Lipschitz continuous ordinary differential equations are polynomial-space complete

Research output: Contribution to journalArticle

23 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)305-332
Number of pages28
JournalComputational Complexity
Volume19
Issue number2
DOIs
Publication statusPublished - May 1 2010
Externally publishedYes

Fingerprint

Ordinary differential equations
Lipschitz
Ordinary differential equation
Polynomials
Polynomial
Tableaux
Lipschitz Function
Lipschitz condition
Volterra Integral Equations
Feedback
Initial Value Problem
Initial value problems
Polynomial time
Continuous Function
Differential equation
Integral equations
Differential equations
Class

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Mathematics(all)
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

Lipschitz continuous ordinary differential equations are polynomial-space complete. / Kawamura, Akitoshi.

In: Computational Complexity, Vol. 19, No. 2, 01.05.2010, p. 305-332.

Research output: Contribution to journalArticle

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