Asynchronous numerical spiking neural P systems

Spiking neural (SN) P systems inspired from biological neural network are not only a kind of distributed and parallel membrane computing model, but also a new third-generation neural network model. It should be noted that SN P systems lack the ability to express information with data, however, numerical spiking neural (NSN) P systems can process information by using numerical variables as data structures. In this work, we investigate asynchronous numerical spiking neural (ANSN) P systems by combining with the knowledge of set theory and threshold control strategy. Moreover, the function of threshold (starting conditions of repartition protocol in NSN P systems) is replaced by the threshold set, that is, the production function can be executed if all of the involved variables are within the range of the threshold set. Under the control strategy of the threshold set and in the asynchronous mode, the computing power of NSN P systems is investigated. It is proved that the superfluous uncertainty introduced by ANSN P systems does not reduce the computing power, and ANSN P systems are still Turing universal as the number generating devices. Specifically, if the traditional threshold control strategy is maintained, the universality of asynchronous NSN P systems cannot be guaranteed, which can only characterize the semilinear set of natural numbers.