{"id":"https://openalex.org/W4401683509","doi":"https://doi.org/10.1142/s0129054124470014","title":"A Characterization of Polynomial Time Computable Functions from the Integers to the Reals Using Discrete Ordinary Differential Equations","display_name":"A Characterization of Polynomial Time Computable Functions from the Integers to the Reals Using Discrete Ordinary Differential Equations","publication_year":2024,"publication_date":"2024-08-17","ids":{"openalex":"https://openalex.org/W4401683509","doi":"https://doi.org/10.1142/s0129054124470014"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054124470014","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054124470014","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/A5081255148","display_name":"Manon Blanc","orcid":"https://orcid.org/0000-0002-6961-089X"},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Manon Blanc","raw_affiliation_strings":["Universit\u00e9 Paris-Saclay, LISN, Gif-sur-Yvette, France","\u00c9cole Polytechnique, Institute Polytechnique de Paris, Palaiseau, France"],"raw_orcid":"https://orcid.org/0000-0002-6961-089X","affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris-Saclay, LISN, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I277688954"]},{"raw_affiliation_string":"\u00c9cole Polytechnique, Institute Polytechnique de Paris, Palaiseau, France","institution_ids":["https://openalex.org/I142476485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067372819","display_name":"Olivier Bournez","orcid":"https://orcid.org/0000-0002-9218-1130"},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Olivier Bournez","raw_affiliation_strings":["\u00c9cole Polytechnique, Institute Polytechnique de Paris, Palaiseau, France"],"raw_orcid":"https://orcid.org/0000-0002-9218-1130","affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique, Institute Polytechnique de Paris, Palaiseau, France","institution_ids":["https://openalex.org/I142476485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081255148"],"corresponding_institution_ids":["https://openalex.org/I142476485","https://openalex.org/I277688954"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15802392,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"36","issue":"07","first_page":"989","last_page":"1016"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","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/T12002","display_name":"Computability, Logic, AI Algorithms","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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7512922286987305},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5842783451080322},{"id":"https://openalex.org/keywords/computable-function","display_name":"Computable function","score":0.5114427804946899},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4953416883945465},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4839073121547699},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.43979620933532715},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2700352370738983},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10521230101585388}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7512922286987305},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5842783451080322},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.5114427804946899},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4953416883945465},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4839073121547699},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.43979620933532715},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2700352370738983},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10521230101585388},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054124470014","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054124470014","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":14,"referenced_works":["https://openalex.org/W51799866","https://openalex.org/W103369326","https://openalex.org/W1505951678","https://openalex.org/W1545819195","https://openalex.org/W1581416890","https://openalex.org/W1958506772","https://openalex.org/W2029948740","https://openalex.org/W2067619114","https://openalex.org/W2069792094","https://openalex.org/W2087950601","https://openalex.org/W2108904240","https://openalex.org/W3184399009","https://openalex.org/W4243563333","https://openalex.org/W4290017128"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3107994849","https://openalex.org/W4247143848","https://openalex.org/W2009883749","https://openalex.org/W2735573198","https://openalex.org/W29442446","https://openalex.org/W330727063","https://openalex.org/W2155009918","https://openalex.org/W2083648745","https://openalex.org/W155750020"],"abstract_inverted_index":{"In":[0,66,94],"a":[1,62,74,98,126],"recent":[2],"article,":[3,68],"the":[4,9,12,34,38,71,79,82,89,106],"class":[5,108],"of":[6,41,52,76,91,100,105,109],"functions":[7,77,102,110],"from":[8,78],"integers":[10,13,80],"to":[11,54,73,81],"computable":[14,84,92],"in":[15,85,88,103],"polynomial":[16,86],"time":[17,87],"has":[18],"been":[19],"characterized":[20],"using":[21],"discrete":[22],"ordinary":[23],"differential":[24],"equations":[25],"(ODE),":[26],"also":[27],"known":[28],"as":[29,50,61],"finite":[30],"differences.":[31],"Doing":[32],"so,":[33],"authors":[35],"pointed":[36],"out":[37],"fundamental":[39],"role":[40],"linear":[42,122],"(discrete)":[43],"ODEs":[44],"and":[45,57,116,125],"classical":[46],"ODE":[47],"tools":[48],"such":[49,101],"changes":[51],"variables":[53],"capture":[55],"computability":[56],"complexity":[58],"measures,":[59],"or":[60],"tool":[63],"for":[64],"programming.":[65],"this":[67],"we":[69,96],"extend":[70],"approach":[72],"characterization":[75,99],"reals":[83],"sense":[90],"analysis.":[93],"particular,":[95],"provide":[97],"terms":[104],"smallest":[107],"that":[111,117],"contains":[112],"some":[113],"basic":[114],"functions,":[115],"is":[118],"closed":[119],"by":[120],"composition,":[121],"length":[123],"ODEs,":[124],"natural":[127],"effective":[128],"limit":[129],"schema.":[130]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}