{"id":"https://openalex.org/W2069547077","doi":"https://doi.org/10.1142/s012905411100809x","title":"ON EQUATIONS OVER SETS OF NUMBERS AND THEIR LIMITATIONS","display_name":"ON EQUATIONS OVER SETS OF NUMBERS AND THEIR LIMITATIONS","publication_year":2011,"publication_date":"2011-02-01","ids":{"openalex":"https://openalex.org/W2069547077","doi":"https://doi.org/10.1142/s012905411100809x","mag":"2069547077"},"language":"en","primary_location":{"id":"doi:10.1142/s012905411100809x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s012905411100809x","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","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/A5077150907","display_name":"Tommi Lehtinen","orcid":"https://orcid.org/0000-0002-1011-6563"},"institutions":[{"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"]},{"id":"https://openalex.org/I183173800","display_name":"Turku Centre for Computer Science","ror":"https://ror.org/00vy7ed73","country_code":"FI","type":"facility","lineage":["https://openalex.org/I130217899","https://openalex.org/I155660961","https://openalex.org/I183173800"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"TOMMI LEHTINEN","raw_affiliation_strings":["Department of Mathematics, University of Turku, Turku FI\u201320014, Finland","Turku Centre for Computer Science, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Turku, Turku FI\u201320014, Finland","institution_ids":["https://openalex.org/I155660961"]},{"raw_affiliation_string":"Turku Centre for Computer Science, Finland","institution_ids":["https://openalex.org/I183173800"]}]},{"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, and Department of Mathematics, University of Turku, Turku FI\u201320014, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Finland, and Department of Mathematics, University of Turku, Turku FI\u201320014, Finland","institution_ids":["https://openalex.org/I112281704","https://openalex.org/I155660961"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3281,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.77672359,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"22","issue":"02","first_page":"377","last_page":"393"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994999766349792,"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/T11567","display_name":"semigroups and automata theory","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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.8247861862182617},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7820734977722168},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6720906496047974},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5288162231445312},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5244467854499817},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47553229331970215},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.41526076197624207},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39243438839912415},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12770625948905945}],"concepts":[{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.8247861862182617},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7820734977722168},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6720906496047974},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5288162231445312},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5244467854499817},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47553229331970215},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.41526076197624207},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39243438839912415},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12770625948905945},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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":1,"locations":[{"id":"doi:10.1142/s012905411100809x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s012905411100809x","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1591825827","https://openalex.org/W1998081523","https://openalex.org/W2002328599","https://openalex.org/W2064508306","https://openalex.org/W2070863577","https://openalex.org/W2098303102","https://openalex.org/W2135734455","https://openalex.org/W2154949534","https://openalex.org/W2765659955","https://openalex.org/W2912209775"],"related_works":["https://openalex.org/W1490569688","https://openalex.org/W2626419576","https://openalex.org/W2527877093","https://openalex.org/W2955814494","https://openalex.org/W3021670515","https://openalex.org/W2023102124","https://openalex.org/W2910576907","https://openalex.org/W2594052908","https://openalex.org/W2415681638","https://openalex.org/W4381747479"],"abstract_inverted_index":{"Systems":[0],"of":[1,3,21,28,64,77,82,84,96,98,121],"equations":[2,118],"the":[4,17],"form":[5,100],"X":[6,12],"=":[7,13,33],"Y":[8],"+":[9,31,35],"Z":[10],"and":[11,44,103],"C,":[14],"in":[15,107],"which":[16],"unknowns":[18],"are":[19],"sets":[20,29,63,83,120],"natural":[22,65],"numbers,":[23],"\"+\"":[24],"denotes":[25],"elementwise":[26],"sum":[27],"S":[30],"T":[32],"{m":[34],"n":[36,41],"|":[37],"m":[38],"\u2208":[39,42],"S,":[40],"T},":[43],"C":[45],"is":[46,101,110,114],"an":[47],"ultimately":[48],"periodic":[49],"constant,":[50],"have":[51],"recently":[52],"been":[53],"proved":[54],"to":[55,117],"be":[56,88],"computationally":[57],"universal":[58],"(Je\u017c,":[59],"Okhotin,":[60],"\"Equations":[61],"over":[62,119],"numbers":[66,85],"with":[67],"addition":[68],"only\",":[69],"STACS":[70],"2009).":[71],"This":[72],"paper":[73],"establishes":[74],"some":[75],"limitations":[76],"such":[78],"systems.":[79],"A":[80],"class":[81,109],"that":[86],"cannot":[87],"represented":[89],"by":[90],"unique,":[91],"least":[92],"or":[93],"greatest":[94],"solutions":[95],"systems":[97],"this":[99,108],"defined,":[102],"a":[104],"particular":[105],"set":[106],"constructed.":[111],"The":[112],"argument":[113],"then":[115],"extended":[116],"integers.":[122]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}