{"id":"https://openalex.org/W2795834488","doi":"https://doi.org/10.1142/s0218196718500285","title":"Birecurrent sets","display_name":"Birecurrent sets","publication_year":2018,"publication_date":"2018-04-12","ids":{"openalex":"https://openalex.org/W2795834488","doi":"https://doi.org/10.1142/s0218196718500285","mag":"2795834488"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196718500285","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196718500285","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1703.10081","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019058972","display_name":"Francesco Dolce","orcid":"https://orcid.org/0000-0001-8936-1395"},"institutions":[{"id":"https://openalex.org/I159129438","display_name":"Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al","ror":"https://ror.org/002rjbv21","country_code":"CA","type":"education","lineage":["https://openalex.org/I159129438","https://openalex.org/I49663120"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Francesco Dolce","raw_affiliation_strings":["Laboratoire de Combinatoire et d\u2019Informatique, Math\u00e9matique, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, Canada"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Combinatoire et d\u2019Informatique, Math\u00e9matique, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, Canada","institution_ids":["https://openalex.org/I159129438"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105510505","display_name":"Dominique Perrin","orcid":"https://orcid.org/0000-0003-4036-141X"},"institutions":[{"id":"https://openalex.org/I4210152518","display_name":"Laboratoire d'Informatique Gaspard-Monge","ror":"https://ror.org/04t50yk91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Dominique Perrin","raw_affiliation_strings":["Laboratoire d\u2019Informatique Gaspard-Mong\u00e9, Universit\u00e9 Paris-Est, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire d\u2019Informatique Gaspard-Mong\u00e9, Universit\u00e9 Paris-Est, France","institution_ids":["https://openalex.org/I4210152518"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024448520","display_name":"Antonio Restivo","orcid":"https://orcid.org/0000-0002-1972-6931"},"institutions":[{"id":"https://openalex.org/I900890020","display_name":"University of Palermo","ror":"https://ror.org/044k9ta02","country_code":"IT","type":"education","lineage":["https://openalex.org/I900890020"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Antonio Restivo","raw_affiliation_strings":["Dipartimento di Matematica e Informatica, Universit\u00e0 degli Studi di Palermo, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Informatica, Universit\u00e0 degli Studi di Palermo, Italy","institution_ids":["https://openalex.org/I900890020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038352414","display_name":"Christophe Reutenauer","orcid":"https://orcid.org/0000-0003-1739-3691"},"institutions":[{"id":"https://openalex.org/I159129438","display_name":"Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al","ror":"https://ror.org/002rjbv21","country_code":"CA","type":"education","lineage":["https://openalex.org/I159129438","https://openalex.org/I49663120"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Christophe Reutenauer","raw_affiliation_strings":["Laboratoire de Combinatoire et d\u2019Informatique, Math\u00e9matique, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, Canada"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Combinatoire et d\u2019Informatique, Math\u00e9matique, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, Canada","institution_ids":["https://openalex.org/I159129438"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035668606","display_name":"Giuseppina Rindone","orcid":null},"institutions":[{"id":"https://openalex.org/I4210152518","display_name":"Laboratoire d'Informatique Gaspard-Monge","ror":"https://ror.org/04t50yk91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Giuseppina Rindone","raw_affiliation_strings":["Laboratoire d\u2019Informatique Gaspard-Mong\u00e9, Universit\u00e9 Paris-Est, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire d\u2019Informatique Gaspard-Mong\u00e9, Universit\u00e9 Paris-Est, France","institution_ids":["https://openalex.org/I4210152518"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5019058972"],"corresponding_institution_ids":["https://openalex.org/I159129438"],"apc_list":null,"apc_paid":null,"fwci":0.2019,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50875239,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"28","issue":"04","first_page":"613","last_page":"652"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T11269","display_name":"Algorithms and Data Compression","score":0.9991999864578247,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9990000128746033,"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/mathematics","display_name":"Mathematics","score":0.8910812139511108},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6275732517242432},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6267773509025574},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.5745878219604492},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.45956093072891235},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4514929950237274},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4444778859615326},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3293599486351013},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30320829153060913},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.09839293360710144},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.072974294424057}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8910812139511108},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6275732517242432},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6267773509025574},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.5745878219604492},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.45956093072891235},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4514929950237274},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4444778859615326},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3293599486351013},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30320829153060913},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.09839293360710144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.072974294424057},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218196718500285","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196718500285","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:arXiv.org:1703.10081","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1703.10081","pdf_url":"https://arxiv.org/pdf/1703.10081","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-03134002v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03134002","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.worldscientific.com/doi/abs/10.1142/S0218196718500285","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1703.10081","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1703.10081","pdf_url":"https://arxiv.org/pdf/1703.10081","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"score":0.5400000214576721,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W139946571","https://openalex.org/W1518573520","https://openalex.org/W2016948883","https://openalex.org/W2025586931","https://openalex.org/W2062655983","https://openalex.org/W2092386826","https://openalex.org/W2124314201","https://openalex.org/W2167954650","https://openalex.org/W2196559987","https://openalex.org/W2604729131","https://openalex.org/W2963982743","https://openalex.org/W4206405967","https://openalex.org/W4206635485","https://openalex.org/W4234145279"],"related_works":["https://openalex.org/W1919101720","https://openalex.org/W2062195135","https://openalex.org/W4390822878","https://openalex.org/W96888382","https://openalex.org/W4386126592","https://openalex.org/W2951907088","https://openalex.org/W4237434372","https://openalex.org/W1976730198","https://openalex.org/W2787593906","https://openalex.org/W2350145249"],"abstract_inverted_index":{"A":[0],"set":[1,38],"is":[2,9,16,32,39,53],"called":[3],"recurrent":[4,17],"if":[5,14],"its":[6,50],"minimal":[7,47],"automaton":[8],"strongly":[10],"connected":[11],"and":[12],"birecurrent":[13,29,37,70],"it":[15],"as":[18,20,66],"well":[19],"reversal.":[21],"We":[22],"prove":[23],"a":[24],"series":[25,52],"of":[26,49,59,69],"results":[27],"concerning":[28],"sets.":[30],"It":[31],"already":[33],"known":[34],"that":[35,45],"any":[36],"completely":[40,54,63],"reducible":[41,64],"(that":[42],"is,":[43],"such":[44],"the":[46],"representation":[48],"characteristic":[51],"reducible).":[55],"The":[56],"main":[57],"result":[58],"this":[60],"paper":[61],"characterizes":[62],"sets":[65,71],"linear":[67],"combinations":[68]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2018-04-13T00:00:00"}
