Homogeneous spiking neural P systems with synaptic failure

Spiking neural P (SN P) systems are a class of neural-like computational models, inspired by the way biological neurons process information through electrical impulses known as spikes. Homogeneous spiking neural P (HSN P) systems are a specialized variant of SN P systems, where all neurons share the same set of rules. In this work, with the biological inspiration that excessive synaptic transmission can lead to short-term failures in signal delivery between neurons in neural systems, the notion of synaptic failure is considered in HSN P systems, termed HSN P systems with synaptic failure (HSNPSF systems). Specifically, synaptic failure is referred to a family of sets of failure-prone synapses: if spikes simultaneously pass along all the synapses in such a set, the transmitted spikes across the synapses are suppressed; if a synapse in the set does not transmit any spike, the spikes pass along the synapses at that time, ultimately reaching the destination neurons. The computational power of HSNPSF systems is investigated by proving that they can achieve computational completeness both in generating and accepting modes. Furthermore, the computational efficiency of HSNPSF systems is examined, and it is demonstrated that with the help of non-deterministic feature, these systems are capable of solving NP-complete (the Subset Sum) problem in a semi-uniform way and within constant time.