Skip to main content
SpringerLink
Log in

Some Aspects of a Complexity Theory for Continuous Time Systems

  • Conference paper
Computation and Logic in the Real World (CiE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4497))

Included in the following conference series:

  • 1268 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bianchini, M., Gori, M., Scarselli, F.: Inside PageRank. ACM Transactions on Internet Technology 5(1), 92–128 (2005)

    Article  Google Scholar 

  2. Blum, L., Cucker, F., Shub, M., Smale, S.: Complexity and Real Computation. Springer, Heidelberg (1998)

    Book  MATH  Google Scholar 

  3. Bournez, O., Campagnolo, M.L.: A Survey on Continuous Time Computations, 2006 (Preprint)

    Google Scholar 

  4. Gori, M., Meer, K.: A step towards a complexity theory for analog systems. Mathematical Logic Quarterly 48(1), 45–58 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Minsky, M., Papert, S.: Perceptrons. The MIT Press, Cambridge (1969)

    MATH  Google Scholar 

  6. Orponen, P.: A survey of continuous-time computation theory. In: Du, D.-Z., Ko, K.-I. (eds.) Advances in Algorithms, Languages, and Complexity, pp. 209–224. Kluwer Academic Publishers, Dordrecht (1997)

    Chapter  Google Scholar 

  7. Shynk, J.J.: Performance Surfaces of a Single-Layer Perceptron. IEEE Transactions on Neural Networks 1(3), 268–274 (1990)

    Article  Google Scholar 

  8. Zak, M.: Introduction to terminal dynamics. Complex Systems 7, 59–87 (1993)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria dell’Informazione, Università di Siena, Via Roma 56, I-53100 Siena, Italy

    Marco Gori

  2. Syddansk Universitet Odense, Dept. of Mathematics and Computer Science, Campusvej 55, DK-5230 Odense M, Denmark

    Klaus Meer

Authors
  1. Marco Gori
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Klaus Meer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Pure Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

  2. Institue for Logic, Language and Computation (ILLC), Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, TV Amsterdam, The Netherlands

    Benedikt Löwe

  3. Dipartimento di Scienze Matematiche ed Informatiche “R. Magari”, University of Siena, 53100, Siena, Italy

    Andrea Sorbi

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gori, M., Meer, K. (2007). Some Aspects of a Complexity Theory for Continuous Time Systems. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_58

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73001-9_58

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73000-2

  • Online ISBN: 978-3-540-73001-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation