{"id":"https://openalex.org/W4230970195","doi":"https://doi.org/10.1007/3-540-45071-8_23","title":"The Complexity of Boolean Matrix Root Computation","display_name":"The Complexity of Boolean Matrix Root Computation","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W4230970195","doi":"https://doi.org/10.1007/3-540-45071-8_23"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-45071-8_23","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45071-8_23","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/A5046440423","display_name":"Martin K\u00fctz","orcid":null},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Martin Kutz","raw_affiliation_strings":["Freie Universit\u00e4t Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Freie Universit\u00e4t Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046440423"],"corresponding_institution_ids":["https://openalex.org/I75951250"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.375467,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"212","last_page":"221"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9984999895095825,"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/graph-isomorphism","display_name":"Graph isomorphism","score":0.590844452381134},{"id":"https://openalex.org/keywords/complete-boolean-algebra","display_name":"Complete Boolean algebra","score":0.5808777809143066},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.5691542625427246},{"id":"https://openalex.org/keywords/logical-matrix","display_name":"Logical matrix","score":0.5435227751731873},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.5298060178756714},{"id":"https://openalex.org/keywords/stones-representation-theorem-for-boolean-algebras","display_name":"Stone's representation theorem for Boolean algebras","score":0.5293149352073669},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5174932479858398},{"id":"https://openalex.org/keywords/boolean-algebras-canonically-defined","display_name":"Boolean algebras canonically defined","score":0.506630003452301},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.500394344329834},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.4862886369228363},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47755107283592224},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4598437547683716},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.4321085512638092},{"id":"https://openalex.org/keywords/parity-function","display_name":"Parity function","score":0.4296700954437256},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41444215178489685},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3858380615711212},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.24812567234039307},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.1985284388065338},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08799740672111511}],"concepts":[{"id":"https://openalex.org/C61665672","wikidata":"https://www.wikidata.org/wiki/Q303100","display_name":"Graph isomorphism","level":4,"score":0.590844452381134},{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.5808777809143066},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.5691542625427246},{"id":"https://openalex.org/C163561899","wikidata":"https://www.wikidata.org/wiki/Q1994977","display_name":"Logical matrix","level":3,"score":0.5435227751731873},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.5298060178756714},{"id":"https://openalex.org/C10021369","wikidata":"https://www.wikidata.org/wiki/Q1166774","display_name":"Stone's representation theorem for Boolean algebras","level":5,"score":0.5293149352073669},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5174932479858398},{"id":"https://openalex.org/C45503250","wikidata":"https://www.wikidata.org/wiki/Q4943350","display_name":"Boolean algebras canonically defined","level":5,"score":0.506630003452301},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.500394344329834},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.4862886369228363},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47755107283592224},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4598437547683716},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.4321085512638092},{"id":"https://openalex.org/C188183281","wikidata":"https://www.wikidata.org/wiki/Q2898309","display_name":"Parity function","level":4,"score":0.4296700954437256},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41444215178489685},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3858380615711212},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.24812567234039307},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.1985284388065338},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08799740672111511},{"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/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-45071-8_23","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45071-8_23","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1251209292","https://openalex.org/W1989114462","https://openalex.org/W1991152766","https://openalex.org/W2001515960","https://openalex.org/W2017987071","https://openalex.org/W2041176939","https://openalex.org/W2048172960","https://openalex.org/W2068718955","https://openalex.org/W2070021900","https://openalex.org/W2077575555","https://openalex.org/W2088939415","https://openalex.org/W2110920860","https://openalex.org/W2139213241","https://openalex.org/W2140232587","https://openalex.org/W2494517118"],"related_works":["https://openalex.org/W4256012180","https://openalex.org/W47695625","https://openalex.org/W4308506997","https://openalex.org/W2940617399","https://openalex.org/W2030362615","https://openalex.org/W1499231756","https://openalex.org/W98542587","https://openalex.org/W1674993422","https://openalex.org/W79932428","https://openalex.org/W2028338342"],"abstract_inverted_index":null,"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}