Universal Boolean Logic in Cascading Networks

  • Galen WilkersonEmail author
  • Sotiris MoschoyiannisEmail author
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 881)


Computational properties of networks that can undergo cascades are examined. It is shown that universal Boolean logic circuits can be computed by a global cascade having antagonistic interactions. Determinism and cascade frequency of this antagonistic model are explored, as well as its ability to perform classification. Universality of cascade logic may have far-reaching consequences, in that it can allow unification of the theory of computation with the theory of percolation.


Functional completeness Boolean logic Complex networks Percolation Cascades Social networks Self-organized criticality Deep learning 


  1. 1.
    Altafini, C.: Consensus problems on networks with antagonistic interactions. IEEE Trans. Autom. Control 58(4), 935–946 (2012)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Arora, S., Barak, B.: Computational Complexity: A Modern Approach. Cambridge University Press, Cambridge (2009)CrossRefGoogle Scholar
  3. 3.
    Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality: an explanation of the 1/f noise. Phys. Rev. Lett. 59(4), 381 (1987)CrossRefGoogle Scholar
  4. 4.
    Beggs, J.M., Plenz, D.: Neuronal avalanches in neocortical circuits. J. Neurosci. 23(35), 11167–11177 (2003)CrossRefGoogle Scholar
  5. 5.
    Easley, D., Kleinberg, J., et al.: Networks, Crowds, and Markets, vol. 8. Cambridge University Press, Cambridge (2010)CrossRefGoogle Scholar
  6. 6.
    Granovetter, M.: Threshold models of collective behavior. Am. J. Sociol. 83(6), 1420–1443 (1978)CrossRefGoogle Scholar
  7. 7.
    Leskovec, J., Huttenlocher, D., Kleinberg, J.: Signed networks in social media. In: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, pp. 1361–1370. ACM (2010)Google Scholar
  8. 8.
    Müller-Schloer, C., Schmeck, H., Ungerer, T.: Organic Computing—A Paradigm Shift for Complex Systems. Springer, Basel (2011)CrossRefGoogle Scholar
  9. 9.
    Prokopenko, M.: Guided self-organization. HFSP J. 3, 287–289 (2009)CrossRefGoogle Scholar
  10. 10.
    Rojas, R.: Neural Networks: A Systematic Introduction. Springer, Heidelberg (2013)zbMATHGoogle Scholar
  11. 11.
    Savage, J.E.: Models of Computation, vol. 136. Addison-Wesley, Reading (1998)zbMATHGoogle Scholar
  12. 12.
    Shew, W.L., Plenz, D.: The functional benefits of criticality in the cortex. Neuroscientist 19(1), 88–100 (2013)CrossRefGoogle Scholar
  13. 13.
    Watts, D.J.: A simple model of global cascades on random networks. Proc. Natl. Acad. Sci. 99(9), 5766–5771 (2002)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Zhao, K., Bianconi, G.: Percolation on interacting, antagonistic networks. J. Stat. Mech. Theor. Exp. 2013(05), P05005 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.University of SurreyGuildfordUK

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