An improved universal spiking neural P system with generalized use of rules

Abstract

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.

A formal framework for spiking neural P systems

“…It seems worthwhile to continue the development of the formal framework for spiking neural P systems with different degrees of parallelism, for example the kind of local parallelism reflected by the exhaustive use of rules, as proposed in [15,18], where in each neuron, an applicable rule must be used as many times as possible. The so-called "white hole rules" were introduced in [1]; they allow for using the whole contents of a neuron and then sending it to other neurons.…”

“…Interesting models related to (n, V, F, ) are spiking neural P systems with white hole rules [1] and spiking neural P systems with exhaustive use of rules [15,18], but there are several technical details to be considered carefully, hence a thorough discussion of such models must be postponed for future research.…”

Spiking neural P systems: main ideas and results

“…If no bound on the number of neuron is set, then SN P systems using this semantics are computationally complete. In Jiang et al (2019) an improved universal system of this type was obtained, where each neuron contains at most 5 rules, each spiking rule consumes at most 4 spikes, and each forgetting rule deletes at most 4 spikes.…”

Proof techniques in Membrane Computing

“…The computational completeness of computing models of membrane systems was initially showed by making use of techniques of formal languages and multisets [4] (i.e. grammars, matrix grammars) as well as simulating the behaviour of well known universal models, as register machines [8,27]. The universality of basic transition P systems with external output, as devices able to compute functions, was obtained by showing that these systems have the capability of computing any partial recursive function on natural numbers [24].…”