Skip to main content
Log in

Representation Operators and Computation

  • Published:
Minds and Machines Aims and scope Submit manuscript

Abstract

This paper analyses the impact of representation and search operators on Computational Complexity. A model of computation is introduced based on a directed graph, and representation and search are defined to be the vertices and edges of this graph respectively. Changing either the representation or the search algorithm leads to different possible complexity classes. The final section explores the role of representation in reducing time complexity in Artificial Intelligence.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Amarel, S. (1971), ‘On Representation of Problems of Reasoning about Actions’, in D. Michie, ed., Machine Intelligence, Vol. 3, Edinburgh: Edinburgh University Press, pp. 131–171.

    Google Scholar 

  • Boden, M. (1994), ‘Préis of the Creative Mind’, Behavioural and Brain Sciences, 17, pp. 519–570.

    Google Scholar 

  • Chudler, E. (1997), Brain Facts and Figures, http://weber.u.washington.edu/_chudler/facts.html# neuron

  • Churchland, P. and Sejnowski, T. (1992), The Computational Brain, Cambridge, MA: MIT Press.

    Google Scholar 

  • Clark, A. and Thornton, C. (forthcoming), ‘Trading Spaces: Computation, Representation and the Limits of Uninformed Learning’, Behavioural and Brain Sciences. Also available as Technical Report, Washington University, St. Louis, MO.

  • Crutchfield, J. (1994), ‘The Calculi of Emergence: Computation, Dynamics, and Induction’, PhysicaD 75, pp. 11–54.

    Google Scholar 

  • Donoho, S. and Rendell, L. (1995), ‘Rerepresenting and Restructuring Domain Theories’, Journal of Artificial Intelligence Research 2, pp. 411–446.

    Google Scholar 

  • Goldberg, D. and Bridges, C. (1990), ‘An Analysis of a Reordering Operator on a GA-Hard Problem’, Biological Cybernetics 62, pp. 397–405.

    Google Scholar 

  • Goldfarb, L., et al. (1994), ‘Can a Vector space-based learning model Discover Inductive Class Generalisations in a Symbolic Environment?’ in Proceedings of the 10th Biennial Conference of the Computer Society for Computational Study of Intelligence, Morgan Kaufmann, CA.

    Google Scholar 

  • Hubel, D., Wiesel, T., and Stryker, P. (1978), “Anatomical Demonstration of Orientation Columns in Macaque Monkey”, Journal of Computational Neurology 177, pp. 361–380.

    Google Scholar 

  • Jones, T. (1995), ‘Evolutionary Algorithms, Fitness Landscapes and Search’, Doctoral Dissertation, University of New Mexico.

  • Kandel, E., Schwartz, J., and Jessell, T. (1992), Principles of Neural Science, Appleton and Lange. CI.

  • Karmiloff-Smith, A. (1992), Beyond Modularity, Cambridge, MA: MIT Press.

    Google Scholar 

  • Kingdon, J. and Dekker, L. (1996), ‘The Shape of Space’, Technical Report, Department of Computer Science, University College London.

  • Kosslyn, S. (1994), Image and Brain: The Resolution of the Imagery Debate, Cambridge, MA: MIT Press.

    Google Scholar 

  • Koza, J. (1994), Genetic Programming II: Automatic Discovery of Reusable Programs, Cambridge, MA: MIT Press.

    Google Scholar 

  • Lenat, D. (1995), ‘CYC: A Large-Scale Investment in Knowledge Infrastructure’ Communications of the ACM, Vol. 38, No. 11, pp. 32–38

    Google Scholar 

  • McCarthy, J. (1968), ‘Programs with Common Sense’, in M. Minsky, ed., Semantic Information Processing, Cambridge, MA: MIT Press.

    Google Scholar 

  • Mendelson, E. (1964), Introduction to Mathematical Logic, New York: Van Nostrand Company.

    Google Scholar 

  • Pinker, S. and Mechler, J. (eds), (1988), Connections and Symbols, Cambridge, MA: MIT Press.

    Google Scholar 

  • Radcliffe, N. (1994), ‘The Algebra of Genetic Algorithms’, Annals of Maths and Artificial Intelligence 10, pp. 339–384.

    Google Scholar 

  • Rumelhart, D., McClelland, J., et al. (1986), Parallel Distributed Processing, Vol. 2, Cambridge, MA: MIT Press.

    Google Scholar 

  • Sah, P. and Bekkers, J. (1996), ‘Apical Dendritic Location of Slow After hyperpolarization Current in Hippocampal Pyramidal Neurons: Implications for the Integration of Long-Term Potentiation’, Journal of Neuroscience 16, No. 15, pp. 4537–4542.

    Google Scholar 

  • Toth, G., Kovacs, S. and Lonncz, A. (1995), ‘Genetic Algorithm with Alphabet Optimisation’, Biological Cybernetics 73, pp. 61–68.

    Google Scholar 

  • Tye, M. (1991), The Imagery Debate, Cambridge, MA: MIT Press.

    Google Scholar 

  • Wnek, J. and Michalski, R. (1994), ‘Hypothesis-driven Constructive Induction in AQl7-HCI: A Method and Experiments’, Machine Learning 14, pp. 139–168.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kitts, B. Representation Operators and Computation. Minds and Machines 9, 223–240 (1999). https://doi.org/10.1023/A:1008312316286

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008312316286

Navigation