Self-Adapting Spiking Neural P Systems with Refractory Period and Propagation Delay

• A novel variant of spiking neural P systems called SARPPD-SN P systems is proposed. • The computational power of SARPPD-SN P systems is proved. • The computational efficiency of SARPPD-SN P systems is proved. • The models of the third generation of neural networks are expanded. • A novel method to identify all solutions to the NP-hard problems is given. This work develops a novel variant of spiking neural P systems (SN P systems), called self-adapting SN P systems with refractory period and propagation delay (SARPPD-SN P systems). Using the refractory period and propagation delay, spikes transmitted from a neuron arrives at the postsynaptic neurons at different times to simulate the complicated mutual conversion between electrical signals, i.e., spikes, and neurotransmitters in the transmission process. Furthermore, a neuron dissolution rule as a new self-adapting feature is used to remove the redundant neurons and synapses. These two characteristics make SARPPD-SN P systems closer to biological neurons. As examples, SARPPD-SN P systems are employed to generate even natural numbers, all natural numbers, and arithmetic progression using fewer neurons than other variants of SN P systems. The Turing universality of SARPPD-SN P systems is studied by using them as number generating and number accepting devices. As an application, a deterministic SARPPD-SN P system is constructed to find uniform solutions to Boolean satisfiability (SAT) problems in linear time. The refractory period and propagation delay can control the flow of the execution of the rules, and the neuron dissolution rule can eliminate invalid solutions. Solutions to SAT problems are encoded as labels of the output neurons.