{"id":"https://openalex.org/W3013312844","doi":"https://doi.org/10.1007/978-3-030-43520-2_9","title":"Verifying the Correctness of Disjoint-Set Forests with Kleene Relation Algebras","display_name":"Verifying the Correctness of Disjoint-Set Forests with Kleene Relation Algebras","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3013312844","doi":"https://doi.org/10.1007/978-3-030-43520-2_9","mag":"3013312844"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-43520-2_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-43520-2_9","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5071961816","display_name":"Walter Guttmann","orcid":"https://orcid.org/0000-0003-2969-1688"},"institutions":[{"id":"https://openalex.org/I185492890","display_name":"University of Canterbury","ror":"https://ror.org/03y7q9t39","country_code":"NZ","type":"education","lineage":["https://openalex.org/I185492890"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Walter Guttmann","raw_affiliation_strings":["Department of Computer Science and Software Engineering, University of Canterbury, Christchurch, New Zealand"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Software Engineering, University of Canterbury, Christchurch, New Zealand","institution_ids":["https://openalex.org/I185492890"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071961816"],"corresponding_institution_ids":["https://openalex.org/I185492890"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.2747,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.5161071,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"134","last_page":"151"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9991000294685364,"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/T11567","display_name":"semigroups and automata theory","score":0.9944000244140625,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.8453662395477295},{"id":"https://openalex.org/keywords/hol","display_name":"HOL","score":0.8430286645889282},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.8182042837142944},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.8025632500648499},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.7046488523483276},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.6696800589561462},{"id":"https://openalex.org/keywords/algebraic-operation","display_name":"Algebraic operation","score":0.6649989485740662},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5394729971885681},{"id":"https://openalex.org/keywords/relation-algebra","display_name":"Relation algebra","score":0.5148636102676392},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.5132891535758972},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49808335304260254},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.4883553683757782},{"id":"https://openalex.org/keywords/algebraic-semantics","display_name":"Algebraic semantics","score":0.4676133394241333},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.46301788091659546},{"id":"https://openalex.org/keywords/disjoint-union","display_name":"Disjoint union (topology)","score":0.4447242021560669},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.42930951714515686},{"id":"https://openalex.org/keywords/set-operations","display_name":"Set operations","score":0.41143253445625305},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37204521894454956},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.3617854714393616},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.2575317919254303},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.18997237086296082},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.13764750957489014},{"id":"https://openalex.org/keywords/database","display_name":"Database","score":0.10907840728759766},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.07657963037490845}],"concepts":[{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.8453662395477295},{"id":"https://openalex.org/C17435882","wikidata":"https://www.wikidata.org/wiki/Q17030435","display_name":"HOL","level":2,"score":0.8430286645889282},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8182042837142944},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.8025632500648499},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.7046488523483276},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.6696800589561462},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.6649989485740662},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5394729971885681},{"id":"https://openalex.org/C10282146","wikidata":"https://www.wikidata.org/wiki/Q5965969","display_name":"Relation algebra","level":5,"score":0.5148636102676392},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.5132891535758972},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49808335304260254},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.4883553683757782},{"id":"https://openalex.org/C2779729104","wikidata":"https://www.wikidata.org/wiki/Q4724013","display_name":"Algebraic semantics","level":3,"score":0.4676133394241333},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.46301788091659546},{"id":"https://openalex.org/C7655956","wikidata":"https://www.wikidata.org/wiki/Q5282259","display_name":"Disjoint union (topology)","level":2,"score":0.4447242021560669},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.42930951714515686},{"id":"https://openalex.org/C2777168461","wikidata":"https://www.wikidata.org/wiki/Q42196253","display_name":"Set operations","level":3,"score":0.41143253445625305},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37204521894454956},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3617854714393616},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2575317919254303},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.18997237086296082},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.13764750957489014},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.10907840728759766},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.07657963037490845},{"id":"https://openalex.org/C100899422","wikidata":"https://www.wikidata.org/wiki/Q5058347","display_name":"Cellular algebra","level":4,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-030-43520-2_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-43520-2_9","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/14","display_name":"Life below water","score":0.7699999809265137}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W70873062","https://openalex.org/W1492131132","https://openalex.org/W1512339036","https://openalex.org/W1536773907","https://openalex.org/W1545329058","https://openalex.org/W1548258731","https://openalex.org/W1571615440","https://openalex.org/W1588115473","https://openalex.org/W1970275691","https://openalex.org/W1998368317","https://openalex.org/W2000616678","https://openalex.org/W2006006495","https://openalex.org/W2011721441","https://openalex.org/W2014430014","https://openalex.org/W2016265082","https://openalex.org/W2022132320","https://openalex.org/W2035448420","https://openalex.org/W2037247941","https://openalex.org/W2037911517","https://openalex.org/W2045246689","https://openalex.org/W2056240511","https://openalex.org/W2060072995","https://openalex.org/W2079388778","https://openalex.org/W2093737074","https://openalex.org/W2096989935","https://openalex.org/W2111706174","https://openalex.org/W2144973245","https://openalex.org/W2145680053","https://openalex.org/W2163152086","https://openalex.org/W2396303865","https://openalex.org/W2607631107","https://openalex.org/W2752885492","https://openalex.org/W2757243080","https://openalex.org/W2892302641","https://openalex.org/W2987907651","https://openalex.org/W3145128584","https://openalex.org/W3146075203","https://openalex.org/W3181441684","https://openalex.org/W4253748132"],"related_works":["https://openalex.org/W2591701982","https://openalex.org/W2058834578","https://openalex.org/W1980823022","https://openalex.org/W115604927","https://openalex.org/W2953113476","https://openalex.org/W2073214104","https://openalex.org/W2151085288","https://openalex.org/W2026028037","https://openalex.org/W1597561867","https://openalex.org/W4318225404"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}