The class of refractory neural nets
We introduce the absolute refractory behaviour into the formal neuron model. While a probabilistic approach to such a refractory model has yet been attempted, in this paper, a deterministic analysis is realized. A first result consists in showing a not expensive algorithm to transform each refractory net into an equivalent not refractory one. Such a result is then exploited to obtain an upper bound to the computational complexity of two classical problems: the reachability and stabilization problems. They find their principal motivations in control and learning theories whenever the necessity to a priori determine the lenght of both transients and limit cycles arises. Finally, we prove that, when the connection matrices of nets are symmetric, the complementary problem of stabilization is NP-complete and reachability is P-complete.
KeywordsBoolean Function Turing Machine Initial Configuration Input Gate Output Gate
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