{"id":"https://openalex.org/W2336446049","doi":"https://doi.org/10.1142/s0129054115400067","title":"Large Aperiodic Semigroups","display_name":"Large Aperiodic Semigroups","publication_year":2015,"publication_date":"2015-11-01","ids":{"openalex":"https://openalex.org/W2336446049","doi":"https://doi.org/10.1142/s0129054115400067","mag":"2336446049"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054115400067","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054115400067","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/A5016883956","display_name":"Janusz Brzozowski","orcid":"https://orcid.org/0000-0003-3390-2767"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Janusz Brzozowski","raw_affiliation_strings":["David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada N2L 3G1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075117503","display_name":"Marek Szyku\u0142a","orcid":"https://orcid.org/0000-0001-5349-468X"},"institutions":[{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]},{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Marek Szyku\u0142a","raw_affiliation_strings":["Institute of Computer Science, University of Wroc\u0142aw, Joliot-Curie 15, PL-50-383 Wroc\u0142aw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, University of Wroc\u0142aw, Joliot-Curie 15, PL-50-383 Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962","https://openalex.org/I4210087266"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8171,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.86923077,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"26","issue":"07","first_page":"913","last_page":"931"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":1.0,"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":1.0,"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/T12029","display_name":"DNA and Biological Computing","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10911","display_name":"Chemical Synthesis and Analysis","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/aperiodic-graph","display_name":"Aperiodic graph","score":0.921555757522583},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.8819045424461365},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7886151075363159},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.7172022461891174},{"id":"https://openalex.org/keywords/special-classes-of-semigroups","display_name":"Special classes of semigroups","score":0.6486945748329163},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5873688459396362},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.5870764255523682},{"id":"https://openalex.org/keywords/krohn\u2013rhodes-theory","display_name":"Krohn\u2013Rhodes theory","score":0.4876910448074341},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48671987652778625},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.47762197256088257},{"id":"https://openalex.org/keywords/bicyclic-semigroup","display_name":"Bicyclic semigroup","score":0.43808290362358093},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43515995144844055},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43067502975463867},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.4213409125804901},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11298525333404541}],"concepts":[{"id":"https://openalex.org/C104247578","wikidata":"https://www.wikidata.org/wiki/Q4779368","display_name":"Aperiodic graph","level":2,"score":0.921555757522583},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.8819045424461365},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7886151075363159},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.7172022461891174},{"id":"https://openalex.org/C46149467","wikidata":"https://www.wikidata.org/wiki/Q7574800","display_name":"Special classes of semigroups","level":3,"score":0.6486945748329163},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5873688459396362},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.5870764255523682},{"id":"https://openalex.org/C30397308","wikidata":"https://www.wikidata.org/wiki/Q6438788","display_name":"Krohn\u2013Rhodes theory","level":4,"score":0.4876910448074341},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48671987652778625},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.47762197256088257},{"id":"https://openalex.org/C40417594","wikidata":"https://www.wikidata.org/wiki/Q3022111","display_name":"Bicyclic semigroup","level":3,"score":0.43808290362358093},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43515995144844055},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43067502975463867},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.4213409125804901},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11298525333404541},{"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0129054115400067","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054115400067","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:uwspace.uwaterloo.ca:10012/12507","is_oa":false,"landing_page_url":"http://hdl.handle.net/10012/12507","pdf_url":null,"source":{"id":"https://openalex.org/S4306401661","display_name":"UWSpace (University of Waterloo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I151746483","host_organization_name":"University of Waterloo","host_organization_lineage":["https://openalex.org/I151746483"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference Paper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W93607743","https://openalex.org/W196301943","https://openalex.org/W587223573","https://openalex.org/W1501444314","https://openalex.org/W1525645762","https://openalex.org/W1526344047","https://openalex.org/W1969737285","https://openalex.org/W2023521199","https://openalex.org/W2052621380","https://openalex.org/W2094423121","https://openalex.org/W2116250539","https://openalex.org/W2402632498","https://openalex.org/W2408564624","https://openalex.org/W2786516640","https://openalex.org/W2798588639","https://openalex.org/W2912226968","https://openalex.org/W2951308870"],"related_works":["https://openalex.org/W3200179526","https://openalex.org/W4297779646","https://openalex.org/W2966310593","https://openalex.org/W2115479925","https://openalex.org/W2107370167","https://openalex.org/W1833412956","https://openalex.org/W20901352","https://openalex.org/W4242339934","https://openalex.org/W2358674569","https://openalex.org/W2090966910"],"abstract_inverted_index":{"We":[0,29,81,109],"search":[1],"for":[2,17,133],"the":[3,18,130],"largest":[4,19,134],"syntactic":[5],"semigroups":[6,21,33,47,107,113,126],"of":[7,22,96],"star-free":[8],"languages":[9],"having":[10],"n":[11,27],"left":[12],"quotients;":[13],"equivalently,":[14],"we":[15,44,66,102],"look":[16],"transition":[20],"aperiodic":[23,76,86,135],"finite":[24],"automata":[25],"with":[26],"states.":[28],"first":[30],"introduce":[31],"unitary":[32,58],"generated":[34,88],"by":[35,89],"transformations":[36,90,105],"that":[37,55,71,91],"change":[38],"only":[39],"one":[40],"state.":[41],"In":[42],"particular,":[43],"study":[45],"unitary-complete":[46,69],"which":[48,114],"have":[49,115],"a":[50,68,93,99,116],"special":[51],"structure,":[52],"and":[53,106],"show":[54],"each":[56],"maximal":[57],"semigroup":[59,70,77],"is":[60,72],"unitary-complete.":[61],"For":[62],"[Formula:":[63],"see":[64],"text]":[65],"exhibit":[67],"larger":[73,85],"than":[74],"any":[75],"known":[78],"to":[79,98],"date.":[80],"then":[82],"present":[83,129],"even":[84],"semigroups,":[87],"map":[92],"non-empty":[94],"subset":[95],"states":[97],"single":[100],"state;":[101],"call":[103],"such":[104],"semiconstant.":[108],"examine":[110],"semiconstant":[111,124],"tree":[112,125],"structure":[117],"based":[118],"on":[119],"full":[120],"binary":[121],"trees.":[122],"The":[123],"are":[127],"at":[128],"best":[131],"candidates":[132],"semigroups.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}