TY - JOUR

T1 - Lipschitz continuous ordinary differential equations are polynomial-space complete

AU - Kawamura, Akitoshi

N1 - Funding Information:
This work was supported in part by the Nakajima Foundation and by the Natural Sciences and Engineering Research Council of Canada. A preliminary versionof this work appeared as Kawamura (2009b).

PY - 2010/5

Y1 - 2010/5

N2 - In answer to Ko's question raised in 1983, we show that an initial value problem given by a polynomial-time computable, Lipschitz continuous function can have a polynomial-space complete solution. The key insight is simple: the Lipschitz condition means that the feedback in the differential equation is weak. We define a class of polynomial-space computation tableaux with equally weak feedback, and show that they are still polynomial-space complete. The same technique also settles Ko's two later questions on Volterra integral equations.

AB - In answer to Ko's question raised in 1983, we show that an initial value problem given by a polynomial-time computable, Lipschitz continuous function can have a polynomial-space complete solution. The key insight is simple: the Lipschitz condition means that the feedback in the differential equation is weak. We define a class of polynomial-space computation tableaux with equally weak feedback, and show that they are still polynomial-space complete. The same technique also settles Ko's two later questions on Volterra integral equations.

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U2 - 10.1007/s00037-010-0286-0

DO - 10.1007/s00037-010-0286-0

M3 - Article

AN - SCOPUS:77953542311

VL - 19

SP - 305

EP - 332

JO - Computational Complexity

JF - Computational Complexity

SN - 1016-3328

IS - 2

ER -