Abstract
A self-repair network consists of nodes capable of repairing other nodes where the repair success rate depends on the state (normal or abnormal) of the repairing node. This recursive structure leads to the double-edged sword of repairing, which could cause outbreaks in case the repairing causes adverse effects. The self-repair network can be equated to a probabilistic cellular automaton. Because of the distinction between repair by normal nodes and that by abnormal nodes, transition probabilities as a probabilistic cellular automaton exhibit symmetry. In this chapter, we observe that duality can serve to make many transition probabilities arranged in order. In particular, the duality that reduces to a self-dual with respect to AND-OR duality when the repair rate is close to 0 is of interest, for the parameter region is the place where computer simulation is hard. The duality also suggests that the case when the repair rate is close to 0 lies between pessimistic estimation (in repair success) of AND-repair and optimistic estimation of OR-repair.
Most results of this chapter are presented in Ishida (2010).
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Ishida, Y. (2015). Duality in Logics of Self-Repair. In: Self-Repair Networks. Intelligent Systems Reference Library, vol 101. Springer, Cham. https://doi.org/10.1007/978-3-319-26447-9_7
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DOI: https://doi.org/10.1007/978-3-319-26447-9_7
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