Universality of Spiking Neural P Systems with Anti-spikes

Abstract

Spiking neural P systems with anti-spikes (in short, SN PA systems) are membrane systems that communicate using two types of objects called spikes and anti-spikes, inspired by neurons communicating through excitatory and inhibitory impulses. This paper shows that computational completeness in an SN PA systems can be achieved with neurons having only two pure spiking rules of the form a → a and $a\rightarrow \overline{a}$ without any forgetting rules. We also construct a small universal SN PA system with 91 simple neurons i.e., neurons having only one rule of the form $a\rightarrow \overline{a}$ or a → a.