Synfire rings are neural circuits capable of conveying synchronous, temporally precise and self-sustained activities in a robust manner. We propose a cell assembly based paradigm for abstract neural computation centered on the concept of synfire rings. More precisely, we empirically show that Hodgkin-Huxley neural networks modularly composed of synfire rings are automata complete. We provide an algorithmic construction which, starting from any given finite state automaton, builds a corresponding Hodgkin-Huxley neural network modularly composed of synfire rings and capable of simulating it. We illustrate the correctness of the construction on two specific examples. We further analyze the stability and robustness of the construction as a function of changes in the ring topologies as well as with respect to cell death and synaptic failure mechanisms, respectively. These results establish the possibility of achieving abstract computation with bio-inspired neural networks. They might constitute a theoretical ground for the realization of biological neural computers.

中文翻译：

---

使用由synfire环组成的Hodgkin-Huxley神经网络进行自动机完整计算。

Synfire环是神经回路，能够以健壮的方式传达同步的，时间精确的和自我维持的活动。我们以synfire环的概念为中心，为抽象神经计算提出了一种基于单元装配的范例。更准确地说，我们从经验上证明，由synfire环组成的Hodgkin-Huxley神经网络是自动机完整的。我们提供了一种算法构造，该构造从任何给定的有限状态自动机开始，构建了一个由synfire环模块化构成并能够对其进行仿真的对应的Hodgkin-Huxley神经网络。我们在两个具体示例上说明构造的正确性。我们将根据环拓扑结构以及细胞死亡和突触衰竭机制的变化，进一步分析结构的稳定性和鲁棒性，分别。这些结果为利用生物启发式神经网络实现抽象计算提供了可能性。它们可能构成实现生物神经计算机的理论基础。