Turing Computation with Neural Networks Composed of Synfire Rings

Abstract

Synfire rings are fundamental neural circuits capable of conveying self-sustained activities in a robust and temporally precise manner. We propose a Turing-complete paradigm for neural computation based on synfire rings. More specifically, we provide an algorithmic procedure which, for any fixed-space Turing machine, builds a corresponding Boolean neural network composed of synfire rings capable of simulating it. As a consequence, any fixed-space Turing machine with tapes of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> can be simulated in linear time by some Boolean neural network composed of O(N) rings and cells. The construction can naturally be extended to general Turing machines. Therefore, any Turing machine can be simulated in linear time by some Boolean neural network composed of infinitely many synfire rings. The linear time simulation relies on the possibility to mimic the behavior of the machines. In the long term, these results might contribute to the realization of biological neural computers.