptions.":[62],"this":[64,101],"note,":[65],"fully":[67],"generalize":[68],"latter":[70],"result.":[71],"Namely,":[72],"show":[74],"an":[85,108],"arbitrary,":[86],"possibly":[87],"erasing,":[88],"Furthermore,":[93],"deterministic":[95],"finite":[96],"automaton":[97],"with":[98],"output":[99],"generating":[100],"provided":[106],"by":[107],"effective":[109],"procedure.":[110],"To":[111],"end,":[113],"discuss":[115],"constant":[117],"recognizability":[119],"and":[123],"related":[125],"cutting":[126],"set.":[127]},"counts_by_year":[],"updated_date":"2026-03-14T06:41:57.775601","created_date":"2025-10-10T00:00:00"}
