TY - GEN

T1 - Computational complexity of smooth differential equations

AU - Kawamura, Akitoshi

AU - Ota, Hiroyuki

AU - Rösnick, Carsten

AU - Ziegler, Martin

PY - 2012

Y1 - 2012

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 in hope of understanding the intrinsic hardness of solving the equation numerically. 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 if g is of class C k .

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 in hope of understanding the intrinsic hardness of solving the equation numerically. 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 if g is of class C k .

UR - http://www.scopus.com/inward/record.url?scp=84865013518&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-32589-2_51

DO - 10.1007/978-3-642-32589-2_51

M3 - Conference contribution

AN - SCOPUS:84865013518

SN - 9783642325885

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 578

EP - 589

BT - Mathematical Foundations of Computer Science 2012 - 37th International Symposium, MFCS 2012, Proceedings

T2 - 37th International Symposium on Mathematical Foundations of Computer Science 2012, MFCS 2012

Y2 - 27 August 2012 through 31 August 2012

ER -