# Spiking Neural P Systems for Basic Arithmetic Operations
## 1 Introduction
This distributed and parallel computing model has been shown to be computationally complete [15,17,18]. SNPS research in theory and application has achieved significant results, including generating numbers and languages, simulating logic circuits, system universality, and variants of spiking neural P systems. In [15], the authors showed that the basic SNPS as a device for generating sets of numbers is computationally complete in both generation mode and acceptance mode. In [16], the authors studied the language-generating capacity of SNPS; the recursively enumerable languages are the inverse image projection of the languages generated by SNPS. In [19], the authors investigated the minimum universality of SNPS as a device for computing functions and generating numbers and provided the minimum number of neurons to produce a universal SNPS using extension rules and standard rules. A restricted-rule universal system requires 76 neurons, while a universal system with extension rules only requires 50 neurons. In [20], the authors introduced a variant of SNP where neurons only contain spikes and the rules are on synapses. When the number of spikes in a given neuron matches the rule on the synapse, the rule is triggered. Compared with the SNPS in [19], a number generator constructed based on this variant SNPS requires only 39 neurons to achieve universality under standard rules, and only 30 neurons are needed when using extension rules. Many variants of SNPS have been proven to be Turing universal, such as the asynchronous spiking neural P system with local synchronization introduced in [21] and the SNPS with weights introduced in [22], where the applicability of the spike rules is controlled by a given discharge threshold. When integers are used to represent the weight, potential, and threshold parameters, this SNPS is universal. When natural numbers are used for these parameters, the characteristic of natural semilinear sets can be obtained. In [23], the aim was to address the limitations of current SNP systems in handling specific real-world data technology. Neural network structures and data processing methods were considered as a reference to improve upon these limitations. By integrating these concepts with membrane computing, spiking neural membrane computing models (SNMC models) were proposed. The paper successfully demonstrated the Turing universality of the SNMC model as a number generator and acceptor. The authors of [24] introduced neuron division and neuron budding into the framework of the spiking neural P system. A neuron can be divided into two and every budding can only produce one new neuron, proving that SNPS with neuron division and neuron budding can solve NP-complete problems in polynomial time. The Directed Hamiltonian Path (DHP) problem is an NP-hard problem, and the algorithm based on SNPS proposed by [25] effectively reduces the time complexity through massive parallelism. In [26], the authors introduced fuzzy reasoning in SNPS to establish a connection between P systems and fault diagnosis applications for the automatic implementation of complex power system fault diagnosis. Reference [27] introduced a Spiking Neural P System with spikes and anti-spikes. Biologically, spikes represent neural excitation while anti-spikes represent neural inhibition. When a spike meets an anti-spike, they cancel each other out and disappear. Based on this rule, the proof of Turing completeness of SNPS and the required rules are simplified: all rules have a singleton regular expression that precisely indicates the number of spikes or anti-spikes to be consumed. Implementing addition, subtraction, multiplication and division on SNPS is the basis for designing a biological CPU based on the SNP system. By encoding the number as the time interval between two spikes, the literature [28] constructed four SNP systems for calculating addition, subtraction, multiplication, and division, respectively.