TY - JOUR

T1 - Computational complexity of smooth differential equations

AU - Kawamura, Akitoshi

AU - Ota, Hiroyuki

AU - Rösnick, Carsten

AU - Ziegler, Martin

PY - 2014/2/11

Y1 - 2014/2/11

N2 - 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.

AB - 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.

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U2 - 10.2168/LMCS-10(1:6)2014

DO - 10.2168/LMCS-10(1:6)2014

M3 - Article

AN - SCOPUS:84893876435

VL - 10

JO - Logical Methods in Computer Science

JF - Logical Methods in Computer Science

SN - 1860-5974

IS - 1

M1 - 6

ER -