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P system simulators become essential for model verification and validation, since they reproduce the semantics of the models in an automatic way. For this reason, in the literature, many authors have proposed several simulation tools. However, in order to handle large instances in an efficient way, parallel simulators come into play. High Performance Computing is a research branch that brings efficient tools for scien- tific purposes. For decades, many parallel platforms and architectures have been designed, with the goal of accelerating compute-demanding applications. But it was 10 years ago, that this field was revolutionized with the dawn of GPU computing through CUDA. This technology allowed programmers to run general-purpose parallel code in GPUs, harnessing in a simplified manner the large amount of processors within a GPU. Many authors have chosen this technology for accelerating the simulation of their P system models. Recently, this topic has captured the attention of more researchers. Therefore, in this paper we survey the related work on GPU-based simulators for P systems, and its evolution over the time until today

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. National Natural Science Foundation of China No 61170030 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

We continue the investigation of the computational power of space- constrained P systems. We show that only a constant amount of space is needed in order to simulate a polynomial-space bounded Turing machine. Due to this result, we propose an alternative de nition of space complexity for P systems, where the amount of information contained in individual objects and membrane labels is also taken into ac- count. Finally, we prove that, when less than a logarithmic number of membrane labels is available, moving the input objects around the membrane structure without rewriting them is not enough to even distinguish inputs of the same length.

Enantioselective gold(I) catalysis is receiving a growing level of credit in the field of asymmetric synthesis. After a pioneering work in the mid-1980s the area remained almost silent for several years, until densely substituted diphosphine chiral ligands were disclosed as competent chiral units for gold-catalyzed stereoselective manipulation of unactivated unsaturated hydrocarbons. The chemistry of alkynes, allenes and most recently also alkenes received significant benefits from the latter developments. More recently, ad hoc designed chiral monodentate ligands have risen to prominence in producing robust, highly tunable (electronic and steric) and efficient chiral cationic mononuclear gold species for asymmetric transformations. In this scenario, electron-deficient phosphorus-based (i.e., phosphoramidites, phosphites) but also axially chiral electron-rich carbene ligands deserve particular mention and the corresponding applications will be summarized herein.

Spiking neural P systems (SN P systems) have been well established as a novel class of distributed parallel computing models. Some features that SN P systems possess are attractive to fault diagnosis. However, handling fuzzy diagnosis knowledge and reasoning is required for many fault diagnosis applications. The lack of ability is a major problem of existing SN P systems when applying them to the fault diagnosis domain. Thus, we extend SN P systems by introducing some new ingredients (such as three types of neurons, fuzzy logic and new firing mechanism) and propose the fuzzy reasoning spiking neural P systems (FRSN P systems). The FRSN P systems are particularly suitable to model fuzzy production rules in a fuzzy diagnosis knowledge base and their reasoning process. Moreover, a parallel fuzzy reasoning algorithm based on FRSN P systems is developed according to neuron’s dynamic firing mechanism. Besides, a practical example of transformer fault diagnosis is used to demonstrate the feasibility and effectiveness of the proposed FRSN P systems in fault diagnosis problem. Ministerio de Ciencia e Innovación TIN2009–13192 Junta de Andalucía P08-TIC-04200

In this article we present a simulator of non-deterministic static P systems using Field Programmable Gate Array (FPGA) technology. Its major feature is a high performance, achieving a constant processing time for each transition. Our approach is based on representing all possible applications as words of some regular context-free language. Then, using formal power series it is possible to obtain the number of possibilities and select one of them following a uniform distribution, in a fair and non-deterministic way. According to these ideas, we yield an implementation whose results show an important speed-up, with a strong independence from the size of the P system. Ministry of Science and Innovation of the Spanish Government under the project TEC2011-27936 (HIPERSYS) European Regional Development Fund (ERDF) Ministry of Education of Spain (FPU grant AP2009-3625) ANR project SynBioTIC

Automatic design of P systems is an attractive research topic in the community of membrane computing. Differing from the previous work that used evolutionary algorithms to fulfill the task, this paper presents the design of a (deterministic transition) P system (without input membrane) of degree 1, capturing the value of an arbitrary k-order (k 2) polynomial p(n) by using a reasoning method. Specifically, the values of p(n) corresponding to a natural number t is equal to the multiplicity of a distinguished object of the system (the output object) in the configuration at instant t. We also discuss the descriptive computational resources required by the designed k-order polynomial P system. Ministerio de Economía y Competitividad TIN2012-37434

We investigate the in uence that the ow of information in membrane systems has on their computational complexity. In particular, we analyse the behaviour of P systems with active membranes where communication only happens from a membrane towards its parent, and never in the opposite direction. We prove that these \monodirectional P systems" are, when working in polynomial time and under standard complexity-theoretic assumptions, much less powerful than unrestricted ones: indeed, they characterise classes of problems de ned by polynomial-time Turing machines with NP oracles, rather than the whole class PSPACE of problems solvable in polynomial space.

Membrane Computing is a discipline aiming to abstract formal computing models, called membrane systems or P systems, from the structure and functioning of the living cells as well as from the cooperation of cells in tissues, organs, and other higher order structures. This framework provides polynomial time solutions to NP-complete problems by trading space for time, and whose efficient simulation poses challenges in three different aspects: an intrinsic massively parallelism of P systems, an exponential computational workspace, and a non-intensive floating point nature. In this paper, we analyze the simulation of a family of recognizer P systems with active membranes that solves the Satisfiability problem in linear time on different instances of Graphics Processing Units (GPUs). For an efficient handling of the exponential workspace created by the P systems computation, we enable different data policies to increase memory bandwidth and exploit data locality through tiling and dynamic queues. Parallelism inherent to the target P system is also managed to demonstrate that GPUs offer a valid alternative for high-performance computing at a considerably lower cost. Furthermore, scalability is demonstrated on the way to the largest problem size we were able to run, and considering the new hardware generation from Nvidia, Fermi, for a total speed-up exceeding four orders of magnitude when running our simulations on the Tesla S2050 server. Agencia Regional de Ciencia y Tecnología - Murcia 00001/CS/2007 Ministerio de Ciencia e Innovación TIN2009–13192 Ministerio de Ciencia e Innovación TIN2009-14475-C04 European Commission Consolider Ingenio-2010 CSD2006-00046

Membrane Computing is a paradigm inspired from biological cellular communication. Membrane computing devices are called P systems. In this paper we calculate some algebraic-topological information of 2D and 3D images in a general and parallel manner using P systems. First, we present a new way to obtain the homology groups of 2D digital images in time logarithmic with respect to the input data involving an improvement with respect to the algorithms development by S. Peltier et al. Second, we obtain an edge-segmentation of 2D and 3D digital images in constant time with respect to the input data.

Under certain well defined conditions, the stream X-machine testing method can produce a test set that is guaranteed to determine the correctness of an implementation. The testing method has originally assumed that an implementation of each processing function or relation is proven to be correct before the actual testing can take place. Such a limitation has been removed in a subsequent paper, but only for deterministic X-machines. This paper extends this result to non-deterministic stream X-machines and considers a conformance relationship between a specification and an implementation, rather than mere equivalence. Furthermore, it shows how this method can be applied to test a P system by building a suitable stream X-machine from the derivation tree associated with a partial computation.

The purpose of the present work is to give a general idea about the existing results and open problems concerning the study of complexity classes within the membrane computing framework. To this aim, membrane systems (seen as computing devices) are briefly introduced, providing the basic definition and summarizing the key ideas, trying to cover the various approaches that are under investigation in this area – of course, special attention is paid to the study of complexity classes. The paper concludes with some final remarks that hint the reasons why this field (as well as other unconventional models of computation) is attracting the attention of a growing community. Ministerio de Educación y Ciencia TIN2005-09345-C04-01 Junta de Andalucía TIC-581

To study systems whose dynamics changes with time, an extension of timed P systems is introduced in which evolution rules may vary with time. The proposed model is a timed automaton with a discrete time domain and in which each state is a timed P system. A result on expressive power and on features of the formalism sufficient for full expressiveness is proved and, as an application example, the model of an ecological system is given.

Metabolic P systems, shortly MP systems, are a special class of P systems, introduced for expressing biological metabolism. An MP system evolution is given by a metabolic algorithm, a deterministic strategy, where the classical viewpoint on metabolic dynamics, in terms of ordinary differential equations, is replaced by suitable generalizations of chemical principles. The basic principles of MP systems are given and their main aspects are explained by means of examples of biological modeling. A new kind of regulation mechanism is outlined, which could be the basis for a more efficient construction of computational models from experimental data of specific metabolic processes.

After a short discussion about similarities and dissimilarities of membrane computing and brane calculi, insisting mainly on some recent ideas of bridging the two areas of research, one recalls some details concerning certain classes of P systems based on brane calculi operations. Several open problems are formulated in this context.

This is a very short discussion of similarities and dissimilarities between membrane computing and brane calculi, insisting mainly on some recent ideas of bridging the two areas of research (from this last point of view, the bibliography tries to be as complete as possible) and proving that, in fact, there is no real dissimilarity...

It is known that P systems with antiport rules simulate register machines, i.e., they are computationally complete. Hence, due to the existence of universal register machines, there exist computationally complete subclasses of antiport P systems with bounded size, i.e., systems where each size parameter is limited by some constant. However, so far there has been no estimation of these numbers given in the literature. In this article, three universal antiport P systems of bounded size are demonstrated, different from each other in their size parameters. We present universal antiport P systems with 73, 43, and 30 rules where the maximum of the weight of the rules is 4, 5, and 6, respectively.

This paper continues the investigation of population P systems model [F. Bernardini, M. Gheorghe, Population P systems, Journal of Universal Computer Science 10 (5) (2004) 509–539] by considering bacterium quorum sensing (QS) phenomena as the basis of the new approach. A new computational model called QS P system is introduced. It is proved that QS P systems are able to simulate counter machines, and hence they are equivalent in power to Turing machines. An example of a QS P system modelling the behaviour of Vibrio fischeri bacteria colonies is also presented and the emergence of the QS mechanism is illustrated.

Fuzzy Reasoning Spiking Neural P systems (FRSN P systems, for short) is a variant of Spiking Neural P systems incorporating fuzzy logic elements that make it suitable to model fuzzy diagnosis knowledge and reasoning required for fault diagnosis applications. In this sense, several FRSN P system variants have been proposed, dealing with real numbers, trapezoidal numbers, weights, etc. The model incorporating real numbers was the first introduced [13], presenting promising applications in the field of fault diagnosis of electrical systems. For this variant, a matrix-based algorithm was provided which, when executed on parallel computing platforms, fully exploits the model maximally parallel capacities. In this paper we introduce a P-Lingua framework extension to parse and simulate FRSN P systems with real numbers. Two simulators, implementing a variant of the original matrix-based simulation algorithm, are provided: a sequential one (written in Java), intended to run on traditional CPUs, and a parallel one, intended to run on CUDAenabled devices. Ministerio de Economía y Competitividad TIN2012-37434

One of the major challenges that current P systems simulators have to deal with is to be as efficient as possible. A P system is syntactically described as a membrane structure delimiting regions where multisets of objects evolve by means of evolution rules. According to that, on each computation step, the applicability of the rules for the current P system configuration must be calculated. In this paper we extend previous works that use Rete-based simulation algorithm in order to improve the time consumed during the checking phase in the selection of rules. A new approach is presented, oriented to the acceleration of Population Dynamics P Systems simulations. Ministerio de Economía y Competitividad TIN2012- 37434

We prove that polynomial-time tissue P systems with cell division or cell separation can be simulated efficiently by Turing machines with oracles for counting problems. This shows that the corresponding complexity classes are included in \(\mathbf{P }^{\varvec{\#}\mathbf{P }}\), thus improving, under standard complexity theory assumptions, the previously known upper bound \(\mathbf{PSPACE }\).

In this paper we propose MPP systems as modelling notation for ecological systems, and we show how they can be used together with simulation and statistical model checking tools to study properties of such kind of systems. As a case study we consider the ecological problem of stability of European water frog populations. The paper shows that MPP systems allow easy and concise modelling of real ecological problems. Moreover, MPP systems models can be easily simulated and translated into the PRISM input language to enable statistical model checking of properties.

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 showhere 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 + msymbols 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. Ministerio de Ciencia y Tecnología TIC2002-04220-C03-01

Generally, for proving universality results about rewriting P systems one considers matrix grammars in the strong binary normal form. Such grammars contain both matrices with rules used in the appearance checking mode and matrices without appearance checking rules. In the proofs of most of the universality theorems reported in the literature, appearance checking matrices are simulated by using only two membranes, while four membranes are used for simulating matrices without appearance checking rules. Thus, a way to improve these theorems is to diminish the number of membranes used for simulating matrices without appearance checking rules. In this paper we address this problem, and give first a general improved result about simulating matrix grammars without appearance checking: three membranes are shown to suffice. This result is then used to improve several universality results from various membrane computing papers, for instance, about P systems with replicated rewriting, with leftmost rewriting, with conditional communication, as well as for hybrid P systems with finite choice.

The original model of P systems with symbol objects introduced by Păun was shown to be computationally universal, provided that catalysts and priorities of rules are used. By reduction via register machines Sosík and Freund proved that the priorities may be omitted from the model without loss of computational power. Freund, Oswald, and Sosík considered several variants of P systems with catalysts (but without priorities) and investigated the number of catalysts needed for these specific variants to be computationally universal. It was shown that for the classic model of P systems with the minimal number of two membranes the number of catalysts can be reduced from six to five; using the idea of final states the number of catalysts could even be reduced to four. In this paper we are able to reduce the number of catalysts again: two catalysts are already sufficient. For extended P systems we even need only one membrane and two catalysts. For the (purely) catalytic systems considered by Ibarra only three catalysts are already enough.