This review addresses structural differences between that type of computation on which computability theory and computational complexity theory have focused so far, and those computations that are usually carried out in biological organisms (either in the brain, or in the form of gene regulation within a single cell). These differences concern the role of time, the way in which the input is presented, the way in which an algorithm is implemented, and in the end also the definition of what a computation is. This article describes liquid computing as a new framework for analyzing those types of computations that are usually carried out in biological organisms.


Input Function Turing Machine Computational Task Input Stream Biological Organism 
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  1. Maass, W., Natschläger, T., Markram, H.: Real-time computing without stable states: A new framework for neural computation based on perturbations. Neural Computation 14(11), 2531–2560 (2002)CrossRefzbMATHGoogle Scholar
  2. Boyd, S., Chua, L.O.: Fading memory and the problem of approximating nonlinear oparators with Volterra series. IEEE Trans. on Circuits and Systems 32, 1150–1161 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  3. Maass, W., Markram, H.: On the computational power of recurrent circuits of spiking neurons. Journal of Computer and System Sciences 69(4), 593–616 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  4. Jäger, H., Haas, H.: Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication. Science 304, 78–80 (2004)CrossRefGoogle Scholar
  5. Maass, W., Joshi, P., Sontag, E.D.: Computational aspects of feedback in neural circuits. PLOS Computational Biology 3(1), 1–20 (2007)MathSciNetCrossRefGoogle Scholar
  6. Branicky, M.S.: Universal computation and other capabilities of hybrid and continuous dynamical systems. Theoretical Computer Science 138, 67–100 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  7. Buonomano, D.V., Merzenich, M.M.: Temporal information transformed into a spatial code by a neural network with realistic properties. Science 267, 1028–1030 (1995)CrossRefGoogle Scholar
  8. Maass, W., Markram, H.: Theory of the computational function of microcircuit dynamics. In: Grillner, S., Graybiel, A.M. (eds.) The Interface between Neurons and Global Brain Function, Dahlem Workshop Report 93, pp. 371–390. MIT Press, Cambridge (2006)Google Scholar
  9. Hopfield, J.J., Brody, C.D.: What is a moment? Transient synchrony as a collective mechanism for spatio-temporal integration. Proc. Nat. Acad. Sci. USA 98(3), 1282–1287 (2001)CrossRefGoogle Scholar
  10. Maass, W., Natschläger, T., Markram, H.: Fading memory and kernel properties of generic cortical microcircuit models. Journal of Physiology – Paris 98(4–6), 315–330 (2004)CrossRefGoogle Scholar
  11. Verstraeten, D., Schrauwen, B., Stroobandt, D., Van Campenhout, J.: Isolated word recognition with the liquid state machine: a case study. Information Processing Letters 95(6), 521–528 (2005)CrossRefzbMATHGoogle Scholar
  12. Fernando, C., Sojakka, S.: Pattern recognition in a bucket: a real liquid brain. In: Banzhaf, W., Ziegler, J., Christaller, T., Dittrich, P., Kim, J.T. (eds.) ECAL 2003. LNCS (LNAI), vol. 2801, pp. 588–597. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. Häusler, S., Maass, W.: A statistical analysis of information processing properties of lamina-specific cortical microcircuit models. Cerebral Cortex 17(1), 149–162 (2007)CrossRefGoogle Scholar
  14. Nikolić, D., Haeusler, S., Singer, W., Maass, W.: Temporal dynamics of information content carried by neurons in the primary visual cortex. In: Proc. of NIPS 2006, Advances in Neural Information Processing Systems, vol. 19, MIT Press, Cambridge (2007)Google Scholar
  15. Hertzberg, J., Jaeger, H., Schoenherr, F.: Learning to ground fact symbols in behavior-based robot. In: van Harmelen, F. (ed.) Proc. of the 15th European Conference on Artificial Intelligence, pp. 708–712. IOS Press, Amsterdam (2002)Google Scholar
  16. Bush, K., Anderson, C.: Modeling reward functions for incomplete state representations via echo state networks. In: Proceedings of the International Joint Conference on Neural Networks, Montreal, Quebec (2005)Google Scholar
  17. Tong, M.H., Bickett, A.D., Christiansen, E.M., Cotrell, G.W.: Learning grammatical structure with echo state networks. Neural Networks (in press 2007)Google Scholar
  18. Jaeger, H., Eck, D.: Can’t get you out of my head: A connectionist model of cyclic rehearsal. In: Wachsmuth, I., Knoblich, G (eds.) Modeling Communication with Robots and Virtual Humans (in press 2007)Google Scholar
  19. Joshi, P., Maass, W.: Movement generation with circuits of spiking neurons. Neural Computation 17(8), 1715–1738 (2005)CrossRefzbMATHGoogle Scholar
  20. White, O.L., Lee, D.D., Sompolinsky, H.: Short-term memory in orthogonal neural networks. Phys. Rev. Letters 92(14), 102–148 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Wolfgang Maass
    • 1
  1. 1.Institute for Theoretical Computer Science, Technische Universitaet Graz, A-8010 GrazAustria

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