Spiking neural P systems with anti-spikes and without annihilating priority working in a 'flip-flop' way

Spiking neural P systems with anti-spikes (shortly named ASN P systems) are a class of distributed and parallel neural-like computing systems. Besides spikes, neurons in ASN P systems can also contain a number of anti-spikes. Whenever spikes and anti-spikes meet in a neuron, they annihilate each other immediately in a maximal manner, that is, the annihilation has priority over neuron’s spiking. In this work, we introduce a variant of ASN P systems, named ASN P systems without annihilating priority. In such systems, when a neuron has both a number of spikes and anti-spikes, the annihilation between spikes and anti-spikes is not obligatory and the neuron can choose non-deterministically spiking or annihilating. The computational power of ASN P systems without annihilating priority as number generators is investigated. As a result, it is obtained that such system with at most two rules per neuron can achieve Turing completeness as number generators. This result gives an answer to an open problem formulated in [INT J COMPUT COMMUN & CONTROL, 3, 273–282, 2009]. As well, the obtained result is optimal in the sense of having a minimal number of rules in neurons of Turing universal ASN P systems. Key-words: Membrane computing, Spiking neural P system, Turing completeness, Register machine, Anti-spike