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We look at spiking neural P systems (SN P systems, for short) all of whose neurons are bounded. We show that a language L ⊆ (0 + 1)* is regular if and only if 1L (i. e., with a supplementary prefix of 1) is generated by a bounded SN P system. This result does not hold when the prefix is replaced by a suffix. For example, 0*1 cannot be generated by a bounded SN P system.

We continue the study of the spiking neural P systems considered as transducers of binary strings or binary infinite sequences, and we investigate their ability to compute morphisms. The class of computed morphisms is rather restricted: length preserving or erasing, and the so-called 2-block morphisms can be computed; however, non-erasing non-length-preserving morphisms cannot be computed.

The paper summarizes recent knowledge about computational power of spiking neural P systems and presents a sequence of new more general results. The concepts of recognizer SN P systems and of uniform families of SN P systems provide a formal framework for this study. We establish the relation of computational power of spiking neural P systems with various limitations to standard complexity classes like P, NP, PSPACE and P/poly.

Membrane systems (also called P systems) refer to the computing models abstracted from the structure and the functioning of the living cell as well as from the cooperation of cells in tissues, organs, and other populations of cells. Spiking neural P systems (SNPS) are a class of distributed and parallel computing models that incorporate the idea of spiking neurons into P systems. To attain the solution of optimization problems, P systems are used to properly organize evolutionary operators of heuristic approaches, which are named as membrane-inspired evolutionary algorithms (MIEAs). This paper proposes a novel way to design a P system for directly obtaining the approximate solutions of combinatorial optimization problems without the aid of evolutionary operators like in the case of MIEAs. To this aim, an extended spiking neural P system (ESNPS) has been proposed by introducing the probabilistic selection of evolution rules and multi-neurons output and a family of ESNPS, called optimization spiking neural P system (OSNPS), are further designed through introducing a guider to adaptively adjust rule probabilities to approximately solve combinatorial optimization problems. Extensive experiments on knapsack problems have been reported to experimentally prove the viability and effectiveness of the proposed neural system.

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.

Several variants of spiking neural P systems (SNPS) have been presented in the literature to perform arithmetic operations. However, each of these variants was designed only for one specific arithmetic operation. In this paper, a complete arithmetic calculator implemented by SNPS is proposed. An application of the proposed calculator to information fusion is also proposed. The information fusion is implemented by integrating the following three elements: (1) an addition and subtraction SNPS already reported in the literature; (2) a modified multiplication and division SNPS; (3) a novel storage SNPS, i.e. a method based on SNPS is introduced to calculate basic probability assignment of an event. This is the first attempt to apply arithmetic operation SNPS to fuse multiple information. The effectiveness of the presented general arithmetic SNPS calculator is verified by means of several examples.

Spiking neural P systems (SNP systems) are a class of distributed and parallel computation models, which are inspired by the way in which neurons process information through spikes, where the integrate-and-fire behavior of neurons and the distribution of produced spikes are achieved by spiking rules. In this work, a novel mechanism for separately describing the integrate-and-fire behavior of neurons and the distribution of produced spikes, and a novel variant of the SNP systems, named evolution-communication SNP (ECSNP) systems, is proposed. More precisely, the integrate-and-fire behavior of neurons is achieved by spike-evolution rules, and the distribution of produced spikes is achieved by spike-communication rules. Then, the computational power of ECSNP systems is examined. It is demonstrated that ECSNP systems are Turing universal as number-generating devices. Furthermore, the computational power of ECSNP systems with a restricted form, i.e. the quantity of spikes in each neuron throughout a computation does not exceed some constant, is also investigated, and it is shown that such restricted ECSNP systems can only characterize the family of semilinear number sets. These results manifest that the capacity of neurons for information storage (i.e. the quantity of spikes) has a critical impact on the ECSNP systems to achieve a desired computational power.

Spiking neural P systems (abbreviated as SNP systems) are models of computation that mimic the behavior of biological neurons. The spiking neural P systems with communication on request (abbreviated as SNQP systems) are a recently developed class of SNP system, where a neuron actively requests spikes from the neighboring neurons instead of passively receiving spikes. It is already known that small SNQP systems, with four unbounded neurons, can achieve Turing universality. In this context, ‘unbounded’ means that the number of spikes in a neuron is not capped. This work investigates the dependency of the number of unbounded neurons on the computation capability of SNQP systems. Specifically, we prove that (1) SNQP systems composed entirely of bounded neurons can characterize the family of finite sets of numbers; (2) SNQP systems containing two unbounded neurons are capable of generating the family of semilinear sets of numbers; (3) SNQP systems containing three unbounded neurons are capable of generating nonsemilinear sets of numbers. Moreover, it is obtained in a constructive way that SNQP systems with two unbounded neurons compute the operations of Boolean logic gates, i.e., OR, AND, NOT, and XOR gates. These theoretical findings demonstrate that the number of unbounded neurons is a key parameter that influences the computation capability of SNQP systems.

Spiking neural P systems (SN P systems), inspired by biological neurons, are introduced as symbolical neural-like computing models that encode information with multisets of symbolized spikes in neurons and process information by using spike-based rewriting rules. Inspired by neuronal activities affected by enzymes, a numerical variant of SN P systems called enzymatic numerical spiking neural P systems (ENSNP systems) is proposed wherein each neuron has a set of variables with real values and a set of enzymatic activation-production spiking rules, and each synapse has an assigned weight. By using spiking rules, ENSNP systems can directly implement mathematical methods based on real numbers and continuous functions. Furthermore, ENSNP systems are used to model ENSNP membrane controllers (ENSNP-MCs) for robots implementing wall following. The trajectories, distances from the wall, and wheel speeds of robots with ENSNP-MCs for wall following are compared with those of a robot with a membrane controller for wall following. The average error values of the designed ENSNP-MCs are compared with three recently fuzzy logical controllers with optimization algorithms for wall following. The experimental results showed that the designed ENSNP-MCs can be candidates as efficient controllers to control robots implementing the task of wall following.

Spiking neural membrane systems (SN P systems) are a class of bio-inspired models inspired by the activities and connectivity of neurons. Extensive studies have been made on SN P systems with synchronization-based communication, while further efforts are needed for the systems with rhythm-based communication. In this work, we design an asynchronous SN P system with resonant connections where all the enabled neurons in the same group connected by resonant connections should instantly produce spikes with the same rhythm. In the designed system, each of the three modules implements one type of the three operations associated with the edge detection of digital images, and they collaborate each other through the resonant connections. An algorithm called EDSNP for edge detection is proposed to simulate the working of the designed asynchronous SN P system. A quantitative analysis of EDSNP and the related methods for edge detection had been conducted to evaluate the performance of EDSNP. The performance of the EDSNP in processing the testing images is superior to the compared methods, based on the quantitative metrics of accuracy, error rate, mean square error, peak signal-to-noise ratio and true positive rate. The results indicate the potential of the temporal firing and the proper neuronal connections in the SN P system to achieve good performance in edge detection.