Zeng Xiangxiang, Zhang Xingyi, Song Tao, Pan Linqiang
Department of Computer Science, Xiamen University, Xiamen 361005, Fujian, China
Neural Comput. 2014 Jul;26(7):1340-61. doi: 10.1162/NECO_a_00605. Epub 2014 Apr 7.
Spiking neural P systems with weights are a new class of distributed and parallel computing models inspired by spiking neurons. In such models, a neuron fires when its potential equals a given value (called a threshold). In this work, spiking neural P systems with thresholds (SNPT systems) are introduced, where a neuron fires not only when its potential equals the threshold but also when its potential is higher than the threshold. Two types of SNPT systems are investigated. In the first one, we consider that the firing of a neuron consumes part of the potential (the amount of potential consumed depends on the rule to be applied). In the second one, once a neuron fires, its potential vanishes (i.e., it is reset to zero). The computation power of the two types of SNPT systems is investigated. We prove that the systems of the former type can compute all Turing computable sets of numbers and the systems of the latter type characterize the family of semilinear sets of numbers. The results show that the firing mechanism of neurons has a crucial influence on the computation power of the SNPT systems, which also answers an open problem formulated in Wang, Hoogeboom, Pan, Păun, and Pérez-Jiménez ( 2010 ).
带权脉冲神经P系统是一类受脉冲神经元启发的新型分布式并行计算模型。在这类模型中，当神经元的电位等于给定值（称为阈值）时，神经元就会放电。在这项工作中，引入了带阈值的脉冲神经P系统（SNPT系统），其中神经元不仅在其电位等于阈值时放电，而且在其电位高于阈值时也会放电。研究了两种类型的SNPT系统。在第一种类型中，我们认为神经元放电会消耗部分电位（消耗的电位量取决于要应用的规则）。在第二种类型中，一旦神经元放电，其电位就会消失（即重置为零）。研究了这两种类型SNPT系统的计算能力。我们证明，前一种类型的系统可以计算所有图灵可计算的数集，而后一种类型的系统刻画了半线性数集族。结果表明，神经元的放电机制对SNPT系统的计算能力有至关重要的影响，这也回答了Wang、Hoogeboom、Pan、Păun和Pérez-Jiménez（2010）中提出的一个开放问题。
