COMPUTATIONAL COMPLEXITY OF SMOOTH DIFFERENTIAL EQUATIONS

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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 C-1; for each k >= 2, the solution h can be hard for the counting hierarchy even if g is of class C-k.
Publisher
TECH UNIV BRAUNSCHWEIG
Issue Date
2014
Language
English
Article Type
Article
Keywords

POLYNOMIAL-TIME

Citation

LOGICAL METHODS IN COMPUTER SCIENCE, v.10, no.1

ISSN
1860-5974
DOI
10.2168/LMCS-10(1:6)2014
URI
http://hdl.handle.net/10203/203388
Appears in Collection
CS-Journal Papers(저널논문)
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