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The standard definition of tissue P systems includes a special alphabet whose elements are assumed to appear in the initial configuration of the system in an arbitrarily large number of copies. These objects reside in a distinguished place of the system, called the environment. Such potentially infinite supply of objects seems an unfair tool when designing efficient solutions to computationally hard problems in the framework of membrane computing, by performing a space–time trade-off. This paper deals with computational aspects of tissue P systems with cell division where there is no environment having the property mentioned above. Specifically, we prove that the polynomial complexity classes associated with tissue P systems with cell division and with or without environment are actually identical. As a consequence, we conclude that it is not necessary to have infinitely many copies of some objects in the initial configuration in order to solveNP–complete problems in an efficient way. [ABSTRACT FROM PUBLISHER]

In 1936 A. Turing showed the existence of a universal machine able to simulate any Turing machine given its description. In 1956, C. Shannon formulated for the first time the problem of finding the smallest possible universal Turing machine according to some critera to measure its size such as the number of states and symbols. Within the framework of Membrane Computing different studies have addressed this problem: small universal symport/antiport P systems (by considering the number of membranes, the weight of the rules and the number of objects as a measure of the size of the system), small universal splicing P systems (by considering the number of rules as a measure of the size of the system), and small universal spiking neural P systems (by considering the number of neurons as a measure of the size of the system). In this paper the problem of determining the smallest possible efficient P system is explicitly formulated. Efficiency within the framework of Membrane Computing refers to the capability of solving computationally hard problems (i.e. problems such that classical electronic computer cannot solve instances of medium/large size in any reasonable amount of time) in polynomial time. A descriptive measure to define precisely the notion of small P system is presented in this paper. [ABSTRACT FROM AUTHOR]

Biological membranes play an active role in the evolution of cells over time. In the framework of Membrane Computing, P systems with active membranes capture this idea, and the possibility to increase the number of membranes during a computation. Classically, it has been considered, by using division rules, inspired in the mitosis process. Initially, the membranes in these models are supposed to have an electrical polarization (positive, negative or neutral) and the semantics is minimalist, in the sense that rules are applied in parallel, but in one transition step, each membrane can be the subject of at most one rule of types communication, dissolution or division. This paper focuses on polarizationless P systems with active membranes in which membrane creation rules are considered instead of membrane division rules as a mechanism to construct an exponential workspace, expressed both in terms of number of objects and membranes, in linear time. Moreover, the minimalist semantics is considered and some complexity results are provided in this framework, allowing to tackle the PversusNP problem from a new perspective. An original frontier of the efficiency in this context is unveiled in this paper: allowing membrane creation rules to be applicable in any membrane of the system, instead of restricting them to only elementary membranes, yields a significant boost on the computational power. More precisely, only problems in P can be efficiently solved in the restricted case, while in the non-restricted case an efficient and uniform solution to a PSPACE-complete problem is provided. [ABSTRACT FROM AUTHOR]

The search for new mechanisms and tools allowing us to tackle the famous P versus NP problem from new perspectives is an important task, due to the relevance of that problem. The concept of efficiency of computing models is associated with the ability to solve intractable (in a classical sense) problems in polynomial time. Assuming that P ≠ NP , that concept is equivalent to the capability to solve NP -complete problems in an efficient way. Different frontiers of the efficiency have been given in Membrane Computing in terms of syntactical or semantic ingredients of the models. In particular, in the framework of tissue P systems with cell division using symport/antiport rules, the length of communication rules (passing from length 1 to length 2) provides an optimal borderline of the efficiency. Cell-like P systems with symport/antiport rules and membrane division is a restricted variant of such tissue P systems in both its structure (rooted tree versus undirected graph) and in the way membranes communicate with each other and with the environment. The limitations of efficient computations in such kind of P systems which use non-cooperative communication rules have been previously established. In this paper, a uniform polynomial time solution for the Hamiltonian cycle problem , a well known NP -complete problem, by means of cell-like P systems with membrane division using minimal cooperation in communication rules (at most two objects are involved), is provided. Hence, a new optimal boundary between tractability and NP -hardness, is provided: passing from non-cooperative rules to cooperative rules in cell-like P systems with symport/antiport rules and membrane division amounts to passing from non-efficiency to efficiency. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This article introduces a general formalism/framework flexible enough to cover descriptions of different variants of P systems having a dynamic membrane structure. Our framework can be useful for the precise definition of new variants of P systems with a dynamic structure and for the comparison of existing definitions as well as for their extension. We give a detailed definition of the formalism and we present some examples of how to translate several existing variants of P systems with a dynamic structure. [ABSTRACT FROM PUBLISHER]

At the beginning of 2005, Gheorghe Păun formulated a conjecture stating that in the framework of recognizer P systems with active membranes (evolution rules, communication rules, dissolution rules and division rules for elementary membranes), polarizations cannot be avoided in order to solve computationally hard problems efficiently (assuming that P ≠ NP). At the middle of 2005, a partial positive answer was given, proving that the conjecture holds if dissolution rules are forbidden. In this paper we give a detailed and complete proof of this result modifying slightly the notion of dependency graph associated with recognizer P systems. [ABSTRACT FROM AUTHOR]

Abstract: Membrane computing is a biologically inspired computational paradigm. Motivated by brane calculi we investigate membrane systems which differ from conventional membrane systems by the following features: (1) biomolecules (proteins) can move through the regions of the systems, and can attach onto (and de-attach from) membranes, and (2) membranes can evolve depending on the attached molecules. The evolution of membranes is performed by using rules that are motivated by the operation of pinocytosis (the pino rule) and the operation of cellular dripping (the drip rule) that take place in living cells. We show that such membrane systems are computationally universal. We also show that if only the second feature is used then one can generate at least the family of Parikh images of the languages generated by programmed grammars without appearance checking (which contains non-semilinear sets of vectors). If, moreover, the use of pino/drip rules is non-cooperative (i.e., not dependent on the proteins attached to membranes), then one generates a family of sets of vectors that is strictly included in the family of semilinear sets of vectors. We also consider a number of decision problems concerning reachability of configurations and boundness. [Copyright &y& Elsevier]

In this paper we discuss the potential usefulness of membrane systems as tools for modelling tumours. The approach is followed both from a macroscopic and a microscopic point of view. In the first case, one considers the tumour as a growing mass of cells, focusing on its external shape. In the second case, one descends to the microscopic level, studying molecular signalling pathways that are crucial to determine if a cell is cancerous or not. In each of these approaches we work with appropriate variants of membrane systems. [ABSTRACT FROM AUTHOR]

Abstract: In the literature, several designs of P systems might be found for performing the same task. The use of different techniques or even different P system models makes it very difficult to compare these designs. In this paper, we introduce a new criterion for such a comparison: the degree of parallelism of a P system. With this aim, we define the labelled dependency graph associated with a P system, and we use this new concept for proving some results concerning the maximum number of applications of rules in a single step through the computation of a P system. [Copyright &y& Elsevier]

We improve, by using register machines, some existing universality results for specific models of P systems. P systems with membrane creation are known to generate all recursively enumerable sets of vectors of non-negative integers, even when no region (except the environment) contains more than one object of the same kind. We show here that they generate all recursively enumerable languages, and that two membrane labels are sufficient (the same result holds for accepting all recursively enumerable vectors of non-negative integers). Moreover, at most two objects are present inside the system at any time in the generative case. We then prove that 10+m symbols are sufficient to generate any recursively enumerable language over m symbols. P systems with active membranes without polarizations are known to generate all recursively enumerable sets of vectors of non-negative integers. We show that they generate all recursively enumerable languages; four starting membranes with three labels or seven starting membranes with two labels are sufficient. P systems with active membranes and two polarizations are known to generate/accept all recursively enumerable sets of vectors of non-negative integers, using only rules of rewriting and sending objects out. We show that accepting can be done by deterministic systems. Finally, we show that P systems with restricted membrane creation (the newly created membrane can only be of the same kind as the parent one) generate at least matrix languages, even when having at most one object in the configuration (except the environment). We conclude by presenting a summary of the main results obtained in this paper and a list of open questions. [ABSTRACT FROM AUTHOR]

Trading (in polynomial time) space for time in the framework of membrane systems is not sufficient to efficiently solve computationally hard problems. On the one hand, an exponential number of objects generated in polynomial time is not sufficient to solve NP-complete problems in polynomial time. On the other hand, when an exponential number of membranes is created and used as workspace, the situation is very different. Two operations in P systems (membrane division and membrane creation) capable of constructing an exponential number of membranes in linear time are studied in this paper. NP-complete problems can be solved in polynomial time using P systems with active membranes and with polarizations, but when electrical charges are not used, then dissolution rules turn out to be very important. We show that in the framework of P systems with active membranes but without polarizations and in the framework of P systems with membrane creation, dissolution rules play a crucial role from the computational efficiency point of view. [ABSTRACT FROM AUTHOR]

Dendrite P systems (DeP systems) are a recently introduced neural-like model of computation. They provide an alternative to the more classical spiking neural (SN) P systems. In this paper, we present the first software simulator for DeP systems, and we investigate the key features of the representation of the syntax and semantics of such systems. First, the conceptual design of a simulation algorithm is discussed. This is helpful in order to shade a light on the differences with simulators for SN P systems, and also to identify potential parallelizable parts. Second, a novel simulator implemented within the P-Lingua simulation framework is presented. Moreover, MeCoSim, a GUI tool for abstract representation of problems based on P system models has been extended to support this model. An experimental validation of this simulator is also covered. [ABSTRACT FROM AUTHOR]

Coupled neural P (CNP) systems are a recently developed Turing-universal, distributed and parallel computing model, combining the spiking and coupled mechanisms of neurons. This paper focuses on how to apply CNP systems to handle the fusion of multi-modality medical images and proposes a novel image fusion method. Based on two CNP systems with local topology, an image fusion framework in nonsubsampled shearlet transform (NSST) domain is designed, where the two CNP systems are used to control the fusion of low-frequency NSST coefficients. The proposed fusion method is evaluated on 20 pairs of multi-modality medical images and compared with seven previous fusion methods and two deep-learning-based fusion methods. Quantitative and qualitative experimental results demonstrate the advantage of the proposed fusion method in terms of visual quality and fusion performance. [ABSTRACT FROM AUTHOR]

This paper discusses a new variant of spiking neural P systems (in short, SNP systems), spiking neural P systems with extended channel rules (in short, SNP–ECR systems). SNP–ECR systems are a class of distributed parallel computing models. In SNP–ECR systems, a new type of spiking rule is introduced, called ECR. With an ECR, a neuron can send the different numbers of spikes to its subsequent neurons. Therefore, SNP–ECR systems can provide a stronger firing control mechanism compared with SNP systems and the variant with multiple channels. We discuss the Turing universality of SNP–ECR systems. It is proven that SNP–ECR systems as number generating/accepting devices are Turing universal. Moreover, we provide a small universal SNP–ECR system as function computing devices. [ABSTRACT FROM AUTHOR]

This paper proposes a new variant of spiking neural P systems (in short, SNP systems), nonlinear spiking neural P systems (in short, NSNP systems). In NSNP systems, the state of each neuron is denoted by a real number, and a real configuration vector is used to characterize the state of the whole system. A new type of spiking rules, nonlinear spiking rules, is introduced to handle the neuron's firing, where the consumed and generated amounts of spikes are often expressed by the nonlinear functions of the state of the neuron. NSNP systems are a class of distributed parallel and nondeterministic computing systems. The computational power of NSNP systems is discussed. Specifically, it is proved that NSNP systems as number-generating/accepting devices are Turing-universal. Moreover, we establish two small universal NSNP systems for function computing and number generator, containing 117 neurons and 164 neurons, respectively. [ABSTRACT FROM AUTHOR]

It was recently found that dendrites are not just a passive channel. They can perform mixed computation of analog and digital signals, and therefore can be abstracted as information processors. Moreover, dendrites possess a feedback mechanism. Motivated by these computational and feedback characteristics, this article proposes a new variant of neural-like P systems, dendrite P (DeP) systems, where neurons simulate the computational function of dendrites and perform a firing–storing process instead of the storing–firing process in spiking neural P (SNP) systems. Moreover, the behavior of the neurons is characterized by dendrite rules that are abstracted by two characteristics of dendrites. Different from the usual firing rules in SNP systems, the firing of a dendrite rule is controlled by the states of the corresponding source neurons. Therefore, DeP systems can provide a collaborative control capability for neurons. We discuss the computational power of DeP systems. In particular, it is proven that DeP systems are Turing-universal number generating/accepting devices. Moreover, we construct a small universal DeP system consisting of 115 neurons for computing functions. • We consider dendrites as information processors. • We propose a new model, dendrite P systems (DeP systems, in short). • We prove that DeP systems are Turing-universal number generating/accepting devices. • We construct a small universal DeP system of 115 neurons for computing functions. [ABSTRACT FROM AUTHOR]

P systems with active membranes is one of the most studied models within the field of Membrane Computing. Simulating the organization and behavior of the living cells through a tree-like structure and abstracting the mechanisms that help the cell to keep alive into rules (evolution, communication, dissolution and division rules), they have been used to solve several computationally hard problems. We are dealing with non-cooperative systems here, that is, the number of reactives in a rule is always one. Even then, it has been proven that problems from the class PSPACE can be solved, so in order to acquire a minimal model that can solve computationally hard problems, polarizations are removed. In this paper we find the relevance of the length of the right-hand side of the rule, being necessary when using separation rules and being irrelevant when division rules are used, improving some solutions previously presented, restricting the right-hand side of the rules, obtaining new frontiers of efficiency in this framework. The state of the art of these systems is presented in a graphical way. [ABSTRACT FROM AUTHOR]

Abstract 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. Highlights • We propose a dynamic threshold neural P systems, inspired from intersecting cortical model. • We prove that Turing universality of dynamic threshold neural P systems as number accepting/generating devices. • We construct an universal dynamic threshold neural P system having 109 neurons for computing functions. [ABSTRACT FROM AUTHOR]

P systems with active membranes use evolution, communication, dissolution and division (or separation) rules. They do not use cooperation neither priorities, but they have electrical charges associated with membranes, which can be modified by rule applications. The inspiration comes from the behaviour of living cells, who “compute” with their proteins in order to obtain energy, create components, send information to other cells, kill themselves (in a process called apoptosis ), and so on. In these models, mitosis is simulated by division rules (for elementary and non-elementary membranes) and meiosis , that is, membrane fission inspiration, is captured in separation rules. The parent's objects are replicated into both child membranes when a division occurs, while in the case of separation, objects are distributed (according to a prefixed partition). In both cases, active membranes have been proved to be too powerful for solving computationally hard problems in an efficient way. Due to this, polarizationless P systems with active membranes have been widely studied from a complexity point of view. Evolution rules simulate the transformation of components in membranes, but it is well known that in Biology elements interact with each other in order to obtain new components. In this paper, (restricted) cooperation in object evolution rules is considered, and the efficiency of the corresponding models is studied. [ABSTRACT FROM AUTHOR]

Fuzzy tissue-like P systems (FTPS), as a new variant of tissue-like P systems (TPS), is proposed in this paper. FTPS inherits the advantages of TPS and has the ability of dealing with incomplete and uncertain information. FTPS is very suitable to model the causal relationship between a fault and its protective devices in power systems. A forward reasoning algorithm based on FTPS is developed, and then the corresponding fault diagnosis model is discussed. In order to evaluate the availability and effectiveness of the proposed fault diagnosis model, three case studies of fault diagnosis of a transmission system are discussed and analyzed, including simple fault, complex faults and multiple faults with uncertain status information. The results of case studies demonstrate that FTPS can be used to diagnose faulty sections in power systems accurately and effectively. [ABSTRACT FROM AUTHOR]

Fuzzy clustering problem is usually posed as an optimization problem. However, the existing research has 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 framework for fuzzy clustering, in which a tissue-like membrane system with a special cell structure is designed to integrate a non-dominated sorting technique and a modified differential evolution mechanism. Based on the 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 six artificial 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 approach on clustering the data sets with different characteristics. [ABSTRACT FROM AUTHOR]

Membrane computing is a computing paradigm providing a class of distributed parallel computing devices of a biochemical type whose process units represent biological membranes. In the cell-like basic model, a hierarchical membrane structure formally described by a rooted tree is considered. It is well known that families of such systems where the number of membranes can only decrease during a computation (for instance by dissolving membranes), can only solve in polynomial time problems in class P. P systems with active membranes is a variant where membranes play a central role in their dynamics. In the seminal version, membranes have an electrical polarization (positive, negative, or neutral) associated in any instant, and besides being dissolved, they can also replicate by using division rules. These systems are computationally universal, that is, equivalent in power to deterministic Turing machines, and computationally efficient, that is, able to solve computationally hard problems in polynomial time. If polarizations in membranes are removed and dissolution rules are forbidden, then only problems in class P can be solved in polynomial time by these systems (even in the case when division rules for non-elementary membranes are permitted). In that framework it has been shown that by considering minimal cooperation (left-hand side of such rules consists of at most two symbols) and minimal production (only one object is produced by the application of such rules) in object evolution rules, such systems provide efficient solutions to NP-complete problems. In this paper, minimal cooperation and minimal production in communication rules instead of object evolution rules is studied, and the computational efficiency of these systems is obtained in the case where division rules for non-elementary membranes are permitted. [ABSTRACT FROM AUTHOR]

This paper focuses on automatic fuzzy clustering problem and proposes a novel automatic fuzzy clustering method that employs an extended membrane system with active membranes that has been designed as its computing framework. The extended membrane system has a dynamic membrane structure; since membranes can evolve, it is particularly suitable for processing the automatic fuzzy clustering problem. A modification of a differential evolution (DE) mechanism was developed as evolution rules for objects according to membrane structure and object communication mechanisms. Under the control of both the object's evolution-communication mechanism and the membrane evolution mechanism, the extended membrane system can effectively determine the most appropriate number of clusters as well as the corresponding optimal cluster centers. The proposed method was evaluated over 13 benchmark problems and was compared with four state-of-the-art automatic clustering methods, two recently developed clustering methods and six classification techniques. The comparison results demonstrate the superiority of the proposed method in terms of effectiveness and robustness. [ABSTRACT FROM AUTHOR]

Membrane computing is a class of distributed parallel computing models. Inspired from the structure and inherent mechanism of membrane computing, a membrane clustering algorithm is proposed to deal with automatic clustering problem, in which a tissue-like membrane system with fully connected structure is designed as its computing framework. Moreover, based on its special structure and inherent mechanism, an improved velocity-position model is developed as evolution rules. Under the control of evolution-communication mechanism, the tissue-like membrane system cannot only find the most appropriate number of clusters but else determine a good clustering partitioning for a data set. Six benchmark data sets are used to evaluate the proposed membrane clustering algorithm. Experiment results show that the proposed algorithm is superior or competitive to three state-and-the-art automatic clustering algorithms recently reported in the literature. [ABSTRACT FROM AUTHOR]

Abstract: Membrane computing (known as P systems) is a novel class of distributed parallel computing models inspired by the structure and functioning of living cells and organs, and its application to the real-world problems has become a hot topic in recent years. This paper discusses an interesting open problem in digital watermarking domain, optimal watermarking problem, and proposes a new optimal image watermarking method under the framework of P systems. A special membrane structure is designed and its cells as parallel computing units are used to find the optimal watermarking parameters for image blocks. Some cells use the position-velocity model to evolve watermarking parameters of image blocks, while another cell evaluates the objects in the system. In addition to the evolution rules, communication rules are used to exchange and share information between the cells. Simulation experiments on large image set compare the proposed framework with other existing watermarking methods and demonstrate its superiority. [Copyright &y& Elsevier]

Sevilla carpets have already been used to compare different solutions of the Subset Sum problem: either designed in the framework of P systems with active membranes (both in the case of membrane division and membrane creation), and in the framework of tissue-like P systems with cell division. Recently, the degree of parallelism and other descriptive complexity details have been found to be relevant when designing parallel simulators running on GPUs. We present here a new way to use the information provided by Sevilla carpets in this context, and a script that allows to generate them automatically from P-Lingua files. [ABSTRACT FROM AUTHOR]

Membrane Computing has recently proved to be a suitable framework for addressing the modelling of dynamical biological systems in general, and ecosystems in particular. Due to the inherent randomness and uncertainty in biological systems, when designing a model the relevant tasks to be addressed are the validation and virtual experimentation processes, rather than the formal verification. It is therefore crucial to rely on software implementations of efficient simulation algorithms. This paper presents a simple (but realistic enough) ecosystem where a carnivore and several herbivorous species interact. The model of this ecosystem has been used to compare experimentally the performance of two different simulation algorithms. [ABSTRACT FROM AUTHOR]

The hand-made graphical representation of the configuration of a P system becomes a hard task when the number of membranes and objects increases. In this paper we present a new software tool, called JPLANT, for computing and representing the evolution of a P system model with membrane creation. We also present some experiments performed with JPLANT and point out new lines for the research in computer graphics with membrane systems. [ABSTRACT FROM AUTHOR]

Abstract: Investigations within the field of tissue-like P systems are being conducted, on one hand studying their computational efficiency, and on the other hand exploring the possibilities to use them as a computational modelling framework to biological phenomena. In both cases it is necessary to develop software that provides simulation tools (simulators) for the existing variety of tissue P systems. Such simulators allow us to carry on computations of solutions to computationally hard problems on certain (small) instances. Moreover, they also provide a way to verify tissue-like models for real biological processes, by means of experimental data. The paper presents an extension of P-Lingua (a specification language intended to become a standard for software devoted to P systems), in order to cover the class of tissue-like P systems, that were not considered in the previous release. This extension involves on one hand defining the syntax to be used, and on the other hand introducing a new built-in simulation algorithm that has been added to the core library of P-Lingua. [Copyright &y& Elsevier]

Abstract: Several examples of the efficiency of cell-like P systems regarding the solution of NP-complete problems in polynomial time can be found in the literature(obviously, trading space for time). Recently, different new models of tissue-like P systems have received much attention from the scientific community. In this paper we present a linear-time solution to an NP-complete problem from graph theory, the 3-coloring problem, and we discuss the suitability of tissue-like P systems as a framework to address the efficient solution to intractable problems. [Copyright &y& Elsevier]

Motivated by the mechanism of inhibitory synapses, a new kind of spiking neural P (SNP) system rules, called inhibitory rules, is introduced in this paper. Based on this, a new variant of SNP systems is proposed, called spiking neural P systems with inhibitory rules (SNP-IR systems). Different from the usual firing rules in SNP systems, the firing condition of an inhibitory rule not only depends on the state of the neuron associated with the rule but also is related to the states of other neurons. Moreover, from the perspective of topological structure, the new variant is shown as a directed graph with inhibitory arcs, and therefore seems to have more powerful control. The computational completeness of SNP-IR systems is discussed. In particular, it is proved that SNP-IR systems are Turing universal number accepting/generating devices. Moreover, we obtain a small universal function-computing device for SNP-IR systems consisting of 100 neurons. • We propose a new kind rule, inhibitory rules, inspired from mechanism of inhibitory synapse. • We propose a new variant, spiking neural P systems with inhibitory rules (SNP-IR systems, in short). • We prove that SNP-IR systems as both number generating and number accepting devices are Turing universal. • We construct a small universal function computing device consisting of 100 neurons for SNP-IR systems. [ABSTRACT FROM AUTHOR]