Computational complexity of smooth differential equations

Akitoshi Kawamura, Hiroyuki Ota, Carsten Rösnick, Martin Ziegler

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


The computational complexity of the solution h to the ordinary differential equation h(0) = 0, h'(t) = g(t,h(t)) under various assumptions on the function g has been investigated. Kawamura showed in 2010 that the solution h can be PSPACE-hard even if g is assumed to be Lipschitz continuous and polynomial-time computable. We place further requirements on the smoothness of g and obtain the following results: the solution h can still be PSPACE-hard if g is assumed to be of class C1; for each k > 2, the solution h can be hard for the counting hierarchy even if g is of class Ck.

Original languageEnglish
Article number6
JournalLogical Methods in Computer Science
Issue number1
Publication statusPublished - Feb 11 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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