{"id":"https://openalex.org/W1483620334","doi":"https://doi.org/10.3233/fi-2010-352","title":"Univariate Equations Over Sets of Natural Numbers","display_name":"Univariate Equations Over Sets of Natural Numbers","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1483620334","doi":"https://doi.org/10.3233/fi-2010-352","mag":"1483620334"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2010-352","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2010-352","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","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/A5066525178","display_name":"Artur Je\u017c","orcid":"https://orcid.org/0000-0003-4321-3105"},"institutions":[{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Artur Je\u017c","raw_affiliation_strings":["Institute of Computer Science, University of Wroc\u0142aw, 50\u2013383 Wroc\u0142aw, Poland. aje@cs.uni.wroc.pl"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, University of Wroc\u0142aw, 50\u2013383 Wroc\u0142aw, Poland. aje@cs.uni.wroc.pl","institution_ids":["https://openalex.org/I219388962","https://openalex.org/I4210087266"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005683089","display_name":"Alexander Okhotin","orcid":"https://orcid.org/0000-0002-1615-2725"},"institutions":[{"id":"https://openalex.org/I112281704","display_name":"Research Council of Finland","ror":"https://ror.org/05k73zm37","country_code":"FI","type":"government","lineage":["https://openalex.org/I112281704"]},{"id":"https://openalex.org/I155660961","display_name":"University of Turku","ror":"https://ror.org/05vghhr25","country_code":"FI","type":"education","lineage":["https://openalex.org/I155660961"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Alexander Okhotin","raw_affiliation_strings":["Academy of Finland, alexander.okhotin@utu.fi","Department of Mathematics, University of Turku, Turku FIN20014, Finland","Department of Mathematics, University of Turku, Turku FIN20014, Finland and Academy of Finland, alexander.okhotin@utu.fi#TAB#"],"affiliations":[{"raw_affiliation_string":"Academy of Finland, alexander.okhotin@utu.fi","institution_ids":["https://openalex.org/I112281704"]},{"raw_affiliation_string":"Department of Mathematics, University of Turku, Turku FIN20014, Finland","institution_ids":["https://openalex.org/I155660961"]},{"raw_affiliation_string":"Department of Mathematics, University of Turku, Turku FIN20014, Finland and Academy of Finland, alexander.okhotin@utu.fi#TAB#","institution_ids":["https://openalex.org/I155660961"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066525178"],"corresponding_institution_ids":["https://openalex.org/I219388962","https://openalex.org/I4210087266"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04305988,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"104","issue":"4","first_page":"329","last_page":"348"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T13234","display_name":"advanced mathematical theories","score":0.9843000173568726,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12504","display_name":"Mathematics and Applications","score":0.9757000207901001,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.8525197505950928},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5486578941345215},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.5147473812103271},{"id":"https://openalex.org/keywords/natural","display_name":"Natural (archaeology)","score":0.49021416902542114},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.41296151280403137},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32200318574905396},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.25221726298332214},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.13684174418449402},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.130194753408432},{"id":"https://openalex.org/keywords/paleontology","display_name":"Paleontology","score":0.05363166332244873}],"concepts":[{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.8525197505950928},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5486578941345215},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.5147473812103271},{"id":"https://openalex.org/C2776608160","wikidata":"https://www.wikidata.org/wiki/Q4785462","display_name":"Natural (archaeology)","level":2,"score":0.49021416902542114},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.41296151280403137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32200318574905396},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25221726298332214},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.13684174418449402},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.130194753408432},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.05363166332244873}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/fi-2010-352","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2010-352","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.6299999952316284,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1480007921","https://openalex.org/W1510299134","https://openalex.org/W1512779672","https://openalex.org/W1560143702","https://openalex.org/W1911379864","https://openalex.org/W1997037354","https://openalex.org/W1998084650","https://openalex.org/W2000118875","https://openalex.org/W2070863577","https://openalex.org/W2115826265","https://openalex.org/W2135734455","https://openalex.org/W2154949534","https://openalex.org/W2185277039","https://openalex.org/W2395218731","https://openalex.org/W2765659955","https://openalex.org/W3145062246","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1828158523","https://openalex.org/W2047547195","https://openalex.org/W204175656","https://openalex.org/W1979597421","https://openalex.org/W2803255289","https://openalex.org/W1512294453","https://openalex.org/W1993992974","https://openalex.org/W2007980826","https://openalex.org/W2550734047"],"abstract_inverted_index":{"It":[0,120],"is":[1,16,121],"shown":[2],"that":[3,82],"equations":[4,53,107,137],"of":[5,19,28,33,52,84,93,101,106,115],"the":[6,13,26,80,91,94,129],"form":[7],"\ufffd(X)":[8,108],"=":[9,38,63,109,143],"\u03c8(X),":[10,110],"in":[11,79,90,128],"which":[12],"unknown":[14],"X":[15,60,70],"a":[17,139],"set":[18],"natural":[20],"numbers":[21],"and":[22,31,103],"\ufffd,":[23],"\u03c8":[24],"use":[25,124],"operations":[27],"union,":[29],"intersection":[30],"addition":[32],"sets":[34],"S":[35],"+":[36,40],"T":[37],"{m":[39],"n":[41,46,61,71],"|,":[42],"m":[43],"\u2208":[44,47],"S,":[45],"T},":[48],"can":[49],"simulate":[50],"systems":[51],"\ufffd":[54,64],"j":[55,65,76],"(X":[56,66],"1":[57,67,74],",":[58,68],"\u2026,":[59,69],")":[62,72],"with":[73],"\u2264":[75,77],"\u2113,":[78],"sense":[81],"solutions":[83,92,105],"any":[85],"such":[86],"system":[87],"are":[88],"encoded":[89],"corresponding":[95],"equation.":[96],"This":[97],"implies":[98],"computational":[99],"universality":[100],"least":[102],"greatest":[104],"as":[111,113],"well":[112],"undecidability":[114],"their":[116],"basic":[117],"decision":[118],"problems.":[119],"sufficient":[122],"to":[123,135],"only":[125],"singleton":[126],"constants":[127],"construction.":[130],"All":[131],"results":[132],"equally":[133],"apply":[134],"language":[136],"over":[138],"one-letter":[140],"alphabet":[141],"\u03a3":[142],"{a}.":[144]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
