{"id":"https://openalex.org/W4389628296","doi":"https://doi.org/10.1038/s41598-023-49593-1","title":"Improving the efficiency of using multivalued logic tools: application of algebraic rings","display_name":"Improving the efficiency of using multivalued logic tools: application of algebraic rings","publication_year":2023,"publication_date":"2023-12-12","ids":{"openalex":"https://openalex.org/W4389628296","doi":"https://doi.org/10.1038/s41598-023-49593-1","pmid":"https://pubmed.ncbi.nlm.nih.gov/38086862","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/10716195"},"language":"en","primary_location":{"id":"doi:10.1038/s41598-023-49593-1","doi":"https://doi.org/10.1038/s41598-023-49593-1","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-023-49593-1","pdf_url":"https://www.nature.com/articles/s41598-023-49593-1.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.nature.com/articles/s41598-023-49593-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030471618","display_name":"Ibragim Esenovich Suleimenov","orcid":"https://orcid.org/0000-0002-7274-029X","observed_orcids":["https://orcid.org/0000-0002-7274-029X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ibragim E. Suleimenov","raw_affiliation_strings":["National Engineering Academy of the Republic of Kazakhstan, Bogenbai Batyr Str. 80, 050010, Almaty, Kazakhstan"],"raw_orcid":"https://orcid.org/0000-0002-7274-029X","affiliations":[{"raw_affiliation_string":"National Engineering Academy of the Republic of Kazakhstan, Bogenbai Batyr Str. 80, 050010, Almaty, Kazakhstan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026106321","display_name":"Yelizaveta Sergeevna Vitulyova","orcid":"https://orcid.org/0000-0002-6075-4870","observed_orcids":["https://orcid.org/0000-0002-6075-4870"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yelizaveta S. Vitulyova","raw_affiliation_strings":["National Engineering Academy of the Republic of Kazakhstan, Bogenbai Batyr Str. 80, 050010, Almaty, Kazakhstan"],"raw_orcid":"https://orcid.org/0000-0002-6075-4870","affiliations":[{"raw_affiliation_string":"National Engineering Academy of the Republic of Kazakhstan, Bogenbai Batyr Str. 80, 050010, Almaty, Kazakhstan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045918395","display_name":"Sherniyaz B. Kabdushev","orcid":"https://orcid.org/0000-0001-9528-084X","observed_orcids":["https://orcid.org/0000-0001-9528-084X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sherniyaz B. Kabdushev","raw_affiliation_strings":["National Engineering Academy of the Republic of Kazakhstan, Bogenbai Batyr Str. 80, 050010, Almaty, Kazakhstan"],"raw_orcid":"https://orcid.org/0000-0001-9528-084X","affiliations":[{"raw_affiliation_string":"National Engineering Academy of the Republic of Kazakhstan, Bogenbai Batyr Str. 80, 050010, Almaty, Kazakhstan","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026086148","display_name":"Akhat Serikuly Bakirov","orcid":"https://orcid.org/0000-0002-2563-307X","observed_orcids":["https://orcid.org/0000-0002-2563-307X"]},"institutions":[{"id":"https://openalex.org/I185571130","display_name":"Al-Farabi Kazakh National University","ror":"https://ror.org/03q0vrn42","country_code":"KZ","type":"education","lineage":["https://openalex.org/I185571130"]},{"id":"https://openalex.org/I247491477","display_name":"Almaty University of Power Engineering and Telecommunications","ror":"https://ror.org/020d95911","country_code":"KZ","type":"education","lineage":["https://openalex.org/I247491477"]}],"countries":["KZ"],"is_corresponding":true,"raw_author_name":"Akhat S. Bakirov","raw_affiliation_strings":["Al-Farabi Kazakh National University, Almaty, 050040, Republic of Kazakhstan. axatmr@mail.ru","Gumarbek Daukeyev Almaty University of Power Engineering and Telecommunications, Baytursynov Str. 126/1, 050013, Almaty, Republic of Kazakhstan. axatmr@mail.ru","Gumarbek Daukeyev Almaty University of Power Engineering and Telecommunications, Baytursynov Str. 126/1, 050013, Almaty, Republic of Kazakhstan"],"raw_orcid":"https://orcid.org/0000-0002-2563-307X","affiliations":[{"raw_affiliation_string":"Al-Farabi Kazakh National University, Almaty, 050040, Republic of Kazakhstan. axatmr@mail.ru","institution_ids":["https://openalex.org/I185571130"]},{"raw_affiliation_string":"Gumarbek Daukeyev Almaty University of Power Engineering and Telecommunications, Baytursynov Str. 126/1, 050013, Almaty, Republic of Kazakhstan. axatmr@mail.ru","institution_ids":["https://openalex.org/I247491477"]},{"raw_affiliation_string":"Gumarbek Daukeyev Almaty University of Power Engineering and Telecommunications, Baytursynov Str. 126/1, 050013, Almaty, Republic of Kazakhstan","institution_ids":["https://openalex.org/I247491477"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026086148"],"corresponding_institution_ids":["https://openalex.org/I185571130","https://openalex.org/I247491477"],"apc_list":{"value":2390,"currency":"USD","value_usd":2390},"apc_paid":{"value":2390,"currency":"USD","value_usd":2390},"fwci":3.5783,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.93794876,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"13","issue":"1","first_page":"22021","last_page":"22021"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.8637999892234802,"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":0.8637999892234802,"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/T11130","display_name":"Coding theory and cryptography","score":0.09220000356435776,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.005100000184029341,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/many-valued-logic","display_name":"many-valued logic","score":0.9869999885559082},{"id":"https://openalex.org/keywords/finite-fields","display_name":"finite fields","score":0.9919999837875366},{"id":"https://openalex.org/keywords/truth-table-reductions","display_name":"truth-table reductions","score":0.7429999709129333},{"id":"https://openalex.org/keywords/algebraic-expressions","display_name":"algebraic expressions","score":0.6100000143051147},{"id":"https://openalex.org/keywords/logical-operations","display_name":"logical operations","score":0.6209999918937683},{"id":"https://openalex.org/keywords/electronic-circuits","display_name":"electronic circuits","score":0.7900000214576721}],"concepts":[{"id":"https://openalex.org/C56949724","wikidata":"https://www.wikidata.org/wiki/Q219079","display_name":"Truth table","level":2,"score":0.7044379711151123},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6474232077598572},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6328150033950806},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5824928879737854},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.57790207862854},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5255391001701355},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5239596366882324},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.5065995454788208},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.49944138526916504},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.436332106590271},{"id":"https://openalex.org/C45235069","wikidata":"https://www.wikidata.org/wiki/Q278425","display_name":"Table (database)","level":2,"score":0.4277036786079407},{"id":"https://openalex.org/C18912844","wikidata":"https://www.wikidata.org/wiki/Q4724001","display_name":"Algebraic expression","level":3,"score":0.4196663200855255},{"id":"https://openalex.org/C148607811","wikidata":"https://www.wikidata.org/wiki/Q746863","display_name":"Algebraic function","level":3,"score":0.4170917868614197},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3942547142505646},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34472495317459106},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23099803924560547},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2112157642841339},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13616067171096802},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1038/s41598-023-49593-1","doi":"https://doi.org/10.1038/s41598-023-49593-1","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-023-49593-1","pdf_url":"https://www.nature.com/articles/s41598-023-49593-1.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},{"id":"pmh:oai:pubmedcentral.nih.gov:10716195","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10716195","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10716195/pdf/41598_2023_Article_49593.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sci Rep","raw_type":"Text"},{"id":"pmid:38086862","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38086862","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific reports","raw_type":"Journal Article"},{"id":"pmh:oai:doaj.org/article:52fba0bff1bb4b6d9a797019c3b28010","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/52fba0bff1bb4b6d9a797019c3b28010","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scientific Reports, Vol 13, Iss 1, Pp 1-17 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1038/s41598-023-49593-1","doi":"https://doi.org/10.1038/s41598-023-49593-1","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-023-49593-1","pdf_url":"https://www.nature.com/articles/s41598-023-49593-1.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310481","display_name":"Uddannelses- og Forskningsministeriet","ror":"https://ror.org/03ge1nb22"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389628296.pdf","grobid_xml":"https://content.openalex.org/works/W4389628296.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W2536203890","https://openalex.org/W2734413985","https://openalex.org/W2751548637","https://openalex.org/W2800496941","https://openalex.org/W2895380069","https://openalex.org/W2901756267","https://openalex.org/W2912590499","https://openalex.org/W2926023027","https://openalex.org/W2931119630","https://openalex.org/W2939073427","https://openalex.org/W2961835343","https://openalex.org/W2964082513","https://openalex.org/W2984441440","https://openalex.org/W3029389934","https://openalex.org/W3034714558","https://openalex.org/W3037305167","https://openalex.org/W3086309464","https://openalex.org/W3093388624","https://openalex.org/W3110186717","https://openalex.org/W3125499840","https://openalex.org/W3132633609","https://openalex.org/W3134082691","https://openalex.org/W3134189445","https://openalex.org/W3173549151","https://openalex.org/W3186038803","https://openalex.org/W3187619230","https://openalex.org/W3191729854","https://openalex.org/W3197680824","https://openalex.org/W3200876719","https://openalex.org/W3209546542","https://openalex.org/W4200468076","https://openalex.org/W4206955021","https://openalex.org/W4242467456","https://openalex.org/W4310094152","https://openalex.org/W4317569126","https://openalex.org/W4361791246"],"related_works":["https://openalex.org/W4317569126","https://openalex.org/W2000709659","https://openalex.org/W2150130365","https://openalex.org/W81049629","https://openalex.org/W316631906","https://openalex.org/W358708875","https://openalex.org/W1528672899","https://openalex.org/W4381232532","https://openalex.org/W2000090444","https://openalex.org/W2162437633"],"abstract_inverted_index":{"It":[0,68],"is":[1,21,49,58,69,102,139,145],"shown":[2],"that":[3,117,176],"in":[4,16,47,65],"order":[5],"to":[6,23,31,51,71,79,84,104,153,157],"increase":[7],"the":[8,43,89,92,118,126,129,163,166],"efficiency":[9],"of":[10,13,34,45,94,108,131,162,165],"using":[11],"methods":[12],"abstract":[14],"algebra":[15],"modern":[17],"information":[18],"technologies,":[19],"it":[20],"important":[22],"establish":[24],"an":[25,73,85,105],"explicit":[26,62],"connection":[27,57],"between":[28],"operations":[29,156],"corresponding":[30],"various":[32],"varieties":[33],"multivalued":[35,41,99,136],"logics":[36],"and":[37],"algebraic":[38,63,74,86,119,158],"operations.":[39],"For":[40],"logics,":[42],"number":[44,93,130],"variables":[46],"which":[48,76],"equal":[50,103],"a":[52,56,98,109,135,146],"prime":[53,110,147],"number,":[54],"such":[55],"naturally":[59],"established":[60],"through":[61],"expressions":[64],"Galois":[66],"fields.":[67],"possible":[70],"define":[72],"\u03b4-function,":[75],"allows":[77,152],"you":[78],"reduce":[80,154],"any":[81],"truth":[82],"table":[83],"expression,":[87],"for":[88,125],"case":[90,127],"when":[91,128],"values":[95,132],"accepted":[96],"by":[97,134],"logic":[100,137],"variable":[101,138],"integer":[106],"power":[107],"number.":[111,148],"In":[112],"this":[113],"paper,":[114],"we":[115],"show":[116],"\u03b4-function":[120],"can":[121],"also":[122,151],"be":[123],"defined":[124],"taken":[133],"p":[140,144],"-":[141],"1,":[142],"where":[143],"This":[149],"function":[150],"logical":[155],"expressions.":[159],"Specific":[160],"examples":[161],"constructiveness":[164],"proposed":[167],"approach":[168],"are":[169],"presented,":[170],"as":[171,173],"well":[172],"electronic":[174],"circuits":[175],"experimentally":[177],"prove":[178],"its":[179],"adequacy.":[180]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":4}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2023-12-13T00:00:00"}
