Abstract.
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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Kawamura, A. Lipschitz Continuous Ordinary Differential Equations are Polynomial-Space Complete. comput. complex. 19, 305–332 (2010). https://doi.org/10.1007/s00037-010-0286-0
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DOI: https://doi.org/10.1007/s00037-010-0286-0
Keywords.
- Computable analysis
- computational complexity
- initial value problem
- Lipschitz condition
- ordinary differential equations
- Picard–Lindelöf theorem
- polynomial space