Spiking neural P systems with anti-spikes and without annihilating priority as number acceptors

Spiking neural P systems with anti-spikes (ASN P sys-tems) are variant forms of spiking neural P systems, which are inspired by inhibitory impulses/spikes or inhibitory synapses. The typical feature of ASN P systems is when a neuron contains both spikes and anti-spikes, spikes and anti-spikes wil immediately an-nihilate each other in a maximal way. In this paper, a restricted variant of ASN P systems, cal ed ASN P systems without anni-hilating priority, is considered, where the annihilating rule is used as the standard rule, i.e., it is not obligatory to use in the neuron associated with both spikes and anti-spikes. If the annihilating rule is used in a neuron, the annihilation wil consume one time unit. As a result, such systems using two categories of spiking rules (iden-tified by (a, a) and (a, ˉa)) can achieve Turing completeness as number accepting devices.