脉冲神经P系统普适性与非普适性的一个界限
A boundary between universality and non-universality in spiking neural P systems
摘要：
在这项工作中，我们提供了一个显着的改进，以前的最小脉冲神经P系统，并解决了问题，找到最小的可能扩展脉冲神经P系统。Paun和Paun给出了一个具有84个神经元的通用脉冲神经P系统，以及另一个具有49个神经元的扩展规则。随后，Zhang等人将用于赋予普适性的神经元数量减少到67个，用于发放神经P系统，用于扩展模型。在这里，我们给出了一个小的通用尖峰神经P系统，只有17个神经元和另一个扩展的规则与5个神经元。当模拟图灵机时，所有上述脉冲神经P系统都遭受指数减慢。使用更宽松的编码技术，我们得到了一个通用的尖峰神经P系统，具有扩展的规则，只有4个神经元。后一种脉冲神经P系统在线性时间内模拟2计数器机器，因此在模拟图灵机时遭受双指数时间开销。我们证明了具有3个神经元的扩展脉冲神经P系统是用对数空间有界的图灵机模拟的，因此不存在这样的具有3个神经元的普适系统。由此可见，我们的4-神经元系统是最小的可能的扩展尖峰神经P系统，是普遍的。最后，我们表明，如果我们推广的输出技术，我们可以得到一个通用的尖峰神经P系统的扩展规则，只有3个神经元。该系统也是同类系统中最小的，因为具有扩展规则和广义输出的通用尖峰神经P系统对于2个神经元是不可能的。
英文摘要：
In this work we offer a significant improvement on the previous smallest spiking neural P systems and solve the problem of finding the smallest possible extended spiking neural P system. Paun and Paun gave a universal spiking neural P system with 84 neurons and another that has extended rules with 49 neurons. Subsequently, Zhang et al. reduced the number of neurons used to give universality to 67 for spiking neural P systems and to 41 for the extended model. Here we give a small universal spiking neural P system that has only 17 neurons and another that has extended rules with 5 neurons. All of the above mentioned spiking neural P systems suffer from an exponential slow down when simulating Turing machines. Using a more relaxed encoding technique we get a universal spiking neural P system that has extended rules with only 4 neurons. This latter spiking neural P system simulates 2-counter machines in linear time and thus suffer from a double exponential time overhead when simulating Turing machines. We show that extended spiking neural P systems with 3 neurons are simulated by log-space bounded Turing machines, and so there exists no such universal system with 3 neurons. It immediately follows that our 4-neuron system is the smallest possible extended spiking neural P system that is universal. Finally, we show that if we generalise the output technique we can give a universal spiking neural P system with extended rules that has only 3 neurons. This system is also the smallest of its kind as a universal spiking neural P system with extended rules and generalised output is not possible with 2 neurons.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
