{"id":"https://openalex.org/W2082911118","doi":"https://doi.org/10.1109/tfuzz.2015.2394396","title":"Hardness of Solving Relational Equations","display_name":"Hardness of Solving Relational Equations","publication_year":2015,"publication_date":"2015-01-21","ids":{"openalex":"https://openalex.org/W2082911118","doi":"https://doi.org/10.1109/tfuzz.2015.2394396","mag":"2082911118"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2015.2394396","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2015.2394396","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Fuzzy Systems","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/A5027925658","display_name":"Eduard Bartl","orcid":"https://orcid.org/0000-0002-1273-0268"},"institutions":[{"id":"https://openalex.org/I70703428","display_name":"Palack\u00fd University Olomouc","ror":"https://ror.org/04qxnmv42","country_code":"CZ","type":"education","lineage":["https://openalex.org/I70703428"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Eduard Bartl","raw_affiliation_strings":["Deparment of Computer Science, Palacky University, Olomouc, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Deparment of Computer Science, Palacky University, Olomouc, Czech Republic","institution_ids":["https://openalex.org/I70703428"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004391892","display_name":"Radim B\u011blohl\u00e1vek","orcid":"https://orcid.org/0000-0003-4924-3233"},"institutions":[{"id":"https://openalex.org/I70703428","display_name":"Palack\u00fd University Olomouc","ror":"https://ror.org/04qxnmv42","country_code":"CZ","type":"education","lineage":["https://openalex.org/I70703428"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Radim Belohlavek","raw_affiliation_strings":["Deparment of Computer Science, Palacky University, Olomouc, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Deparment of Computer Science, Palacky University, Olomouc, Czech Republic","institution_ids":["https://openalex.org/I70703428"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I70703428"],"apc_list":null,"apc_paid":null,"fwci":1.7646,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.85636298,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"23","issue":"6","first_page":"2435","last_page":"2438"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9944999814033508,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9944999814033508,"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/T10538","display_name":"Data Mining Algorithms and Applications","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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":0.9897000193595886,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6251306533813477},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5718441009521484},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4637032151222229},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3728429973125458},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3494514226913452},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32895010709762573}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6251306533813477},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5718441009521484},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4637032151222229},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3728429973125458},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3494514226913452},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32895010709762573},{"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:10.1109/tfuzz.2015.2394396","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2015.2394396","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1770451094","display_name":null,"funder_award_id":"CZ.1.07/2.3.00/20.0059","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"},{"id":"https://openalex.org/G5376844316","display_name":null,"funder_award_id":"14-11585S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W127405698","https://openalex.org/W1714045541","https://openalex.org/W1898259180","https://openalex.org/W1990673965","https://openalex.org/W1991764565","https://openalex.org/W1997100226","https://openalex.org/W2005441399","https://openalex.org/W2012201562","https://openalex.org/W2019716713","https://openalex.org/W2029338278","https://openalex.org/W2030273176","https://openalex.org/W2042960352","https://openalex.org/W2046250921","https://openalex.org/W2061821032","https://openalex.org/W2071200009","https://openalex.org/W2078846431","https://openalex.org/W2099459744","https://openalex.org/W2134691152","https://openalex.org/W2147015530","https://openalex.org/W2154274300","https://openalex.org/W2159441390","https://openalex.org/W2496338429","https://openalex.org/W2506954980"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W2189341500"],"abstract_inverted_index":{"Minimal":[0],"solutions":[1,9,21],"play":[2],"a":[3],"crucial":[4],"role":[5],"in":[6],"describing":[7],"all":[8,89],"of":[10,18,41,51,75,77,96],"relational":[11],"equations.":[12],"For":[13],"this":[14,62],"reason,":[15],"the":[16,42,55,66,70,73],"problem":[17,43,74],"computing":[19,33,78,88],"minimal":[20,34,79,90],"has":[22],"for":[23,32],"long":[24],"been":[25],"examined.":[26],"The":[27,46],"literature":[28],"contains":[29],"several":[30],"algorithms":[31],"solutions.":[35],"Recently,":[36],"contributions":[37],"regarding":[38],"computational":[39],"complexity":[40,47,76],"itself":[44],"appeared.":[45],"aspect":[48],"is":[49,84],"clearly":[50],"fundamental":[52],"importance.":[53],"However,":[54],"existing":[56,67],"results":[57],"contain":[58],"serious":[59],"flaws.":[60],"In":[61],"paper,":[63],"we":[64],"inspect":[65],"contributions,":[68],"clarify":[69],"flaws,":[71],"examine":[72],"solutions,":[80,91],"prove":[81],"that":[82],"there":[83],"no":[85],"efficient":[86],"algorithm":[87],"and":[92],"discuss":[93],"further":[94],"ramifications":[95],"our":[97],"observations.":[98]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}