Some Aspects of a Complexity Theory for Continuous Time Systems

  • Authors:

  • Marco Gori;Klaus Meer

  • Affiliations:

  • Dipartimento di Ingegneria dell'Informazione, Università di Siena, Via Roma 56, I-53100 Siena, Italy;Syddansk Universitet Odense, Dept. of Mathematics and Computer Science, Campusvej 55, DK-5230 Odense M, Denmark

  • Venue:
  • CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
  • Year:
  • 2007

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Abstract

In this paper we survey previous work by the authors defining a complexity measure for certain continuous time systems. Starting point are energy functions of a particular structure. Global minimizers of such energies correspond to solutions of a given problem, for example an equilibrium point of an ordinary differential equation. The structure of such energies is used to define complexity classes for continuous problems and to obtain completeness results for those classes. We discuss as well algorithmic aspects of minimizing energy functions.