Fen Luo's research while affiliated with Chongqing Technology and Business University and other places

Taken inspiration from biological phenomenon that neurons communicate via spikes, spiking neural P systems (SN P systems, for short) are a class of distributed and parallel computing devices. So far firing rules in most of the SN P systems usually work in a sequential way or in an exhaustive way. Recently, a combination of the two ways mentioned above is considered in SN P systems. This new strategy of using rules, which is called a generalized way of using rules, is applicable for both firing rules and forgetting rules. In SN P systems with generalized use of rules (SNGR P systems, for short), if a rule is used at some step, it can be applied any possible number of times, nondeterministically chosen. In this work, the computational completeness of SNGR P systems is investigated. Specifically, a universal SNGR P system is constructed, where each neuron contains at most 5 rules, and for each time each firing rule consumes at most 6 spikes and each forgetting rule removes at most 4 spikes. This result makes an improvement regarding to these related parameters, thus provides an answer to the open problem mentioned in original work. Moreover, with this improvement we can use less resources (neurons and spikes involved in the evolution of system) to construct universal SNGR P systems.

This paper is an attempt to relax the condition of using the rules in a maximally parallel manner in the framework of spiking neural P systems with exhaustive use of rules. To this aim, we consider the minimal parallelism of using rules: if one rule associated with a neuron can be used, then the rule must be used at least once (but we do not care how many times). In this framework, we study the computational power of our systems as number generating devices. Weak as it might look, this minimal parallelism still leads to universality, even when we eliminate the delay between firing and spiking and the forgetting rules at the same time.