Abstract

Membrane computing or P-systems is a subfield of natural computing, which models living systems with mathematical tools. In classical membrane-computing, cells or organs are surrounded by a simple membrane and computational events take place in either side of the membrane. We have developed a new conceptual tool to better fit P-systems to higher-order organisms, which rely on the actual membrane structure of the cell and on the biochemical reactions (rules), which take place on the membrane of different organs in our body. To demonstrate the power of this new concept, we modeled the process of maintaining normoglycemia in healthy individuals as well as in type-I and type-II diabetes patients. The main challenge was to prioritize the insulin-producing P-cells over other organs, i.e., once glucose has entered the body, it must first enter specifically into pancreatic P-cells in order to release the hormone Insulin. However, using classical membrane computing, we could not implement this hierarchy. Therefore, we chose to utilize the membrane actual physiology and add its properties to the current definitions of membrane computing. In particular, we use enzymes and protein-transporters (as well as channels) to apply algebraic rules. In addition, we show that the defined systems are universal, by simulating register machines. Thus, allowing deterministic manner operations in a non-deterministic system by giving membrane-specific rules. To our gratification, we succeeded to adequately describe the process of glucose homeostasis in health and disease while bringing the science of membrane-computing closer to the natural world. (C) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Abstract

We partially answer an open question on small computational devices: how many neurons are needed by a spiking neural P system with communication on request (SNQ P Systems) to achieve universality? We provide an answer in the case when the SNQ P System uses at least 5 types of spikes. Our work shows that 6 neurons are enough to achieve universality as number generators, number accepters and function computation device. We achieve this result by using only two neuron to simulate the instructions labels and one type of spike to emulate a register. (C) 2020 Elsevier B.V. All rights reserved.

Abstract

We investigate the spiking neural P systems with communication on request (SNQ P systems) that are devices in the area of neural like P systems abstracting the way in which neurons work and process information. Here we discuss the SNQ P systems using the rule application strategy as defined by Linqiang Pan and collaborators and we are able to improve their result of universality of such systems using two types of spikes. In the current work, we prove that only one type of spikes is sufficient for reaching the computational power of Turing Machines for these devices, bringing closer to implementation such a device. The result holds both in maximum parallel manner application of the rules as well as the maximum-sequentiality application of rules.

Abstract

Abstract

Spiking neural P systems are a class of third generation neural networks belonging to the framework of membrane computing. Spiking neural P systems with communication on request (SNQ P systems) are a type of spiking neural P system where the spikes are requested from neighboring neurons. SNQ P systems have previously been proved to be universal (computationally equivalent to Turing machines) when two types of spikes are considered. This paper studies a simplified version of SNQ P systems, i.e. SNQ P systems with one type of spike. It is proved that one type of spike is enough to guarantee the Turing universality of SNQ P systems. Theoretical results are shown in the cases of the SNQ P system used in both generating and accepting modes. Furthermore, the influence of the number of unbounded neurons (the number of spikes in a neuron is not bounded) on the computation power of SNQ P systems with one type of spike is investigated. It is found that SNQ P systems functioning as number generating devices with one type of spike and four unbounded neurons are Turing universal.