Lipschitz continuous ordinary differential equations are polynomial-space complete

Akitoshi Kawamura

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)


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
Issue number2
Publication statusPublished - May 2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Mathematics
  • Computational Theory and Mathematics
  • Computational Mathematics


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