Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Some results on the computational complexity of symmetric connectionist networks

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

Connectionists models are currently being investigated actively by many researchers in artificial intelligence, information theory and computational neuroscience. These networks have been shown to be applicable to a wide range of domains such as content addressable memories, semantic nets, computer vision, natural language parsing, speech recognition, and approximation schemes for difficult optimization problems. In this paper, we address several basic problems related to the computational complexity of discrete Hopfield nets (connectionist networks with symmetric connections).

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. N. Alon, Asynchronous threshold circuits.Graphs and Combinatorics (1985) pp. 305–310.

  2. J. Amit,Modelling Brain Functin (Cambridge University Press, 1989).

  3. J.A. Feldman, Energy and the behavior of connectionist models, Technical Report No. 155, Computer Science Department, University of Rochester (November 1985).

  4. S.E. Fahlman, G.E. Hinton and T. Sejnowski, Massively parallel architectures for AI: NETL, THISTLE and Boltzmann machines, in:Proc. AAAI-83 (August 1983) pp. 109–113.

  5. M.R. Garey and D.S. Johnson,Computers and Intractability: A Guide to the Theory of NP-completeness (Freeman, San Francisco, 1979).

    Google Scholar 

  6. G.H. Godbeer, The computational complexity of the stable configuration problem for connectionist models, Technical Report, Computer Science Department, University of Toronto (1987).

  7. A. Haken and M. Luby, Steepest descent can take exponential time for symmetric connection networks, Complex Systems 2(1988)191–196.

    Google Scholar 

  8. J.J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, in:Proc. National Academy of Sciences, Vol. 79 (1982) pp. 2554–2558.

    Google Scholar 

  9. J.J. Hopfield and D. Tank, “Neural” computation of decisions in optimization problems, Biol. Cybem. 52(1985)141–152.

    Google Scholar 

  10. D. Johnson, C. Papadimitriou and M. Yannakakis, How easy is local search?, in:26th Annual Symp. on Foundations of Computer Science (1985) pp. 39–42.

  11. R.M. Karp, Reducibility among combinatorial problems, in:Complexity of Computer Computations, ed. R.E. Miller and J.W. Thatcher (Plenum Press, New York, 1972) pp. 85–103.

    Google Scholar 

  12. S. Kasif, S. Banerjee, A. Delcher and S. Sullivan, Some results on the computational complexity of symmetric connectionist networks, Technical Report No. JHU/EECS-87/18, Department of EECS, Johns Hopkins University (1987).

  13. M. Lepley and G. Miller, Computational powers of threshold devices in an asynchronous environment, Technical Report, Computer Science Department, University of Southern California (1986).

  14. B. Muller and J. Reihardt,Neural Networks (Springer, 1991).

  15. C.H. Papadimitriou and K. Steiglitz,Combinatorial Optimization: Algorithms and Complexity (Prentice-Hall, Englewood Cliffs, NJ, 1982).

    Google Scholar 

  16. C. Papadimitriou, A. Schaffer and M. Yannakakis, On the complexity of local search, in:ACM Symp. on the Theory of Computation (1990) pp. 438–445.

  17. D.E. Rumelhart and J.L. McClelland,Parallel Distributed Processing (MIT Press, Cambridge, MA, 1986).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research was supported in part by AFOSR Grant No. AFOSR-89-1151 and NSF Grant No. IRI-88-09324.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kasif, S., Banerjee, S., Delcher, A.L. et al. Some results on the computational complexity of symmetric connectionist networks. Ann Math Artif Intell 9, 327–344 (1993). https://doi.org/10.1007/BF01530937

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01530937

Keywords