{"id":"https://openalex.org/W2126946720","doi":"https://doi.org/10.1142/s0218196708004913","title":"EQUATIONAL COMPLEXITY OF THE FINITE ALGEBRA MEMBERSHIP PROBLEM","display_name":"EQUATIONAL COMPLEXITY OF THE FINITE ALGEBRA MEMBERSHIP PROBLEM","publication_year":2008,"publication_date":"2008-12-01","ids":{"openalex":"https://openalex.org/W2126946720","doi":"https://doi.org/10.1142/s0218196708004913","mag":"2126946720"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196708004913","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196708004913","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":["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/A5005130857","display_name":"George F. McNulty","orcid":null},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"GEORGE F. McNULTY","raw_affiliation_strings":["Department of Mathematics, University of South Carolina, Columbia SC 29208, USA","Department of Mathematics, University of South Carolina, Columbia SC, 29208, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of South Carolina, Columbia SC 29208, USA","institution_ids":["https://openalex.org/I155781252"]},{"raw_affiliation_string":"Department of Mathematics, University of South Carolina, Columbia SC, 29208, USA","institution_ids":["https://openalex.org/I155781252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076653855","display_name":"ZOLT\u00c1N SZ\u00c9KELY","orcid":null},"institutions":[{"id":"https://openalex.org/I80276326","display_name":"University of Guam","ror":"https://ror.org/00376bg92","country_code":"GU","type":"education","lineage":["https://openalex.org/I80276326"]}],"countries":["GU"],"is_corresponding":false,"raw_author_name":"ZOLT\u00c1N SZ\u00c9KELY","raw_affiliation_strings":["Division of Mathematical Sciences, College of Natural and Applied Sciences, University of Guam, UOG Station, Mangilao, GU 96923, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, College of Natural and Applied Sciences, University of Guam, UOG Station, Mangilao, GU 96923, USA","institution_ids":["https://openalex.org/I80276326"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078983016","display_name":"Ross Willard","orcid":"https://orcid.org/0000-0002-3297-0453"},"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":"ROSS WILLARD","raw_affiliation_strings":["Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada","Department of Pure mathematics , University of Waterloo , Waterloo, Ontario, N2L 3G1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Pure mathematics , University of Waterloo , Waterloo, Ontario, N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005130857"],"corresponding_institution_ids":["https://openalex.org/I155781252"],"apc_list":null,"apc_paid":null,"fwci":1.2415,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.8165116,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"18","issue":"08","first_page":"1283","last_page":"1319"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998000264167786,"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":0.9998000264167786,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9993000030517578,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9933000206947327,"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/variety","display_name":"Variety (cybernetics)","score":0.8565301895141602},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8196347951889038},{"id":"https://openalex.org/keywords/signature","display_name":"Signature (topology)","score":0.5836154818534851},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5166507363319397},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4796871840953827},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.4211263060569763},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40772348642349243},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33745232224464417},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.0865010917186737}],"concepts":[{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.8565301895141602},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8196347951889038},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.5836154818534851},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5166507363319397},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4796871840953827},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.4211263060569763},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40772348642349243},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33745232224464417},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0865010917186737},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218196708004913","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196708004913","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:CiteSeerX.psu:10.1.1.140.2468","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.2468","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.sc.edu/~mcnulty/preprints/eqcomplexity.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.63.8079","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.63.8079","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.sc.edu/~mcnulty/preprints/eqcomplex.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W150924307","https://openalex.org/W179270118","https://openalex.org/W215178276","https://openalex.org/W1509821411","https://openalex.org/W1976933099","https://openalex.org/W1978813353","https://openalex.org/W1980258696","https://openalex.org/W1983812198","https://openalex.org/W1987243149","https://openalex.org/W1989784721","https://openalex.org/W2005100072","https://openalex.org/W2008752834","https://openalex.org/W2013983766","https://openalex.org/W2031000173","https://openalex.org/W2048119309","https://openalex.org/W2049352524","https://openalex.org/W2058241424","https://openalex.org/W2062722007","https://openalex.org/W2067775876","https://openalex.org/W2081115664","https://openalex.org/W2086302789","https://openalex.org/W2087792324","https://openalex.org/W2106133727","https://openalex.org/W2232601223","https://openalex.org/W2320130150","https://openalex.org/W2327813532","https://openalex.org/W2463338882","https://openalex.org/W3048232945","https://openalex.org/W4213197861","https://openalex.org/W4231792667"],"related_works":["https://openalex.org/W2032233321","https://openalex.org/W3121970507","https://openalex.org/W2110028391","https://openalex.org/W54497855","https://openalex.org/W217960748","https://openalex.org/W3125814499","https://openalex.org/W2090827041","https://openalex.org/W187246281","https://openalex.org/W2565703248","https://openalex.org/W2143548620"],"abstract_inverted_index":{"We":[0,51,80],"associate":[1],"to":[2,41,48,99],"each":[3],"variety":[4,37],"of":[5,7,20,28,31,35,64,104],"algebras":[6,72,85],"finite":[8,45,78,84],"signature":[9],"a":[10,26,36,44],"function":[11,24],"on":[12,61],"the":[13,17,21,32,49,62,92],"positive":[14],"integers":[15],"called":[16],"equational":[18,33,65],"complexity":[19,66],"variety.":[22,50],"This":[23],"is":[25],"measure":[27],"how":[29],"much":[30],"theory":[34],"must":[38],"be":[39,97],"tested":[40],"determine":[42],"whether":[43],"algebra":[46],"belongs":[47],"provide":[52,69],"general":[53],"methods":[54],"for":[55],"giving":[56],"upper":[57],"and":[58,68,76,106],"lower":[59],"bounds":[60],"growth":[63],"functions":[67],"examples":[70],"using":[71],"created":[73],"from":[74,77],"graphs":[75],"automata.":[79],"also":[81],"show":[82],"that":[83],"which":[86],"are":[87],"inherently":[88],"nonfinitely":[89],"based":[90],"via":[91],"shift":[93],"automorphism":[94],"method":[95],"cannot":[96],"used":[98],"settle":[100],"an":[101],"old":[102],"problem":[103],"Eilenberg":[105],"Sch\u00fctzenberger.":[107]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-09T13:55:54.758798","created_date":"2025-10-10T00:00:00"}
