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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]

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]

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 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]

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]

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]