{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:38:27Z","timestamp":1760132307906,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2014,2,11]],"date-time":"2014-02-11T00:00:00Z","timestamp":1392076800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>The computational complexity of the solutions $h$ to the ordinary\ndifferential equation $h(0)=0$, $h'(t) = g(t, h(t))$ under various assumptions\non the function $g$ has been investigated. Kawamura showed in 2010 that the\nsolution $h$ can be PSPACE-hard even if $g$ is assumed to be Lipschitz\ncontinuous and polynomial-time computable. We place further requirements on the\nsmoothness of $g$ and obtain the following results: the solution $h$ can still\nbe PSPACE-hard if $g$ is assumed to be of class $C^1$; for each $k\\ge2$, the\nsolution $h$ can be hard for the counting hierarchy even if $g$ is of class\n$C^k$.<\/jats:p>","DOI":"10.2168\/lmcs-10(1:6)2014","type":"journal-article","created":{"date-parts":[[2014,7,15]],"date-time":"2014-07-15T09:40:14Z","timestamp":1405417214000},"source":"Crossref","is-referenced-by-count":12,"title":["Computational Complexity of Smooth Differential Equations"],"prefix":"10.46298","volume":"Volume 10, Issue 1","author":[{"given":"Akitoshi","family":"Kawamura","sequence":"first","affiliation":[]},{"given":"Hiroyuki","family":"Ota","sequence":"additional","affiliation":[]},{"given":"Carsten","family":"R\u00f6snick","sequence":"additional","affiliation":[]},{"given":"Martin","family":"Ziegler","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2014,2,11]]},"reference":[{"key":"824:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/960\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/960\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T19:59:54Z","timestamp":1681243194000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/960"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,2,11]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-10(1:6)2014","relation":{"is-same-as":[{"id-type":"arxiv","id":"1311.5414","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1311.5414","asserted-by":"subject"}],"is-referenced-by":[{"id-type":"doi","id":"10.1093\/imamci\/dnu054","asserted-by":"subject"},{"id-type":"doi","id":"10.3182\/20130904-3-fr-2041.00031","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2014,2,11]]},"article-number":"960"}}