{"id":"https://openalex.org/W2592641503","doi":"https://doi.org/10.1007/s00224-018-9859-0","title":"Primitivity, Uniform Minimality, and State Complexity of Boolean Operations","display_name":"Primitivity, Uniform Minimality, and State Complexity of Boolean Operations","publication_year":2018,"publication_date":"2018-03-26","ids":{"openalex":"https://openalex.org/W2592641503","doi":"https://doi.org/10.1007/s00224-018-9859-0","mag":"2592641503"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-018-9859-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-018-9859-0","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1702.00877","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050424365","display_name":"Sylvie Davies","orcid":"https://orcid.org/0000-0002-5010-4831"},"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":true,"raw_author_name":"Sylvie Davies","raw_affiliation_strings":["Department of Pure Mathematics, University of Waterloo, 200 University Ave. W., Waterloo, Ontario, N2L3G1, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, University of Waterloo, 200 University Ave. W., Waterloo, Ontario, N2L3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050424365"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.2137,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.51131834,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"62","issue":"8","first_page":"1952","last_page":"2005"},"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":0.9891999959945679,"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":0.9853000044822693,"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/mathematics","display_name":"Mathematics","score":0.6608462333679199},{"id":"https://openalex.org/keywords/product-term","display_name":"Product term","score":0.5928482413291931},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5884524583816528},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.5771828293800354},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.49758532643318176},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4841247498989105},{"id":"https://openalex.org/keywords/boolean-network","display_name":"Boolean network","score":0.4791804552078247},{"id":"https://openalex.org/keywords/direct-product","display_name":"Direct product","score":0.47536391019821167},{"id":"https://openalex.org/keywords/permutation-group","display_name":"Permutation group","score":0.45760416984558105},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.4425099194049835},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.439744770526886},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.4250474274158478},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.4183495044708252},{"id":"https://openalex.org/keywords/parity-function","display_name":"Parity function","score":0.41397517919540405},{"id":"https://openalex.org/keywords/complete-boolean-algebra","display_name":"Complete Boolean algebra","score":0.41261938214302063},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.213724285364151},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.14032602310180664},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09441065788269043}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6608462333679199},{"id":"https://openalex.org/C9429942","wikidata":"https://www.wikidata.org/wiki/Q1781698","display_name":"Product term","level":5,"score":0.5928482413291931},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5884524583816528},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.5771828293800354},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.49758532643318176},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4841247498989105},{"id":"https://openalex.org/C134444547","wikidata":"https://www.wikidata.org/wiki/Q585230","display_name":"Boolean network","level":3,"score":0.4791804552078247},{"id":"https://openalex.org/C58193220","wikidata":"https://www.wikidata.org/wiki/Q1778193","display_name":"Direct product","level":2,"score":0.47536391019821167},{"id":"https://openalex.org/C92957085","wikidata":"https://www.wikidata.org/wiki/Q1412905","display_name":"Permutation group","level":3,"score":0.45760416984558105},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.4425099194049835},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.439744770526886},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.4250474274158478},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.4183495044708252},{"id":"https://openalex.org/C188183281","wikidata":"https://www.wikidata.org/wiki/Q2898309","display_name":"Parity function","level":4,"score":0.41397517919540405},{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.41261938214302063},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.213724285364151},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.14032602310180664},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09441065788269043},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00224-018-9859-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-018-9859-0","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1702.00877","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1702.00877","pdf_url":"https://arxiv.org/pdf/1702.00877","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1702.00877","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1702.00877","pdf_url":"https://arxiv.org/pdf/1702.00877","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3764228066","display_name":null,"funder_award_id":"OGP0000871","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1492009014","https://openalex.org/W1501444314","https://openalex.org/W1510563045","https://openalex.org/W1519107695","https://openalex.org/W1976677460","https://openalex.org/W1988896922","https://openalex.org/W2001273190","https://openalex.org/W2006629323","https://openalex.org/W2015787121","https://openalex.org/W2025521996","https://openalex.org/W2054220885","https://openalex.org/W2061771611","https://openalex.org/W2103084752","https://openalex.org/W2106875872","https://openalex.org/W2120980679","https://openalex.org/W2146948339","https://openalex.org/W2233446306","https://openalex.org/W2265316437","https://openalex.org/W2406664471","https://openalex.org/W2408564624","https://openalex.org/W2430843852","https://openalex.org/W2529588972","https://openalex.org/W2786516640","https://openalex.org/W2798943694","https://openalex.org/W2962772080","https://openalex.org/W2962795882","https://openalex.org/W2963175946","https://openalex.org/W2963660011","https://openalex.org/W3103352697","https://openalex.org/W3144974373","https://openalex.org/W4234295943","https://openalex.org/W4245103550"],"related_works":["https://openalex.org/W2150272262","https://openalex.org/W4243283211","https://openalex.org/W2234833091","https://openalex.org/W2480828397","https://openalex.org/W1534775143","https://openalex.org/W98542587","https://openalex.org/W1499231756","https://openalex.org/W2495817859","https://openalex.org/W2740171735","https://openalex.org/W1972882023"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2017-03-16T00:00:00"}