Spiking neural P systems: An improved normal form
Spiking neural P systems: An improved normal form
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DOI：
10.1016/j.tcs.2009.11.010
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发表时间：
2010-02
期刊：
影响因子：
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通讯作者：
L. Pan;G. Paun
中科院分区：
文献类型：
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作者：
L. Pan;G. Paun
脉冲神经系统（简称snp系统）是一种基于神经元通过电脉冲（脉冲）交流方式的计算设备。这些系统包含各种成分；其中，我们提到了忘记规则和延迟解雇规则。然而，众所周知，不使用这两个特征也可以获得通用性。在本文中，我们从两个方面改进了这个结果：(i)每个神经元最多包含两个规则（这对于在生成模式下使用的系统是最优的），（ii）使用两个规则的神经元中的规则具有相同的正则表达式来控制它们的触发。这一结果回答了文献中遗留的一个问题，并且在此背景下，消除了先前一些与消除遗忘规则相关的证明的不完全性。此外，该结果显示了能够模拟图灵机的SN - P系统中神经元的一致性，这既是理论上的兴趣，似乎也符合生物现实。当在计算的任何一步对神经元中出现的尖峰数施加一个界限时（这样的SN - P系统被称为有限的），得到两个令人惊讶的结果。首先，在生成情况下获得有限数集的特征（这与其他类型的SN - P系统的情况形成对比，在这些情况下，有限SN - P系统获得了半线性数集的特征）。其次，接受情况严格地比生成情况强大：所有有限集和某些等差数列都可以接受。在不忘记规则和延迟的情况下接受有限SN - P系统的能力的精确表征仍有待发现。
Spiking neural P systems (in short, SN P systems) are computing devices based on the way the neurons communicate through electrical impulses (spikes). These systems involve various ingredients; among them, we mention forgetting rules and the delay in firing rules. However, it is known that the universality can be obtained without using these two features. In this paper we improve this result in two respects: (i) each neuron contains at most two rules (which is optimal for systems used in the generative mode), and (ii) the rules in the neurons using two rules have the same regular expression which controls their firing. This result answers a problem left open in the literature, and, in this context, an incompleteness in some previous proofs related to the elimination of forgetting rules is removed. Moreover, this result shows a somewhat surprising uniformity of the neurons in the SN P systems able to simulate Turing machines, which is both of a theoretical interest and it seems to correspond to a biological reality. When a bound is imposed on the number of spikes present in a neuron at any step of a computation (such SN P systems are called finite), two surprising results are obtained. First, a characterization of finite sets of numbers is obtained in the generative case (this contrasts the case of other classes of SN P systems, where characterizations of semilinear sets of numbers are obtained for finite SN P systems). Second, the accepting case is strictly more powerful than the generative one: all finite sets and also certain arithmetical progressions can be accepted. A precise characterization of the power of accepting finite SN P systems without forgetting rules and delay remains to be found.