Spiking neural P systems with polarizations and astrocytes

Spiking neural P systems with polarizations (PSN P systems) use charges (+,-,0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(+,-,0)$$\end{document} instead of regular expression to obtain excellent computation power and broad application prospect. In this work, astrocyte control mechanism is introduced into PSN P systems, spiking neural P systems with polarizations and astrocytes (PASN P systems) are constructed. Astrocytes are both excitatory and inhibitory influences on synapses, which can effectively reduce the consumption of computing resources (the use of fewer neurons). Because of the effects of astrocytes, PASN P systems are proved to have the computation power equivalent to Turing machines in generation and accepting modes. Furthermore, a small universal PASN P system with 82 neurons is given for computing any Turing computable function, that is, fewer neurons are used to construct the relatively simple and universal PASN P systems.