{"id":"https://openalex.org/W7166819948","doi":"https://doi.org/10.4230/lipics.icalp.2026.158","title":"Revisiting Finiteness of Matrix Monoids","display_name":"Revisiting Finiteness of Matrix Monoids","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7166819948","doi":"https://doi.org/10.4230/lipics.icalp.2026.158"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26574","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.158","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol374-icalp2026/LIPIcs.ICALP.2026.158/LIPIcs.ICALP.2026.158.pdf","source":{"id":"https://openalex.org/S4306402524","display_name":"Leibniz-Zentrum f\u00fcr Informatik (Schloss Dagstuhl)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},"type":"conference-paper","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol374-icalp2026/LIPIcs.ICALP.2026.158/LIPIcs.ICALP.2026.158.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100258060","display_name":"Rida Ait El Manssour","orcid":"https://orcid.org/0000-0001-6228-9071"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ait El Manssour, Rida","raw_affiliation_strings":["University of Oxford, UK"],"raw_orcid":"https://orcid.org/0000-0001-6228-9071","affiliations":[{"raw_affiliation_string":"University of Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085414641","display_name":"Roland Guttenberg","orcid":"https://orcid.org/0000-0001-6140-6707"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Guttenberg, Roland","raw_affiliation_strings":["University of Warsaw, Poland"],"raw_orcid":"https://orcid.org/0000-0001-6140-6707","affiliations":[{"raw_affiliation_string":"University of Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076829560","display_name":"Nathan Lhote","orcid":"https://orcid.org/0000-0003-3303-5368"},"institutions":[{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"id":"https://openalex.org/I4210114274","display_name":"Laboratoire d\u2019Informatique et Syst\u00e8mes","ror":"https://ror.org/0257sgk90","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I143002897","https://openalex.org/I21491767","https://openalex.org/I4210114274"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Lhote, Nathan","raw_affiliation_strings":["Aix-Marseille Universit\u00e9, LIS, France"],"raw_orcid":"https://orcid.org/0000-0003-3303-5368","affiliations":[{"raw_affiliation_string":"Aix-Marseille Universit\u00e9, LIS, France","institution_ids":["https://openalex.org/I4210114274","https://openalex.org/I21491767"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005502598","display_name":"Mahsa Shirmohammadi","orcid":"https://orcid.org/0000-0002-7779-2339"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210117673","display_name":"Institut de Recherche en Informatique Fondamentale","ror":"https://ror.org/02krdtz55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210089394","https://openalex.org/I4210117673","https://openalex.org/I4210139971"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Shirmohammadi, Mahsa","raw_affiliation_strings":["CNRS & IRIF, Paris, France"],"raw_orcid":"https://orcid.org/0000-0002-7779-2339","affiliations":[{"raw_affiliation_string":"CNRS & IRIF, Paris, France","institution_ids":["https://openalex.org/I4210117673","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068165188","display_name":"James Worrell","orcid":"https://orcid.org/0000-0001-8151-2443"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Worrell, James Ben","raw_affiliation_strings":["University of Oxford, UK"],"raw_orcid":"https://orcid.org/0000-0001-8151-2443","affiliations":[{"raw_affiliation_string":"University of Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":null,"topics":[],"keywords":[{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.8090000152587891},{"id":"https://openalex.org/keywords/syntactic-monoid","display_name":"Syntactic monoid","score":0.6392999887466431},{"id":"https://openalex.org/keywords/free-monoid","display_name":"Free monoid","score":0.6180999875068665},{"id":"https://openalex.org/keywords/noncommutative-geometry","display_name":"Noncommutative geometry","score":0.6179999709129333},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5005999803543091},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.48350000381469727},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4472000002861023},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4253000020980835}],"concepts":[{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.8090000152587891},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.807200014591217},{"id":"https://openalex.org/C119903167","wikidata":"https://www.wikidata.org/wiki/Q3321297","display_name":"Syntactic monoid","level":4,"score":0.6392999887466431},{"id":"https://openalex.org/C149685015","wikidata":"https://www.wikidata.org/wiki/Q5500266","display_name":"Free monoid","level":3,"score":0.6180999875068665},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.6179999709129333},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5005999803543091},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.48350000381469727},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4472000002861023},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4253000020980835},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4196000099182129},{"id":"https://openalex.org/C90988201","wikidata":"https://www.wikidata.org/wiki/Q255912","display_name":"Word problem (mathematics education)","level":2,"score":0.3986999988555908},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3765999972820282},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3763999938964844},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.375900000333786},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.34119999408721924},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.3034999966621399},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.2639999985694885}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:26574","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.158","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol374-icalp2026/LIPIcs.ICALP.2026.158/LIPIcs.ICALP.2026.158.pdf","source":{"id":"https://openalex.org/S4306402524","display_name":"Leibniz-Zentrum f\u00fcr Informatik (Schloss Dagstuhl)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},{"id":"doi:10.4230/lipics.icalp.2026.158","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.icalp.2026.158","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26574","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.158","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol374-icalp2026/LIPIcs.ICALP.2026.158/LIPIcs.ICALP.2026.158.pdf","source":{"id":"https://openalex.org/S4306402524","display_name":"Leibniz-Zentrum f\u00fcr Informatik (Schloss Dagstuhl)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7166819948.pdf","grobid_xml":"https://content.openalex.org/works/W7166819948.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0,67],"paper":[1],"concerns":[2],"decision":[3],"problems":[4],"related":[5],"to":[6,72,107],"finite":[7,39,65],"monoids":[8,41],"of":[9,17,55,75,82,86,102,110],"rational":[10,103],"matrices.":[11,112],"We":[12,31],"show":[13,33],"that":[14,34],"determining":[15],"finiteness":[16],"a":[18,56,94,100,108],"given":[19],"finitely":[20],"presented":[21],"monoid":[22,101,109],"is":[23,42,68,105],"in":[24,64],"PSpace,":[25],"improving":[26,44],"the":[27,35,45,73,79],"known":[28,46],"coNExp^NP":[29],"bound.":[30,48],"also":[32,91],"membership":[36],"problem":[37],"for":[38,97],"matrix":[40,62,76,87],"PSpace-complete,":[43],"NExp-upper":[47],"Our":[49,89],"two":[50],"complexity":[51],"results":[52],"are":[53],"corollaries":[54],"new":[57],"polynomial":[58],"bit-size":[59],"bound":[60],"on":[61],"entries":[63],"monoids.":[66,88],"obtained":[69],"by":[70],"reduction":[71],"case":[74],"groups,":[77],"using":[78],"structure":[80],"theory":[81],"noncommutative":[83],"algebras":[84],"and":[85],"techniques":[90],"give":[92],"us":[93],"polynomial-time":[95],"algorithm":[96],"deciding":[98],"whether":[99],"matrices":[104],"conjugate":[106],"integer":[111]},"counts_by_year":[],"updated_date":"2026-07-04T07:58:01.006859","created_date":"2026-07-02T00:00:00"}
