Computational complexity of smooth differential equations

Akitoshi Kawamura, Hiroyuki Ota, Carsten Rösnick, Martin Ziegler

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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
Volume10
Issue number1
DOIs
Publication statusPublished - Feb 11 2014

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Computational complexity
Computational Complexity
Differential equations
Differential equation
G-function
Lipschitz
Continuous Time
Smoothness
Counting
Polynomial time
Ordinary differential equation
Requirements
Ordinary differential equations
Polynomials
Class
Hierarchy

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Computational complexity of smooth differential equations. / Kawamura, Akitoshi; Ota, Hiroyuki; Rösnick, Carsten; Ziegler, Martin.

In: Logical Methods in Computer Science, Vol. 10, No. 1, 6, 11.02.2014.

Research output: Contribution to journalArticle

Kawamura, Akitoshi ; Ota, Hiroyuki ; Rösnick, Carsten ; Ziegler, Martin. / Computational complexity of smooth differential equations. In: Logical Methods in Computer Science. 2014 ; Vol. 10, No. 1.
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