Sequential dynamic threshold neural P systems
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Sequential dynamic threshold neural P systems Tingting Bao1 · Nan Zhou1 · Zeqiong Lv1 · Hong Peng1 · Jun Wang2 Received: 10 June 2020 / Accepted: 9 October 2020 © Springer Nature Singapore Pte Ltd. 2020
Abstract Dynamic threshold neural P systems (DTNP systems, for short) are a kind of distributed parallel computing systems abstracted from the spiking and dynamic threshold mechanisms of neurons. A DTNP system consists of several dynamic threshold neurons, and each neuron has a data unit and a threshold unit. The computational completeness of DTNP systems has been investigated. DTNP systems are synchronous systems, and a global clock is assumed to synchronize all threshold neurons. However, the assumption is biologically non-realistic. In this paper, we discuss DTNP systems working in sequential mode, i.e., sequential DTNP systems (SDTNP systems, in short). Based on the number of spikes of active neurons and the ruleapplication strategy, four sequentiality strategies are considered. It is proven that SDTP systems working in four sequentiality strategies are Turing universal number generating/accepting devices. Keywords Neural-like P system · Dynamic threshold neural P system · Sequential mode · Computational completeness
1 Introduction Membrane computing is a class of distributed parallel computing systems abstracted from the mechanisms of biological cells [1, 2], known as P systems. According to the topological structure, P systems are of three main categories: cell-like P systems (the arrangement between the membranes is a hierarchical structure), tissue-like P systems (the arrangement between cells is a network), and neural-like P systems (the arrangement between cells is a directed graph). P systems have been widely investigated [3, 4], and most of them can be used as universal number-generating/-accepting * Hong Peng [email protected] Tingting Bao [email protected] Nan Zhou [email protected] Zeqiong Lv [email protected] Jun Wang [email protected] 1
School of Computer and Software Engineering, Xihua University, Chengdu, Sichuan 610039, China
School of Electrical Engineering and Electronic Information, Xihua University, Chengdu 610039, China
2
devices and function computing devices. Some P systems can be used as universal language-generating devices and can solve a lot of NP-complete problems efficiently [5–9]. In addition, P systems have been successfully applied in realworld problems [10–12]. Spiking neural P systems (SN P systems, for short) [13] are one of neural-like P systems, inspired by the neurophysiological behavior of spiking neurons. From topological structure, an SN P system can be expressed as a directed graph, where the nodes are the neurons and the arcs denote the synapses between these neurons. Generally, SN P systems have two ingredients: spikes and rules. A neuron has one or more spikes (the spike is often denoted by symbol “a”), which are used to characterize the state of the neuron. The states of neurons evolve by rules. Usually, SN P systems hav
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