{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T08:27:31Z","timestamp":1762504051207,"version":"build-2065373602"},"reference-count":27,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2025,11]]},"abstract":"<jats:p>In a recent article, the class of functions from the integers to the integers computable in polynomial time has been characterized using discrete ordinary differential equations (ODE), also known as finite differences. Doing so, the authors pointed out the fundamental role of linear (discrete) ODEs and classical ODE tools such as changes of variables to capture computability and complexity measures, or as a tool for programming.<\/jats:p>\n                  <jats:p>In this article, we extend the approach to a characterization of functions from the integers to the reals computable in polynomial time in the sense of computable analysis. In particular, we provide a characterization of such functions in terms of the smallest class of functions that contains some basic functions, and that is closed by composition, linear length ODEs, and a natural effective limit schema.<\/jats:p>","DOI":"10.1142\/s0129054124470014","type":"journal-article","created":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T01:46:16Z","timestamp":1724031976000},"page":"989-1016","source":"Crossref","is-referenced-by-count":0,"title":["A Characterization of Polynomial Time Computable Functions from the Integers to the Reals Using Discrete Ordinary Differential Equations"],"prefix":"10.1142","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6961-089X","authenticated-orcid":false,"given":"Manon","family":"Blanc","sequence":"first","affiliation":[{"name":"\u00c9cole Polytechnique, Institute Polytechnique de Paris, Palaiseau, France"},{"name":"Universit\u00e9 Paris-Saclay, LISN, Gif-sur-Yvette, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9218-1130","authenticated-orcid":false,"given":"Olivier","family":"Bournez","sequence":"additional","affiliation":[{"name":"\u00c9cole Polytechnique, Institute Polytechnique de Paris, Palaiseau, France"}]}],"member":"219","published-online":{"date-parts":[[2024,8,17]]},"reference":[{"volume-title":"Ordinary Differential Equations","year":"1978","author":"Arnold V. I.","key":"S0129054124470014BIB001"},{"key":"S0129054124470014BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF01201998"},{"key":"S0129054124470014BIB003","volume-title":"Ordinary Differential Equations","author":"Birkhoff G.","year":"1989","edition":"4"},{"key":"S0129054124470014BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-13502-6_4"},{"key":"S0129054124470014BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jco.2006.12.005"},{"key":"S0129054124470014BIB006","series-title":"LIPIcs","first-page":"23:1","volume-title":"44th Int Symposium on Mathematical Foundations of Computer Science, MFCS","volume":"138","author":"Bournez O.","year":"2019"},{"issue":"7","key":"S0129054124470014BIB007","volume":"32","author":"Bournez O.","year":"2023","journal-title":"Computational Complexity"},{"volume-title":"Handbook of Computability and Complexity in Analysis","year":"2020","author":"Bournez O.","key":"S0129054124470014BIB008"},{"key":"S0129054124470014BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(95)00249-9"},{"key":"S0129054124470014BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-68546-5_18"},{"key":"S0129054124470014BIB011","first-page":"589","volume-title":"Handbook of Computability Theory","author":"Clote P.","year":"1998"},{"volume-title":"Boolean Functions and Computation Models","year":"2013","author":"Clote P.","key":"S0129054124470014BIB012"},{"key":"S0129054124470014BIB013","first-page":"24","volume-title":"Proceedings of the International Conference on Logic, Methodology, and Philosophy of Science","author":"Cobham A.","year":"1962"},{"volume-title":"Theory of Ordinary Differential Equations","year":"1955","author":"Coddington E. A.","key":"S0129054124470014BIB014"},{"volume-title":"International Monographs on Advanced Mathematics and Physics","year":"1971","author":"Gel\u2019fond A. O.","key":"S0129054124470014BIB015"},{"journal-title":"Stanford University","year":"2005","author":"Gleich D.","key":"S0129054124470014BIB016"},{"key":"S0129054124470014BIB017","doi-asserted-by":"publisher","DOI":"10.1063\/1.4822863"},{"key":"S0129054124470014BIB018","doi-asserted-by":"publisher","DOI":"10.2174\/97816080508641090101"},{"key":"S0129054124470014BIB019","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-6802-1"},{"key":"S0129054124470014BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-60178-3_84"},{"key":"S0129054124470014BIB022","first-page":"320","volume-title":"Feasible Mathematics II","author":"Leivant D.","year":"1994"},{"issue":"2","key":"S0129054124470014BIB023","first-page":"184","volume":"19","author":"Leivant D.","year":"1993","journal-title":"Fundamenta Informatica"},{"key":"S0129054124470014BIB024","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0022277"},{"key":"S0129054124470014BIB025","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/exab042"},{"key":"S0129054124470014BIB026","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0707-8"},{"key":"S0129054124470014BIB027","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1995.1013"},{"key":"S0129054124470014BIB028","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-56999-9"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054124470014","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T08:17:03Z","timestamp":1762503423000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0129054124470014"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,17]]},"references-count":27,"journal-issue":{"issue":"07","published-print":{"date-parts":[[2025,11]]}},"alternative-id":["10.1142\/S0129054124470014"],"URL":"https:\/\/doi.org\/10.1142\/s0129054124470014","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"type":"print","value":"0129-0541"},{"type":"electronic","value":"1793-6373"}],"subject":[],"published":{"date-parts":[[2024,8,17]]}}}