A formal framework for spiking neural P systems
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A formal framework for spiking neural P systems Sergey Verlan1 · Rudolf Freund2 · Artiom Alhazov3 · Sergiu Ivanov4 · Linqiang Pan5 Received: 16 June 2020 / Accepted: 30 September 2020 © Springer Nature Singapore Pte Ltd. 2020
Abstract Spiking neural P systems are a class of distributed parallel computing models, inspired by the way in which neurons process information and communicate with each other by means of spikes. In 2007, Freund and Verlan developed a formal framework for P systems to capture most of the essential features of P systems and to define their functioning in a formal way. In this work, we present an extension of the formal framework related to spiking neural P systems by considering the applicability of each rule to be controlled by specific conditions on the current contents of the cells. The main objective of this extension is to also capture spiking neural P systems in the formal framework. Another goal of our extension is to incorporate the notions of input and output. Finally, we also show that in the case of spiking neural P systems, the rules have a rather simple form and in that way spiking neural P systems correspond to vector addition systems where the application of rules is controlled by semi-linear sets. Keywords Natural computing · Membrane computing · Spiking neural P system · Formal framework
1 Introduction
* Sergey Verlan verlan@u‑pec.fr Rudolf Freund [email protected] Artiom Alhazov [email protected] Sergiu Ivanov sergiu.ivanov@univ‑evry.fr Linqiang Pan [email protected] 1
Univ Paris Est Creteil, LACL, F‑94010 Creteil, France
2
Faculty of Informatics, TU Wien, Favoritenstraße 9–11, 1040 Wien, Austria
3
Vladimir Andrunachievici Institute of Mathematics and Computer Science, Academiei 5, MD‑2028 Chişinău, Moldova
4
IBISC, Univ. Évry, Université Paris-Saclay, 23 Boulevard de France, 91025 Évry, France
5
Key Laboratory of Image Information Processing and Intelligent Control of Education Ministry of China, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China
Based on the biological background of neurons sending electrical impulses along axons to other neurons, spiking neural P systems were introduced in [17]. In spiking neural P systems, the contents of a cell—a neuron—consists of a number of so-called spikes. The rules assigned to a cell allow for sending information to other neurons in the form of spikes corresponding to electrical impulses, which are summed up in the target cells. The application of the rules depends on the current contents of the neuron and in the general case is described by a filter language (e.g., a regular set). As inspired from biology, the cell sending out spikes may be closed for a specific time period corresponding to the refractory period of a neuron. During this refractory period, the neuron is closed for new input and cannot get excited— fire—for spiking. As already shown in [14], considering such a delay usually is not needed to obtain
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