TY - GEN

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

AU - Kawamura, Akitoshi

PY - 2009

Y1 - 2009

N2 - in answer to Ko's question raised in 1983, we show that an initial value problem given by a polynomialtime 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 restricted feedback, and show that they are still polynomialspace 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 polynomialtime 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 restricted feedback, and show that they are still polynomialspace complete. The same technique also settles Ko's two later questions on Volterra integral equations.

UR - http://www.scopus.com/inward/record.url?scp=70350662398&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350662398&partnerID=8YFLogxK

U2 - 10.1109/CCC.2009.34

DO - 10.1109/CCC.2009.34

M3 - Conference contribution

AN - SCOPUS:70350662398

SN - 9780769537177

T3 - Proceedings of the Annual IEEE Conference on Computational Complexity

SP - 149

EP - 160

BT - Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009

T2 - 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009

Y2 - 15 July 2009 through 18 July 2009

ER -