{"id":"https://openalex.org/W2092388212","doi":"https://doi.org/10.1007/s11083-008-9083-7","title":"Word Problem of the Perkins Semigroup via Directed Acyclic Graphs","display_name":"Word Problem of the Perkins Semigroup via Directed Acyclic Graphs","publication_year":2008,"publication_date":"2008-08-01","ids":{"openalex":"https://openalex.org/W2092388212","doi":"https://doi.org/10.1007/s11083-008-9083-7","mag":"2092388212"},"language":"en","primary_location":{"id":"doi:10.1007/s11083-008-9083-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11083-008-9083-7","pdf_url":null,"source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Order","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/A5024451009","display_name":"Sergey Kitaev","orcid":"https://orcid.org/0000-0003-3324-1647"},"institutions":[{"id":"https://openalex.org/I123185442","display_name":"Reykjav\u00edk University","ror":"https://ror.org/05d2kyx68","country_code":"IS","type":"education","lineage":["https://openalex.org/I123185442"]}],"countries":["IS"],"is_corresponding":true,"raw_author_name":"Sergey Kitaev","raw_affiliation_strings":["Institute of Mathematics, Reykjav\u00edk University, Ofanleiti 2, IS-103, Reykjav\u00edk, Iceland","Reykjavik University"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Reykjav\u00edk University, Ofanleiti 2, IS-103, Reykjav\u00edk, Iceland","institution_ids":["https://openalex.org/I123185442"]},{"raw_affiliation_string":"Reykjavik University","institution_ids":["https://openalex.org/I123185442"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045328222","display_name":"Steve Seif","orcid":null},"institutions":[{"id":"https://openalex.org/I4210143137","display_name":"University of Louisville Hospital","ror":"https://ror.org/04sq8k219","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210143137"]},{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steve Seif","raw_affiliation_strings":["Mathematics Department, University of Louisville, Louisville, KY, 40292, USA","University of Louisville"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of Louisville, Louisville, KY, 40292, USA","institution_ids":["https://openalex.org/I142740786"]},{"raw_affiliation_string":"University of Louisville","institution_ids":["https://openalex.org/I4210143137"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024451009"],"corresponding_institution_ids":["https://openalex.org/I123185442"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.6438,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.8451502,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"25","issue":"3","first_page":"177","last_page":"194"},"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9900000095367432,"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/alternation","display_name":"Alternation (linguistics)","score":0.8772663474082947},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8072720766067505},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.779025673866272},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.6823947429656982},{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.6732214689254761},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.626754879951477},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.5997530221939087},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.49959731101989746},{"id":"https://openalex.org/keywords/free-monoid","display_name":"Free monoid","score":0.44095373153686523},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.4350457787513733},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38921183347702026}],"concepts":[{"id":"https://openalex.org/C26826806","wikidata":"https://www.wikidata.org/wiki/Q438358","display_name":"Alternation (linguistics)","level":2,"score":0.8772663474082947},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8072720766067505},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.779025673866272},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.6823947429656982},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.6732214689254761},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.626754879951477},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.5997530221939087},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.49959731101989746},{"id":"https://openalex.org/C149685015","wikidata":"https://www.wikidata.org/wiki/Q5500266","display_name":"Free monoid","level":3,"score":0.44095373153686523},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.4350457787513733},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38921183347702026},{"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":3,"locations":[{"id":"doi:10.1007/s11083-008-9083-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11083-008-9083-7","pdf_url":null,"source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Order","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.145.6607","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.145.6607","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ru.is/static/papers/KiSe08__Word_problem.pdf","raw_type":"text"},{"id":"pmh:oai:strathprints.strath.ac.uk:34552","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/34552/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402226","display_name":"Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I181647926","host_organization_name":"University of Strathclyde","host_organization_lineage":["https://openalex.org/I181647926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1572220122","https://openalex.org/W1790169885","https://openalex.org/W1862096312","https://openalex.org/W1971234560","https://openalex.org/W1996460289","https://openalex.org/W2005496785","https://openalex.org/W2006336761","https://openalex.org/W2015426235","https://openalex.org/W2023679149","https://openalex.org/W2024093817","https://openalex.org/W2036285489","https://openalex.org/W2051518176","https://openalex.org/W2055685510","https://openalex.org/W2064411534","https://openalex.org/W2092296506","https://openalex.org/W2092435018","https://openalex.org/W2132524082","https://openalex.org/W2312279077","https://openalex.org/W2971064764"],"related_works":["https://openalex.org/W2375401910","https://openalex.org/W2383679568","https://openalex.org/W1568230924","https://openalex.org/W2367541594","https://openalex.org/W3083664609","https://openalex.org/W2133525467","https://openalex.org/W4289887511","https://openalex.org/W1979037305","https://openalex.org/W2949546376","https://openalex.org/W2092388212"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
