{"id":"https://openalex.org/W2010163765","doi":"https://doi.org/10.1137/0214050","title":"A Lower Bound for the Formula Size of Rational Functions","display_name":"A Lower Bound for the Formula Size of Rational Functions","publication_year":1985,"publication_date":"1985-08-01","ids":{"openalex":"https://openalex.org/W2010163765","doi":"https://doi.org/10.1137/0214050","mag":"2010163765"},"language":"en","primary_location":{"id":"doi:10.1137/0214050","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0214050","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5039537659","display_name":"K. Kalorkoti","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"K. A. Kalorkoti","raw_affiliation_strings":["School of Informatics"],"affiliations":[{"raw_affiliation_string":"School of Informatics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039537659"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7411,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.78699893,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"14","issue":"3","first_page":"678","last_page":"687"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9855999946594238,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.977400004863739,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.694175124168396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6940351724624634},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.6930827498435974},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.5738134384155273},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5573011636734009},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5457295179367065},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5263575315475464},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5124897956848145},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.5054628849029541},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.48839515447616577},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.4793456494808197},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.46773797273635864},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.45026615262031555},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.44846874475479126},{"id":"https://openalex.org/keywords/algebraic-function","display_name":"Algebraic function","score":0.4442160427570343},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.25037455558776855},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.18944504857063293},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08507049083709717}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.694175124168396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6940351724624634},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.6930827498435974},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5738134384155273},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5573011636734009},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5457295179367065},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5263575315475464},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5124897956848145},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.5054628849029541},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.48839515447616577},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.4793456494808197},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.46773797273635864},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.45026615262031555},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.44846874475479126},{"id":"https://openalex.org/C148607811","wikidata":"https://www.wikidata.org/wiki/Q746863","display_name":"Algebraic function","level":3,"score":0.4442160427570343},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25037455558776855},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.18944504857063293},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08507049083709717},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0214050","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0214050","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W2004589512","https://openalex.org/W2113097540","https://openalex.org/W4210445513","https://openalex.org/W4239191450"],"related_works":["https://openalex.org/W3171743997","https://openalex.org/W4200629753","https://openalex.org/W2382093415","https://openalex.org/W2000290939","https://openalex.org/W2408391212","https://openalex.org/W2783825445","https://openalex.org/W3024476512","https://openalex.org/W2127443636","https://openalex.org/W2005027240","https://openalex.org/W2352592347"],"abstract_inverted_index":{"We":[0,64,103],"establish":[1],"a":[2,51],"lower":[3,37,52,114],"bound":[4,38,53,115],"for":[5,39,54,116],"the":[6,55,89,110,117],"formula":[7,16,56,96],"size":[8,57,97],"of":[9,58],"quolynomials":[10],"over":[11,61,75,86],"arbitrary":[12],"fields.":[13,63,77],"Our":[14],"basic":[15],"operations":[17],"are":[18,80],"addition,":[19],"subtraction,":[20],"multiplication":[21],"and":[22,42],"division.":[23],"The":[24],"proof":[25],"is":[26],"based":[27],"on":[28],"Ne\u010diporuk\u2019s":[29,70],"[Soviet":[30,123],"Math.":[31,124],"Doklady,":[32,125],"7":[33,126],"(1966),":[34,127],"pp.":[35,128],"999\u20131000]":[36],"Boolean":[40,118],"functions":[41,60,74],"uses":[43],"formal":[44],"power":[45],"series.":[46],"This":[47],"result":[48],"immediately":[49],"yields":[50],"rational":[59,73],"infinite":[62],"also":[65],"show":[66,84],"how":[67],"to":[68,72,83,109,121],"adapt":[69],"method":[71],"finite":[76],"These":[78],"results":[79],"then":[81],"used":[82],"that,":[85],"any":[87],"field,":[88],"$n":[90],"\\times":[91],"n$":[92],"determinant":[93,119],"function":[94],"has":[95],"at":[98],"least":[99],"$\\Omega":[100,111],"(n^3":[101,112],")$.":[102],"thus":[104],"have":[105],"an":[106],"algebraic":[107],"analogue":[108],")$":[113],"due":[120],"Kloss":[122],"1537\u20131540].":[129]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}