{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T22:43:00Z","timestamp":1757630580071,"version":"3.44.0"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T00:00:00Z","timestamp":1723075200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T00:00:00Z","timestamp":1723075200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1900716"],"award-info":[{"award-number":["1900716"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1545028"],"award-info":[{"award-number":["1545028"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat Comput"],"published-print":{"date-parts":[[2025,9]]},"DOI":"10.1007\/s11047-024-09994-1","type":"journal-article","created":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T01:01:58Z","timestamp":1723078918000},"page":"383-397","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Real-time computing and robust memory with deterministic chemical reaction networks"],"prefix":"10.1007","volume":"24","author":[{"given":"Willem","family":"Fletcher","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Titus H.","family":"Klinge","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James I.","family":"Lathrop","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dawn A.","family":"Nye","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthew","family":"Rayman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,8,8]]},"reference":[{"key":"9994_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-33099-2","volume-title":"Algorithms in real algebraic geometry","author":"S Basu","year":"2006","unstructured":"Basu S, Pollack R, Roy M-F (2006) Algorithms in real algebraic geometry. Springer, New York, NY, USA"},{"key":"9994_CR2","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1007\/11750321_60","volume-title":"Theory and applications of models of computation","author":"O Bournez","year":"2006","unstructured":"Bournez O, Campagnolo ML, Gra\u00e7a DS, Hainry E (2006) The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation. In: Cai J-Y, Cooper SB, Li A (eds) Theory and applications of models of computation. Springer, Berlin, Heidelberg, pp 631\u2013643"},{"key":"9994_CR3","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1007\/978-3-642-32589-2_23","volume-title":"Mathematical foundations of computer science 2012","author":"O Bournez","year":"2012","unstructured":"Bournez O, Fraigniaud P, Koegler X (2012) Computing with large populations using interactions. In: Rovan B, Sassone V, Widmayer P (eds) Mathematical foundations of computer science 2012. Springer, Berlin, pp 234\u2013246"},{"key":"9994_CR4","doi-asserted-by":"publisher","unstructured":"Bournez O, Gra\u00e7a DS, Pouly A (2017) Polynomial time corresponds to solutions of polynomial ordinary differential equations of polynomial length. J ACM 64(6). https:\/\/doi.org\/10.1145\/3127496","DOI":"10.1145\/3127496"},{"key":"9994_CR5","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1016\/j.tcs.2019.08.013","volume":"801","author":"D Cappelletti","year":"2020","unstructured":"Cappelletti D, Ortiz-Mu\u00f1oz A, Anderson DF, Winfree E (2020) Stochastic chemical reaction networks for robustly approximating arbitrary probability distributions. Theor Comput Sci 801:64\u201395. https:\/\/doi.org\/10.1016\/j.tcs.2019.08.013","journal-title":"Theor Comput Sci"},{"issue":"166","key":"9994_CR6","doi-asserted-by":"publisher","first-page":"20190790","DOI":"10.1098\/rsif.2019.0790","volume":"17","author":"S Clamons","year":"2020","unstructured":"Clamons S, Qian L, Winfree E (2020) Programming and simulating chemical reaction networks on a surface. J R Soc Interface 17(166):20190790. https:\/\/doi.org\/10.1098\/rsif.2019.0790","journal-title":"J R Soc Interface"},{"key":"9994_CR7","doi-asserted-by":"crossref","unstructured":"Epstein IR, Pojman JA (1998) an introduction to nonlinear chemical dynamics: oscillations, waves, patterns, and chaos. Oxford University Press, Inc., 198 Madison Avenue, New York, NY 10016, USA","DOI":"10.1093\/oso\/9780195096705.001.0001"},{"key":"9994_CR8","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1007\/978-3-319-67471-1_7","volume-title":"Computational methods in systems biology","author":"F Fages","year":"2017","unstructured":"Fages F, Le Guludec G, Bournez O, Pouly A (2017) Strong Turing completeness of continuous chemical reaction networks and compilation of mixed analog-digital programs. In: Feret J, Koeppl H (eds) Computational methods in systems biology. Springer, Cham, pp 108\u2013127"},{"key":"9994_CR9","doi-asserted-by":"publisher","unstructured":"Fletcher W, Klinge TH, Lathrop JI, Nye DA, Rayman M (2021) Robust real-time computing with chemical reaction networks. In: Kostitsyna I, Orponen P (eds) 19th International conference on unconventional computation and natural computation, pp 35\u201350. Springer, Cham. https:\/\/doi.org\/10.1007\/978-3-030-87993-8_3","DOI":"10.1007\/978-3-030-87993-8_3"},{"key":"9994_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2021.02.001","author":"D Furcy","year":"2021","unstructured":"Furcy D, Summers SM, Wendlandt C (2021) Self-assembly of and optimal encoding within thin rectangles at temperature-1 in 3D. Theor Comput Sci. https:\/\/doi.org\/10.1016\/j.tcs.2021.02.001","journal-title":"Theor Comput Sci"},{"key":"9994_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/s11047-021-09846-2","author":"D Hader","year":"2021","unstructured":"Hader D, Patitz MJ (2021) Geometric tiles and powers and limitations of geometric hindrance in self-assembly. Nat Comput. https:\/\/doi.org\/10.1007\/s11047-021-09846-2","journal-title":"Nat Comput"},{"key":"9994_CR12","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1090\/S0002-9947-1965-0170805-7","volume":"117","author":"J Hartmanis","year":"1965","unstructured":"Hartmanis J, Stearns RE (1965) On the computational complexity of algorithms. Trans Am Math Soc 117:285\u2013306","journal-title":"Trans Am Math Soc"},{"key":"9994_CR13","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-031-15034-0_1","volume-title":"Computational methods in systems biology","author":"M Hemery","year":"2022","unstructured":"Hemery M, Fages F (2022) Algebraic biochemistry: a framework for analog online computation in cells. In: Petre I, P\u0103un A (eds) Computational methods in systems biology. Springer, Cham, pp 3\u201320"},{"key":"9994_CR14","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/978-3-030-26807-7_3","volume-title":"DNA computing and molecular programming","author":"X Huang","year":"2019","unstructured":"Huang X, Klinge TH, Lathrop JI (2019) Real-time equivalence of chemical reaction networks and analog computers. In: Thachuk C, Liu Y (eds) DNA computing and molecular programming. Springer, Cham, pp 37\u201353"},{"issue":"1","key":"9994_CR15","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/s11047-018-9706-x","volume":"18","author":"X Huang","year":"2019","unstructured":"Huang X, Klinge TH, Lathrop JI, Li X, Lutz JH (2019) Real-time computability of real numbers by chemical reaction networks. Nat Comput 18(1):63\u201373. https:\/\/doi.org\/10.1007\/s11047-018-9706-x","journal-title":"Nat Comput"},{"key":"9994_CR16","doi-asserted-by":"publisher","unstructured":"Klinge TH, Lathrop JI, Moreno S, Potter HD, Raman NK, Riley MR (2020) ALCH: An Imperative Language for Chemical Reaction Network-Controlled Tile Assembly. In: Geary C, Patitz MJ (eds) 26th International conference on DNA computing and molecular programming (DNA 26). Leibniz international proceedings in informatics (LIPIcs), vol 174, pp 6\u20131622. Schloss Dagstuhl\u2013Leibniz-Zentrum f\u00fcr Informatik, Dagstuhl, Germany (2020). https:\/\/doi.org\/10.4230\/LIPIcs.DNA.2020.6","DOI":"10.4230\/LIPIcs.DNA.2020.6"},{"key":"9994_CR17","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1016\/j.tcs.2020.01.008","volume":"816","author":"TH Klinge","year":"2020","unstructured":"Klinge TH, Lathrop JI, Lutz JH (2020) Robust biomolecular finite automata. Theor Comput Sci 816:114\u2013143. https:\/\/doi.org\/10.1016\/j.tcs.2020.01.008","journal-title":"Theor Comput Sci"},{"key":"9994_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-8134-0","volume-title":"A primer of real analytic functions","author":"SG Krantz","year":"2002","unstructured":"Krantz SG, Parks HR (2002) A primer of real analytic functions. Birkh\u00e4user, Boston, MA, USA"},{"key":"9994_CR19","unstructured":"Lewis AD (2014) Notes on global analysis. https:\/\/mast.queensu.ca\/~andrew\/teaching\/math942\/pdf\/1chapter1.pdf"},{"key":"9994_CR20","doi-asserted-by":"publisher","DOI":"10.1017\/9781316716991","volume-title":"Model theory of fields","author":"D Marker","year":"2017","unstructured":"Marker D, Messmer M, Pillay A (2017) Model theory of fields, vol 5. Cambridge University Press, New York, NY, USA"},{"key":"9994_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/s00446-020-00378-z","author":"EE Severson","year":"2020","unstructured":"Severson EE, Haley D, Doty D (2020) Composable computation in discrete chemical reaction networks. Distribut Comput. https:\/\/doi.org\/10.1007\/s00446-020-00378-z","journal-title":"Distribut Comput"},{"key":"9994_CR22","doi-asserted-by":"publisher","unstructured":"Turing AM (1937) On computable numbers, with an application to the Entscheidungsproblem. In: Proceedings of the London mathematical society s2-42(1):230\u2013265. https:\/\/doi.org\/10.1112\/plms\/s2-42.1.230","DOI":"10.1112\/plms\/s2-42.1.230"},{"issue":"1","key":"9994_CR23","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1017\/S0022481200028899","volume":"53","author":"L Van Den Dries","year":"1988","unstructured":"Van Den Dries L (1988) Alfred Tarski\u2019s elimination theory for real closed fields. J Symbolic Logic 53(1):7\u201319. https:\/\/doi.org\/10.1017\/S0022481200028899","journal-title":"J Symbolic Logic"}],"container-title":["Natural Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11047-024-09994-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11047-024-09994-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11047-024-09994-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,10]],"date-time":"2025-09-10T19:19:41Z","timestamp":1757531981000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11047-024-09994-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,8]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["9994"],"URL":"https:\/\/doi.org\/10.1007\/s11047-024-09994-1","relation":{},"ISSN":["1567-7818","1572-9796"],"issn-type":[{"type":"print","value":"1567-7818"},{"type":"electronic","value":"1572-9796"}],"subject":[],"published":{"date-parts":[[2024,8,8]]},"assertion":[{"value":"5 July 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 August 2024","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no conflicts of interest to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}