Abstract
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.
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Notes
- 1.
Percolation is a classic model in physics and graph theory describing the sudden appearance of a giant component as a function of connection probability in Erdos-Renyi graphs. It can also be related to flow of liquid through a porous medium.
- 2.
A half-adder is a Boolean circuit that adds two bits and outputs a sum and carry bit, much like standard base 10 addition.
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Wilkerson, G., Moschoyiannis, S. (2020). Universal Boolean Logic in Cascading Networks. In: Cherifi, H., Gaito, S., Mendes, J., Moro, E., Rocha, L. (eds) Complex Networks and Their Applications VIII. COMPLEX NETWORKS 2019. Studies in Computational Intelligence, vol 881. Springer, Cham. https://doi.org/10.1007/978-3-030-36687-2_50
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DOI: https://doi.org/10.1007/978-3-030-36687-2_50
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