Lipschitz continuous ordinary differential equations are polynomial-space complete

Akitoshi Kawamura

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationProceedings of the 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009
Pages149-160
Number of pages12
DOIs
Publication statusPublished - Nov 9 2009
Event2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009 - Paris, France
Duration: Jul 15 2009Jul 18 2009

Publication series

NameProceedings of the Annual IEEE Conference on Computational Complexity
ISSN (Print)1093-0159

Other

Other2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009
CountryFrance
CityParis
Period7/15/097/18/09

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Computational Mathematics

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