Inhomogeneous Weighted Spiking Neural P Systems with Local Homogeneous

Homogeneous Spiking Neural P Systems(HSN P systems, for short) are a class of neural-like computing models in membrane computing, which are inspired by neurons that they are "designed" by nature to have the same "set of rules", "working" in a uniform way to transform input into output. HSN P systems can be converted to Weighted Homogeneous SNP systems and the using of weights can simplify the structure of the system. In this work, based on the above two known systems, we consider a restricted variant of SN P systems called inhomogeneous weighted SN P systems with local homogeneous, where neurons in same module have the same set of rules. As a result, we prove that such systems can achieve Turing completeness. Specifically, it is proved that using only standard spiking rules is sufficient to compute the family of sets of Turing computable natural numbers, and local homogeneity reduces the time required for the execution of the system.