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Methods for optimizing and evolving spiking neural P systems (in short, SN P systems) have been previously developed with the use of a genetic algorithm framework. So far, these computations, both evolving and simulating, were done only sequentially. Due to the non-deterministic and parallel nature of SN P systems, it is natural to harness parallel processors in implementing its evolution and simulation. In this work, a parallel framework for the evolution of SN P Systems is presented. This is the result of extending our previous work by implementing it on a CUDA-enabled graphics processing unit and adapting CuSNP design in simulations. Using binary addition and binary subtraction with 3 different categories each as initial SN P systems, the GPU-based evolution runs up to 9x faster with respect to its CPU-based evolution counterparts. Overall, when considering the whole process, the GPU framework is up to 3 times faster than the CPU version. Junta de Andalucía P20_00486

P-Systems are abstract machines inspired to the behaviour of cells which we can see like simple biological processing units. Many types of P-Systems have been developed considering different aspects of the cells working principles, obtaining different computational models. In this paper we introduce Active P-Colonies (APC), a variant of the model P-Colony systems. P-Colony systems are a model of computation based on the collaboration among different agents placed in a shared passive environment (i.e. a space where no computing operations take place). First of all, we show that using the P-Colony system basic model it is not possible to solve problems in the computational class NP (unless P=NP). Inspired by what has been done for the basic variant of P-Systems, we extend the original model by including new types of rules and new biological behaviours like duplication and membrane dissolution. In fact, in APC the agents are able to duplicate themselves obtaining new processing units having the same computational power as the original unit. The cells can also dissolve their membrane, releasing the contents into the environment. The obtained systems are able to solve in polynomial time (and exponential space) computationally hard problems. In particular, we focus on the development of systems able to solve problems in the classes NP (SAT), coNP (UNSAT) and #P (#SAT).

International audience; Numerical P systems (NPS) are a very particular class of P systems having important differences from most models in this area. The main particularity of the model is the usage of numerical variables whose values are shared among applicable rules, contrary to the concurrence for objects in the multiset for the traditional P systems case. In 2007, Freund and Verlan developed a formal framework for P systems to capture most of the essential features of P systems and to define their functioning in a formal way. Subsequent papers developed versions of this framework for the case of spiking neural P systems and P systems with dynamically evolving structure. These results permitted to obtain a different view on P systems giving a general framework to analyze, relate and extend different variants of P systems and other related models, like Petri nets or register machines. This paper aims to provide a similar generalization for the case of numerical P systems (NPS) and related variants like enzymatic or generalized NPS. We call the obtained model Numerical Networks of Cells (NNC). As in the case of the formal framework it allows to accurately describe NPS, as well as other types of P systems like those using fuzzy sets as computation support. Also, the new model generalizes other well-known models like Boolean networks or reaction systems and this can potentially help to bring bridges between P systems and these areas.

A further exploration is presented of recent approaches to morphogenetic processes where geometry and form are fundamental primitives. Prior bottom-up approaches in morphogenetic modeling usually target a specific biological process aiming for optimal fidelity. We take a novel, more integrative and more abstract view of these phenomena and aim at properties such as (computational) universality, homeostasis, self-reproduction or self-healing, in both living and artificial evolving systems with explicit geometric 3D arrangements. We refine the recently introduced model of M systems (for morphogenetic systems) that leverages certain constructs in membrane computing and DNA self-assembly. The model is still based on local interactions of simple atomic components under explicit geometric constraints given by their shapes and spatial arrangements. We demonstrate two types of capabilities of the extended models. First, they are computationally universal in the Turing sense because they can simulate Turing machines very efficiently, with only a linear slowdown factor. Furthermore, they have the theoretical capability to probabilistically solve NP-hard problems in polynomial time. Second, more importantly, they unfold to exhibit certain macro-properties characteristic of living organisms (particularly, the ability of self-assembly of complex structures, self-reproduction and self-healing) as global properties observable at the macro-level, without explicit programming of these properties beyond simple rules of interaction. Besides providing a new theoretical background for this type of model, we provide quantitative evidence of these properties in a simple cell-like M system model. These results have been obtained using an M system simulator and visualizer that is available as open source software for further research in this area.

Spiking neural P systems (SN P systems) refer to a type of distributed parallel neural computation model in the membrane computing framework. In this work, a new type of SN P system is examined, i.e., spiking neural P systems with polarizations (PSN P systems), by taking inspiration from the polarized cell membrane of a neuron. For the PSN P system, the firing condition of rules is the neuron-associated polarization. This work focuses on examining the computation power of the PSN P systems adopting the sequential mode induced by the minimum spike number, where at a computation step, one (resp., all) of neurons that hold the minimum spike number within the neurons which can fire will fire, i.e., the min-sequentiality strategy (resp., min-pseudo-sequentiality strategy). We prove that PSN P systems adopting the min-sequentiality strategy or min-pseudo-sequentiality strategy are Turing universal as the number generating devices. These results indicate the computation power of PSN P systems is robust regarding their strategies of sequentiality.

In the Membrane Computing area, P systems are unconventional devices of computation inspired by the structure and processes taking place in living cells. Main successful P system applications lie in computability and computational complexity theories, as well as in biological modelling. Given that models become too complex to deal with, simulators for P systems are essential tools and their efficiency is critical. In order to handle the diverse situations that may arise during the computation, these simulators have to take into account that worst-case scenarios can happen, even though they rarely occur. As a result, there is a significant loss of performance. In this paper, the concept of adaptative simulation for P systems is introduced to palliate this problem. This is achieved by passing high-level information provided directly by P system model designers to the simulator, helping it to better adapt to the target model. For this purpose, an existing simulator for an ecosystem modelling framework, named Population Dynamics P systems, is extended to include the information of modules, that are usually employed to define ecosystem models. Moreover, the standard description language for P systems, P-Lingua, has been re-engineered in its version 5. It now includes a new syntactical item, called feature, to express this kind of high-level semantic information. Experiments show that this simple adaptative simulator supporting modules as features doubles the performance when running on GPUs and on multicore processors.

Cell-like P systems where communication between the regions are carried out by rules of type symport/antiport are considered. These systems compute by changing the places of objects with respect to the membranes, and not by changing the objects themselves. The environment plays an active role in the sense that it not only can receive objects from the system, but also send objects into it. There is an alphabet associated with the environment whose elements appear in an arbitrary large number of copies at the initial configuration. This property seems too strong from a complexity view, but it has been widely exploited in the design of efficient solutions to computationally hard problems when some mechanisms (inspired by mitosis and membrane fission) allowing to construct an exponential workspace in linear time, are considered. In this paper, complexity aspects of P systems with symport/antiport rules and membrane division are considered when the set associated with the environment is the emptyset. It is shown that the role of the environment is irrelevant for such kind of P systems, in contrast with the well known results concerning to its relevance when membrane separation is used instead of membrane division.

Inferring the structure and operation of a computing model, given some observations of its behavior, is in general a desirable but daunting task. In this paper we try to solve a constrained version of this problem. We consider a P system Pi with active membranes and using cooperative rewriting, communication, and division rules and a collection of pairs of its consecutive configurations. Then, we feed this collection of configurations as input to a (mu+lambda) evolutionary algorithm that evolves a population of (initially random) P systems, each with its own rules, with the aim of obtaining an individual that approximates as well as possible. We discuss the results obtained on different benchmark problems, designed to test the ability to infer cooperative rewriting, communication, and membrane division rules. We will also provide a description of how fitness results are influenced by different setting of the hyperparameters of the evolutionary algorithm. The results show that the proposed approach is able to find correct solutions for small problems, and it is a promising research direction for the automatic synthesis of P systems.

In this paper, the problem about image segmentation on the basis of pulse-coupled neural network (PCNN) is studied. Simulated annealing particle swarm optimization (SAPSO) is introduced into membrane computing to design algorithm to achieve image segmentation with better performance. Corresponding typical numerical experiment results illuminate the effectiveness and superiority of the proposed method.

Spiking neural P systems (SN P systems, in short) are the latest branch of membrane computing; inspired by the biological behavior of spiking neurons. They are considered true distributed and parallel systems; modeled to solve time consumption problem and presented the concept of parallelism usage in the computing field. This paper proposes novel strategies for solving non-determinism problem of SN P systems. The proposed algorithm relies on the parallelism feature to simulate the social hierarchy, tracking, encircling, and attacking behaviors in the grey wolf optimizer. It is modeled by collaboration between a set of SN P systems to get a feasible solution in polynomial time. Moreover, a new method named the power of signal is proposed to control the copying spikes process between neurons and differentiate between the arithmetic operations. Additionally, a time control approach is proposed to avoid non-determinism inside neurons that applied the determinism feature during firing rules. The theoretical and empirical experiments proved that the algorithm can successfully halt and in addition to the effectiveness of the proposed neural systems in getting an optimal solution in a reasonable time. As a result, this study is counted as a significant advancement in intelligent and optimization systems, whereas it has a direct impact on enhancing the performance of these systems and their applications.

In membrane computing, researchers have designed various P systems to solve problems, for example, NP-hard problems. The research of verification methods and simulation tools for these P systems is one of the main topics in membrane computing. In this paper, we present a general-purpose P system simulator named UPSimulator for cell-like, tissue-like and neural-like P systems. UPSimulator can serve as both a simulator and a development library for P system models, which processes objects in the regions defined by membranes. UPSimulator provides a feasible solution for the simulation of hybrid P systems by supporting the complex evolutionary rules and structures in different types of P systems.

In this paper, a membrane evolutionary artificial potential field (memEAPF) approach for solving the mobile robot path planning problem is proposed, which combines membrane computing with a genetic algorithm (membrane-inspired evolutionary algorithm with one-level membrane structure) and the artificial potential field method to find the parameters to generate a feasible and safe path. The memEAPF proposal consists of delimited compartments where multisets of parameters evolve according to rules of biochemical inspiration to minimize the path length. The proposed approach is compared with artificial potential field based path planning methods concerning to their planning performance on a set of twelve benchmark test environments, and it exhibits a better performance regarding path length. Experiments to demonstrate the statistical significance of the improvements achieved by the proposed approach in static and dynamic environments are shown. Moreover, the implementation results using parallel architectures proved the effectiveness and practicality of the proposal to obtain solutions in considerably less time.

Pulse coupled neural networks (PCNN, for short) are models abstracting the synchronization behavior observed experimentally for the cortical neurons in the visual cortex of a cat’s brain, and the intersecting cortical model is a simplified version of the PCNN model. Membrane computing (MC) is a kind computation paradigm abstracted from the structure and functioning of biological cells that provide models working in cell-like mode, neural-like mode and tissue-like mode. Inspired from intersecting cortical model, this paper proposes a new kind of neural-like P systems, called dynamic threshold neural P systems (for short, DTNP systems). DTNP systems can be represented as a directed graph, where nodes are dynamic threshold neurons while arcs denote synaptic connections of these neurons. DTNP systems provide a kind of parallel computing models, they have two data units (feeding input unit and dynamic threshold unit) and the neuron firing mechanism is implemented by using a dynamic threshold mechanism. The Turing universality of DTNP systems as number accepting/generating devices is established. In addition, an universal DTNP system having 109 neurons for computing functions is constructed. National Natural Science Foundation of China No 61472328 Research Fund of Sichuan Science and Technology Project No. 2018JY0083 Chunhui Project Foundation of the Education Department of China No. Z2016143 Chunhui Project Foundation of the Education Department of China No. Z2016148 Research Foundation of the Education Department of Sichuan province No. 17TD0034

Spiking neural P (SNP) systems are a class of neural-like membrane computing models that are abstracted by applying the mechanisms of spiking neurons. In SNP systems, each spiking neuron has three characteristics: (i) internal state, (ii) spike consumption, and (iii) spike generation. These three characteristics are used to form a parameterised nonlinear SNP system, which has a nonlinear spiking mechanism, three nonlinear gate functions, and trainable parameters. Based on the parameterised nonlinear SNP system, we develop a novel variant of long short-term memory (LSTM), called the LSTM-SNP model. LSTM-SNP is a recurrent-type model that can process sequential data. Time series forecasting problems are used to conduct a case study. Five benchmark time series are used to evaluate the proposed LSTM-SNP model and compare seven state-of-the-art prediction models and five baseline prediction models. The comparison results show the effectiveness of the proposed LSTM-SNP model for time series forecasting.

A kernel P system integrates in a coherent and elegant manner some of the most successfully used features of the P systems employed in modelling various applications. It also provides a theoretical framework for analysing these applications and a software environment for simulating and verifying them. In this paper, we illustrate the modelling capabilities of kernel P systems by showing how other classes of P systems can be represented with this formalism and providing a number of kernel P system models for a sorting algorithm and a broadcasting problem. We also show how formal verification can be used to validate that the given models work as desired. Finally, a test generation method based on automata is extended to non-deterministic kernel P systems.

The 3-COL problem consists on deciding if the regions of a map can be coloured with only three colors bearing in mind that two adjacent regions must be coloured with di erent colors. It is a NP problem and it has been previously used in complexity studies in membrane computing to check the ability of a model for solving problems of such complexity class. Recently, tissue P systems with proteins on cells have been presented and its ability to solve NP-problems has been proved, but it remained as an open question to know if such model was still able to solve such problems if the environment was removed. In this paper we provide an a rmative answer to this question by showing a uniform family of tissue P systems without environment and with proteins on cells which solves the 3-COL problem in linear time.

The integration of symbolic reasoning systems based on logic and connectionist systems based on the functioning of living neurons is a vivid research area in computer science. In the literature, one can find many efforts where different reasoning systems based on different logics are linked to classic artificial neural networks. In this paper, we study the relation between the semantics of reasoning systems based on propositional logic and the connectionist model in the framework of membrane computing, namely, spiking neural P systems. We prove that the fixed point semantics of deductive databases without negation can be implemented in the spiking neural P systems model and such a model can also deal with negation if it is endowed with anti-spikes and annihilation rules.

A mobile robot acting in a human environment should follow social conventions, keeping safety distances and navigating at moderate speeds, in order to respect people in its surroundings and avoid obstacles in real-time. The problem is more complex in differential-drive wheeled robots, with trajectories constrained by nonholonomic and kinematics restrictions. It is an NP-hard problem widely studied in the literature, combining disciplines such as Psychology, Mathematics, Computer Science and Engineering. In this work, we propose a novel solution based on Membrane Computing, Social Force Model and Dynamic Window Approach Algorithm. The resulting model is able to compute, in logarithmic time, the best motion command for the robot, given its current state, considering the surrounding people and obstacles. The model is compatible with other membrane computing models for robotics and suitable for an implementation on parallel hardware. Finally, a visual simulator was implemented in ROS and C++ for validation and testing.

Spiking neural P systems (SNP systems, in short) are a class of distributed parallel computing systems inspired from the neurophysiological behavior of biological spiking neurons. In this paper, we investigate a new variant of SNP systems in which each neuron has one or more synaptic channels, called spiking neural P systems with multiple channels (SNP-MC systems, in short). The spiking rules with channel label are introduced to handle the firing mechanism of neurons, where the channel labels indicate synaptic channels of transmitting the generated spikes. The computation power of SNP-MC systems is investigated. Specifically, we prove that SNP-MC systems are Turing universal as both number generating and number accepting devices.

From a computational complexity point of view, some syntactical ingredients play differentroles depending on the kind of combination considered. Inspired by the fact that the passing of a chemical substance through a biological membrane is often done by an interaction with the membrane itself, systems with active membranes were considered.Several combinations of different ingredients have been used in order to know which kindof problems could they solve efficientlyIn this paper, minimal cooperation with a minimal expression (the left-hand side of every object evolution rule has at most two objects and its right-hand side contains only one object) in object evolution rules is considered and a polynomial-time uniform solution to the SAT problem is presented. Consequently, a new way to tackle the P versus NP problem is provided. National Natural Science Foundation of China No 61472328 National Natural Science Foundation of China No 61320106005

Fuzzy clustering problem is usually posed as an optimization problem. However, the existing researchhas shown that clustering technique that optimizes a single cluster validity index may not provide satisfactory results on different kinds of data sets. This paper proposes a multiobjective clustering frameworkfor fuzzy clustering, in which a tissue-like membrane system with a special cell structure is designed tointegrate a non-dominated sorting technique and a modified differential evolution mechanism. Based onthe multiobjective clustering framework, a fuzzy clustering approach is realized to optimize three cluster validity indices that can capture different characteristics. The proposed approach is evaluated on sixartificial and ten real-life data sets and is compared with several multiobjective and singleobjective techniques. The comparison results demonstrate the effectiveness and advantage of the proposed approachon clustering the data sets with different characteristics. National Natural Science Foundation of China No 61472328 Chunhui Project Foundation of the Education Department of China No. Z2016148 Chunhui Project Foundation of the Education Department of China No. Z2016143 Research Foundation of the Education Department of Sichuan province No. 17TD0034

We extend to spiking neural P systems a notion investigated in the “standard” membrane systems: the language of the traces of a distinguished object. In our case, we distinguish a spike by “marking” it and we follow its path through the neurons of the system, thus obtaining a language. Several examples are discussed and some preliminary results about this way of associating a language with a spiking neural P system are given, together with a series of topics for further research. For instance, we show that each regular language is the morphic image of a trace language intersected with a very particular regular language, while each recursively enumerable language over the one-letter alphabet is the projection of a trace language. In all proofs we try to keep the size of used systems (number of neurons, of rules in each neuron, of spikes consumed or removed by rules) as small as possible.

Numerical P systems (for short, NP systems) are distributed and parallel computing models inspired both from the structure of living cells and from the economic reality, where the values of variables evolve by programs that are composed by production functions and repartition protocols: the value of a production function is distributed to variables according to the corresponding repartition protocol. In this work, we introduce a new method of using evolution programs into NP systems, where thresholds are associated with production functions. The computation power of NP systems with production thresholds is investigated. Specifically, we prove that NP systems with lower-thresholds (the production function value can be distributed only when it is not smaller than a given constant), with one membrane working both in the all-parallel mode and in the sequential mode, are universal. The universal results of NP systems with lower-thresholds are extended to NP systems with upper-thresholds (the production function value can be distributed only when it is not greater than a given constant) by simulating the former with the latter. These universality results show that NP systems with production thresholds have the potential to implement any computer program or robot behavior.

Tissue P systems with symport/antiport rules are a class of distributed parallel computing models inspired by the cell intercommunication in tissues, where objects are never modified in the process of communication, just changing their place within the system. In this work, a variant of tissue P systems, called tissue P systems with evolutional symport/antiport rules is introduced, where objects are moved from one region to another region and may be evolved during this process. The computational power of such P systems is studied. Specifically, it is proved that such P systems with one cell and using evolutional symport rules of length at most 3 or using evolutional antiport rules of length at most 4 are Turing universal (only the family of all finite sets of positive integers can be generated by such P systems if standard symport/antiport rules are used). Moreover, cell division rules are considered in tissue P systems with evolutional symport/antiport rules, and a limit on the efficiency of such P systems is provided with evolutional communication rules of length at most 2. The computational efficiency of this kind of models is shown when using evolutional communication rules of length at most 4.

Display Omitted Harmony Search is enhanced by improving the speed of convergence while preventing premature convergence to a local minimum.Membrane computing model is employed to execute parallelized HS efficiently to increase the diversity of HS and improving the performance of HS.Simulation results showed that the application of the proposed approach to different variants of harmony search yielded better performance than previous approaches.We applied the parallel membrane-inspired HS to the flexible job shop scheduling problem and well-known benchmark instances to demonstrate the effectiveness of the proposed algorithm. Harmony search is an emerging meta-heuristic optimization algorithm that is inspired by musical improvisation processes, and it can solve various optimization problems. Membrane computing is a distributed and parallel model for solving hard optimization problems. First, we employed some previously proposed approaches to improve standard harmony search by allowing its parameters to be adaptive during the processing steps. Information from the best solutions was used to improve the speed of convergence while preventing premature convergence to a local minimum. Second, we introduced a parallel framework based on membrane computing to improve the harmony search. Our approach utilized the parallel membrane computing model to execute parallelized harmony search efficiently on different cores, where the membrane computing communication characteristics were used to exchange information between the solutions on different cores, thereby increasing the diversity of harmony search and improving the performance of harmony search. Our simulation results showed that the application of the proposed approach to different variants of harmony search yielded better performance than previous approaches. Furthermore, we applied the parallel membrane inspired harmony search to the flexible job shop scheduling problem. Experiments using well-known benchmark instances showed the effectiveness of the algorithm.

This note considers three basic research directions in membrane computing – characterizations of the computing power of Turing machines, computing more than Turing machines, efficiency (solving computationally hard problems in a feasible time) – by basic classes of P systems (cell and tissue multiset rewriting systems, symport/antiport systems, spiking neural P systems, numerical P systems). (Types of) Results reported in the literature are briefly mentioned, several unsolved cases are pointed out, and directions of further research are proposed.

P system is a new kind of distributed parallel computing model. In the P system, objects in each membrane can follow the evolution of the maximum parallelism principle, so we can solve NP-hard problem in polynomial time. In this paper, we design a family of P system with to judge whether there is a Hamiltonian cycle and find all Hamiltonian cycle in an undirected graph, and then an instance is given to illustrate the feasibility and effectiveness of our designed P systems.

Membrane systems are a framework of distributed parallel computing models, inspired by some basic features of biological membranes. In this paper, a membrane computing system named Π MM is proposed to solve multiplication operation with matrices by its parallelism. It mainly includes three stages: firstly, construct new embedded membranes and input the values of two matrices; secondly, divide the membranes to generate new membranes according to the rows of matrix; finally, the solutions are obtained in each row membranes under the relatively calculation rules side by side. An instance is given to show the whole procedure how to solve the matrix multiplication by the Π MM .

Numerical P systems are a class of P systems inspired both from the structure of living cells and from economics, where variables are associated with the membranes, and these associations are not changed during the computation. However, in the standard P systems, a crucial character for objects is that they can pass through membranes, between regions of the same cell, between cells, or between cells and their environment. We introduce this character also to numerical P systems, and call the new variant numerical P systems with migrating variables (MNP systems). The computational power of MNP systems is investigated both as number generators and as string generators, working in the one-parallel or the sequential modes. Specially, as number generators, MNP systems are proved to be universal working in the above two modes. As string generators, the generative capacity of such systems is investigated having as a reference the families of languages in the Chomsky hierarchy, and a characterization of recursively enumerable languages is obtained.

In this paper, a new hybrid algorithm is proposed to solve the single objective real-parameter numerical optimization problems, named as CETMS. The proposed CETMS is based on tissue membrane systems(TMS), and the evolution strategy with covariance matrix adaptation (CMA-ES) algorithm is employed to find the optimal solution in each cell of TMS. Some features of Tissue Membrane Systems, such as membrane structure, evolution mechanism and communication mechanism among cells, are introduced into CETMS. In addition, the optimal information of different cells can be shared by communication mechanism of TMS after the appointed cycle. The simulation experiments are conducted on thirty benchmark functions on the CEC14 test suite, which evaluate the performance of the proposed algorithm on solving single objective real-parameter numerical optimization problems. Numerical results show that the proposed CETMS has a very good performance in comparison with some of the state-of-the-art algorithms.

The applications of quantitative structure activity relationships (QSAR) are used to establish a correlation between structure and biological response. Similarity searching is one of QSAR major phases. Innovating new strategies for similarity searching is an urgent task in cheminformatics research for three reasons: (i) the increasing size of chemical search space of compound databases; (ii) the importance of similarity measurements to (2D) and (3D) QSAR models; and (iii) similarity searching is a time consuming process in drug discovery. In this study, we introduce theoretical similarity searching strategy based on membrane computing. It solves time consumption problem. We adopt a ranking sorting algorithm with P System to rank probabilities of similarity according to a predefined similarity threshold. That bio-inspired model, simulating biological living cell, presents a high performance parallel processing system, we called it PQSAR. It relies on a set of rules to apply ranking algorithm on probabilities of similarity. The simulated experiments show how the effectiveness of PQSAR method enhanced the performance of similarity searching significantly; and introduced a standard ranking algorithm for similarity searching.

Spiking neural P systems, shortly called SN P systems, are a class of distributed and parallel neural-like computing models, inspired from the way of neurons spiking and communicating with each other by means of spikes. In this work, we propose a new variant of SN P systems, called SN P systems with request rules. In such a system, besides spiking and forgetting rules, a neuron can have request rules, with which the neuron can sense "stimulus" from the environment by receiving a certain number of spikes. We investigate the computation power of SN P systems with request rules. It is obtained that such systems are Turing universal, even with a small number of neurons. Specifically, (i) SN P systems with request rules having 4 neurons can compute any set of Turing computable natural numbers and (ii) with 47 neurons such systems can compute any Turing computable function.

With mathematical motivation, we consider a combination of basic features of multiset-rewriting P systems and of spiking neural P systems, that is, we consider cell-like P systems with spiking rules in their membranes (hence dealing with only one kind of objects, the spikes). The universality of these systems as number generating devices is proved for the two usual ways to define the output (internally or externally) and for various restrictions on the spiking rules. Several research topics are also pointed out.

In spite of the fact that many ways of using the evolution rules in a P system were already investigated, there is still a case, which we call the flat maximal parallelism, which appeared in several papers, but which deserves a more careful attention: in each step, in each membrane, a maximal set of applicable rules is chosen and each rule in the set is applied exactly once. In this work, flat maximal parallelism is studied for non-cooperating P systems with promoters. Specifically, we prove that non-cooperating P systems with at most one promoter associated with any rule, working in the flat maximally parallel way, are Turing universal (the Turing universality of such P systems is open if they work in the maximally parallel way). Moreover, a uniform solution to the SAT problem is provided by using non-cooperating P systems with promoters and membrane division, working in the flat maximal parallel way.

The paper contributes to the topic of (purely) catalytic P systems. Catalytic P systems represent the original and likely the simplest class of membrane computing models. It is known that (purely) catalytic P systems with two (respectively three) catalysts and one membrane can simulate any Minsky register machine and, hence, they are computationally complete. However, the problem of minimal size of such a universal catalytic P system remains open for about ten years. We improve known results about small catalytic P systems simulating register machines in three different modes (generating, accepting, computing functions). Together with some specific universal register machine [7], one could eventually construct a small universal catalytic P system. As a consequence, we also improve the previous construction of a minimal catalytic P system generating a non-semilinear set, diminishing the number of necessary rules from 29 to 24.

For adaptively learning the parameters of extreme learning machine (ELM), a novel learning algorithm is proposed on the basis of a multiobjective membrane algorithm. More specifically, first, a multiobjective mathematical model is established to learn the parameters of ELM, which is constructed by three objective functions. These objective functions include the root mean squared error, L_1 norm of output weights and the number of hidden nodes. Second, a series of the trade-off solutions with respect to the above-mentioned objective functions are found by the multiobjective membrane algorithm. Finally, a trade-off solution with the best generalization performance of ELM, which is chosen from the Pareto front obtained by the multiobjective algorithm, will become the final parameters for initializing the ELM network. The simulation experiments are run on the approximation of ‘SinC’ function, real-world regression problems and real-world classification problems. Experimental results indicate that the proposed framework is able to achieve good generalization performance in the most cases with many compact networks.

Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired by spiking neurons. SN P systems with anti-spikes (ASN P systems) are a variant of SN P systems, which were inspired by inhibitory impulses/spikes or inhibitory synapses. In this work, we consider ASN P systems with the restrictions: (1) systems are simple in the sense that each neuron has only one rule; (2) at each step the neuron(s) with the maximum number of spikes among the neurons that are active (can spike) will fire; (3) the feature of delays and forgetting rules are not used. These restrictions make the systems working in a sequential way. We investigate the computational power of ASN P systems under these restrictions. Specifically, we prove that such systems with spiking rules of categories ( a , a ) and ( a , a ? ) are universal as both number generating and accepting devices. We also prove that ASN P systems with inhibitory synapses using spiking rules of category ( a , a ) are universal as both generating and accepting devices. These results show that ASN P systems are still powerful working with these restrictions.

Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired from the way neurons process information and communicate by means of spikes, where neurons are different in the sense that they can have different sets of spiking rules. In this work, we consider a variant of SN P systems with two restrictions: (1) all neurons contain only spikes (neurons are homogeneous in this case, since they can be considered as containers of spikes), while the spiking rules are moved on the synapses; (2) all synapses are homogeneous in the sense that each synapse has the same set of rules. These restrictions correspond to the fact that the SN P system consists of only one kind of neurons and one kind of synapses. The computational power of SN P systems with homogeneous neurons and synapses is investigated. Specifically, it is proved that such systems are Turing universal as both number generating and number accepting devices.

Membrane computing is a new branch of natural computing, whose aim is to abstract computing ideas from the structure and the functioning of living cells to construct computing models and algorithms. The obtained algorithms are generally called membrane-inspired algorithms or membrane algorithms, which are known as a class of intelligent algorithms inspired by biological behaviors of living cells. In this work, a membrane algorithm with a three-levels of hierarchical cell-like structure is proposed, where elementary membranes can dynamically evolve to generating working space (performing cell division) during the computation. We test our method by solving 14 instances of a benchmark of the vehicle routing problem, as well as a numerical example of solid waste management in Chengdu, China. Experimental results show that our method performs well on solving the 14 instances of the benchmark of the vehicle routing problem comparing with the genetic algorithm, tabu search algorithm, simulated annealing algorithm, ant system algorithm, and evolutionary algorithm. In practice, our method can quickly obtain the global optimal solution of the numerical example of solid waste management.

Cell division is a process that produces two or more cells from one cell by replicating the original chromosomes so that each daughter cell gets a copy of them. Membrane fission is a process by which a biological membrane is split into two new ones in such a manner that the contents of the initial membrane get distributed or separated among the new membranes. Inspired by these biological phenomena, new kinds of models were considered in the discipline of Membrane Computing, in the context of P systems with active membranes, and tissue P systems that use symport/antiport rules, respectively.This paper combines the two approaches: cell-like P systems with symport/antiport rules and membrane separation are studied, from a computational complexity perspective. Specifically, the role of the environment in the context of cell-like P systems with membrane separation is established, and additional borderlines between tractability and NP-hardness are summarized.

Membrane computing is a computational paradigm inspired by the structure and behavior of a living cell. P Systems are the computing devices that are used to realize membrane computing models. Numerous theoretical studies on many variants of P Systems have shown them to be computationally universal. There is a wide range of applications of P Systems from modeling of biological processes to image processing. Among many variants of P Systems, one of the most important is Enzymatic Numerical P System (ENPS). ENPS is a class of P System in which membranes operate on numerical values. To realize the power of ENPS there are a few simulators developed. Each and every simulator has some advantages as well as some disadvantages. Here, a GPU based simulator using Python as a user interaction language is developed. This tool is a completely parallel variant, compatible with a Python based sequential simulator (PeP) which was the first Python based work for ENPS. The developed simulator uses CUDA to interact with GPU and gives the desired speed up, while processing the membranes. There are two important case studies which show the performance of the developed tool to be far better than the other serial simulators.

This paper focuses on power system fault diagnosis based on Weighted Corrective Fuzzy Reasoning Spiking Neural P Systems with real numbers (rWCFRSNPSs) to propose a graphic fault diagnosis method, called FDWCFRSNPS. In the FD-WCFRSNPS, an rWCFRSNPS is proposed to model the logical relationships between faults and potential warning messages triggered by the corresponding protective devices. In addition, a matrixbased reasoning algorithm for the rWCFRSNPS is devised to reason about the fault alarm messages using parallel representations. Besides, a layered modeling method based on rWCFRSNPSs is developed to adapt to topological changes in power systems and a Temporal Order Information Processing Method based on Cause– Effect Networks is designed to correct fault alarm messages before the fault reasoning. Finally, in a case study considering a local subsystem of a 220kV power system, the diagnosis results of five test cases prove that the proposed FD-WCFRSNPS is viable and effective. Ministerio de Economía, Industria y Competitividad TIN2017-89842-P (MABICAP)

Membrane computing is a new natural computing paradigm inspired by the functioning and structure of biological cells, and has been successfully applied to many different areas, from biology to engineering. In this paper, we present kPWorkbench , a software framework developed to support membrane computing and its applications. kPWorkbench offers unique features, including modelling, simulation, agent-based high performance simulation and verification, which allow modelling and computational analysis of membrane systems. The kPWorkbench formal verification component provides the opportunity to analyse the behaviour of a model and validate that important system requirements are met and certain behaviours are observed. The platform also features a property language based on natural language statements to facilitate property specification.

Tissue P systems, which are inspired from the structures and functions of biological tissues, are a class of distributed and parallel computing models. In traditional tissue P systems, each rule (abstracted from biochemical reaction) has precise global execution time. The restriction on the execution time does not coincide with the biological fact, since the execution time of biochemical reaction can vary because of external uncontrollable conditions. In this work, we investigate a class of tissue P systems with no restriction on the execution time of each rule, named time-free tissue P systems. As a result, it is proved that the execution time of the rules has no influence on the computation results of the systems. Moreover, we consider the computational efficiency of time-free tissue P systems and prove that the Maximum Clique Problem and Hamilton Path Problem can be solved in this way in polynomial time with respect to the size of the problems.

Splicing systems were introduced by Tom Head 3,4] on biological considerations to model certain recombinant behaviour of DNA molecules. An effective extension of this operation to images was introduced by Helen Chandra et al. 5] and H array splicing systems were considered. A new method of applying the splicing operation on images of hexagonal arrays was introduced by Thomas et al. 12] and generated a new class of hexagonal array languages HASSL. On the other hand, P systems, introduced by Paun 6] generating rectangular arrays and hexagonal arrays have been studied in the literature, bringing together the two areas of theoretical computer science namely membrane computing and picture languages. P system with array objects and parallel splicing operation on arrays is introduced as a simple and effective extension of P system with operation of splicing on strings and this new class of array languages is compared with the existing families of array languages. Also we propose another P system with hexagonal array objects and parallel splicing operation on hexagonal arrays is introduced and this new class of hexagonal array languages is compared with the existing families of hexagonal array languages.

This paper focuses on the unsupervised learning problem within membrane computing, and proposes an innovative solution inspired by membrane computing techniques, the fuzzy membrane clustering algorithm. An evolution–communication P system with nested membrane structure is the core component of the algorithm. The feasible cluster centers are represented by means of objects, and three types of membranes are considered: evolution, local store, and global store. Based on the designed membrane structure and the inherent communication mechanism, a modified differential evolution mechanism is developed to evolve the objects in the system. Under the control of the evolution–communication mechanism of the P system, the proposed fuzzy clustering algorithm achieves good fuzzy partitioning for a data set. The proposed fuzzy clustering algorithm is compared to three recently-developed and two classical clustering algorithms for five artificial and five real-life data sets. National Natural Science Foundation of China No 61170030 National Natural Science Foundation of China No 61472328 Chunhui Project Foundation of the Education Department of China No. Z2012025 Chunhui Project Foundation of the Education Department of China No. Z2012031 Sichuan Key Technology Research and Development Program No. 2013GZX0155

Spiking neural P systems (shortly called SN P systems) are a group of neural-like computing models inspired by the functioning of spiking neurons. Recently, a new variant of SN P systems, called SN P systems with rules on synapses (RSSN P systems for short) were proposed. In such systems, at any moment the synapses with enabled rules should use one of the enabled rules, and all the synapses work in the synchronous manner. In this work, we consider RSSN P systems with a non-synchronized (i.e., asynchronous) use of rules: in any step, the synapses with enabled rules are not obligated to use the enabled rules. It is proved that the non-synchronization does not decrease the computing power in the case of using extended rules (several spikes can be produced for once spiking). We obtain again the equivalence with Turing machines (interpreted as generators of sets of natural numbers). Moreover, we construct a universal asynchronous RSSN P system with 94 neurons, which can compute any Turing computable function.

P systems are abstract distributed computing models inspired by the information flows in living cells and their networks, with applications, e.g., in systems biology and optimization. A tissue P system is a variant based on the interchange of objects between cells due to an underlying communication graph. The model is further enriched with the operation of cell division. This operation allows to produce an exponential number of cells in polynomial time. The paper studies the computational power of polynomially uniform families of these systems. Previous studies demonstrated that they can cover problems ranging between P and NP � co-NP due to the length of communication rules, thus characterizing a borderline between tractability and intractability. We show that, in spite of the exponential space the model can use, the problems solvable by these families in polynomial time lie within the class PSPACE.

P systems are a class of computational models inspired by the structure and the functioning of a living cell. In the semantics of P systems, there exists a global clock, which marks the time for the system, and the execution time of each rule takes exactly one time unit. However, in living cells, the execution time of different biochemical reactions is dependent on many uncontrollable factors, and it is hard to know precisely the specific execution time of a reaction. In this work, with this biological inspiration, we consider the class of P systems with active membranes that are "robust" against the execution time of rules. Specifically, we give a time-free uniform solution to the SAT problem using P systems with active membranes, where the constructed P system can solve a family of instances with an arbitrarily given size, and the execution time of the involved rules has no influence on the correctness of the solution. We also prove that any Turing computable set of numbers can be generated by a time-free P system with active membranes in the sense that the set of numbers generated by the given P system with active membranes does not depend on the execution time of rules.

In most studies about the expressiveness of Petri nets, the focus has been put either on adding suitable arcs or on assuring that a complete snapshot of the system can be obtained. While the former still complies with the intuition on Petri nets, the second is somehow an orthogonal approach, as Petri nets are distributed in nature. Here, inspired by membrane computing, we study some classes of Petri nets where the distribution is partially kept and which are still Turing complete.