Automata Computation with Hodgkin-Huxley Based Neural Networks Composed of Synfire Rings

Recent results have shown that finite state automata can be simulated by recurrent neural networks composed of synfire rings. The simulation process was shown to work correctly in the cases of Boolean neural networks and of Izhikevich spiking neural networks. In this paper, we generalize these results to the very biological context of the Hodgkin-Huxley neural model. We prove that any finite state automaton can be simulated by a Hodgkin-Huxley based recurrent neural network composed of synfire rings. In this framework, the inhibitory system ensuring the transition between the successive rings can be significantly simplified. These results show that a neuro-inspired paradigm of abstract computation based on sustained activities of neural assemblies is indeed possible, and potentially harnessable. They also constitute a first step towards the implementation of biological neural computers.

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