The last decade has seen the rise of neuromorphic architectures based on artificial spiking neural networks, such as the SpiNNaker, TrueNorth, and Loihi systems. The massive parallelism and co-locating of computation and memory in these architectures potentially allows for an energy usage that is orders of magnitude lower compared to traditional Von Neumann architectures. However, to date a comparison with more traditional computational architectures (particularly with respect to energy usage) is hampered by the lack of a formal machine model and a computational complexity theory for neuromorphic computation. In this paper we take the first steps towards such a theory. We introduce spiking neural networks as a machine model where---in contrast to the familiar Turing machine---information and the manipulation thereof are co-located in the machine. We introduce canonical problems, define hierarchies of complexity classes and provide some first completeness results.

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关于尖峰神经网络的计算能力和复杂性

过去十年见证了基于人工尖峰神经网络的神经形态架构的兴起，例如 SpiNNaker、TrueNorth 和 Loihi 系统。与传统的冯诺依曼架构相比，这些架构中计算和内存的大规模并行和协同定位可能允许能源使用量低几个数量级。然而，迄今为止，由于缺乏正式的机器模型和神经形态计算的计算复杂性理论，与更传统的计算架构（特别是在能源使用方面）的比较受到阻碍。在本文中，我们朝着这样一个理论迈出了第一步。我们引入脉冲神经网络作为机器模型，其中——与熟悉的图灵机相反——信息及其操作位于机器中。