IEEE Trans Neural Netw Learn Syst. 2015 Nov;26(11):2816-29. doi: 10.1109/TNNLS.2015.2396940. Epub 2015 Feb 10.
Axon P systems are computing models with a linear structure in the sense that all nodes (i.e., computing units) are arranged one by one along the axon. Such models have a good biological motivation: an axon in a nervous system is a complex information processor of impulse signals. Because the structure of axon P systems is linear, the computational power of such systems has been proved to be greatly restricted; in particular, axon P systems are not universal as language generators. It remains open whether axon P systems are universal as number generators. In this paper, we prove that axon P systems are universal as both number generators and function computing devices, and investigate the number of nodes needed to construct a universal axon P system. It is proved that four nodes (respectively, nine nodes) are enough for axon P systems to achieve universality as number generators (respectively, function computing devices). These results illustrate that the simple linear structure is enough for axon P systems to achieve a desired computational power.
轴突 P 系统是一种具有线性结构的计算模型，因为所有节点（即计算单元）都沿着轴突一个一个地排列。这种模型具有很好的生物学动机：神经系统中的轴突是脉冲信号的复杂信息处理器。由于轴突 P 系统的结构是线性的，因此已经证明这种系统的计算能力受到了很大的限制；特别是，轴突 P 系统作为语言生成器并不通用。轴突 P 系统是否作为数字生成器通用仍未解决。在本文中，我们证明了轴突 P 系统作为数字生成器和函数计算设备都是通用的，并研究了构建通用轴突 P 系统所需的节点数。证明了四个节点（分别为九个节点）足以使轴突 P 系统作为数字生成器（分别为函数计算设备）实现通用性。这些结果表明，简单的线性结构足以使轴突 P 系统实现所需的计算能力。
