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

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An optimization spiking neural p system for approximately solving combinatorial optimization problems.

Besides usual spikes employed in spiking neural P systems, we consider “anti-spikes", which participate in spiking and forgetting rules, but also annihilate spikes when meeting in the same neuron. This simple extension of spiking neural P systems is shown to considerably simplify the universality proofs in this area: all rules become of the form bc → b′ or bc → lambda , where b,b′ are spikes or anti-spikes. Therefore, the regular expressions which control the spiking are the simplest possi- ble, identifying only a singleton. A possible variation is not to produce anti-spikes in neurons, but to consider some “inhibitory synapses", which transform the spikes which pass along them into anti-spikes. Also in this case, universality is rather easy to obtain, with rules of the above simple forms.

/pdf/spiking-neural-p-systems-with-anti-spikes-1ri7s0eq78.pdf

Spiking Neural P Systems with Anti-Spikes

http://www.gcn.us.es/files/Tissue%20P%20systems%20with%20channel%20states.pdf

Tissue P systems with channel states

This is intended as a survey article covering recent developments in the area of hamiltonian graphs, that is, graphs containing a spanning cycle. This article also contains some material on related topics such as traceable, hamiltonian-connected and pancyclic graphs and digraphs, as well as an extensive bibliography of papers in the area.

http://www.mathcs.emory.edu/~rg/updating.pdf

Updating the Hamiltonian problem—a survey

This is a comprehensive (and friendly) introduction to membrane computing (MC), meant to offer both computer scientists and non-computer scientists an up-to-date overview of the field. That is why the set of notions introduced here is rather large, but the presentation is informal, without proofs and with rigorous definitions given only for the basic types of P systems — symbol object P systems with multiset rewriting rules, systems with symport/antiport rules, systems with string objects, tissue-like P systems, and neural-like P systems. Besides a list of (biologically inspired or mathematically motivated) ingredients/features which can be used in systems of these types, we also mention a series of results, as well as a series of research trends and topics.

/pdf/introduction-to-membrane-computing-5cngwvz0yk.pdf

Introduction to Membrane Computing

The original model of P systems with symbol objects introduced by Paun was shown to be computationally universal, provided that catalysts and priorities of rules are used. By reduction via register machines Sosik and Freund proved that the priorities may be omitted from the model without loss of computational power. Freund, Oswald, and Sosik 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.

Computationally universal P systems without priorities: two catalysts are sufficient

A Short Note on Analysing P Systems with Antiport Rules.

We investigate a variant of purely communicating P systems, where multisets of activators can open channels for certain objects to pass through membranes in one direction; however, the permeability of a channel can be controlled by multisets of prohibitors, too.We will show that for such systems with only one membrane and using only singleton activator and prohibitor sets, we already obtain universal computational power. When using systems with activating multisets for membrane channels only, we obtain a similar result. By showing a close correspondence to P systems with symport/antiport as introduced in [13] we can optimize some results given there.

P Systems with Activated/Prohibited Membrane Channels

We consider extended variants of GP systems, i.e., membrane systems with sequential applications of evolution rules. The main features we explore are applicability conditions (context conditions) on single objects as well as on the remaining contents of the underlying compartment. For a special very restricted variant only using forbidding context conditions we already obtain universal computational power.

GP Systems with Forbidding Context

We consider tissue P systems with antiport rules and investigate their computational power when using only a (very) small number of symbols and cells. Even when using only one symbol, any recursively enumerable set of natural numbers can be generated with at most seven cells. On the other hand, with only one cell we can only generate regular sets when using one channel with the environment, whereas one cell with two channels between the cell and the environment obtains computational completeness with at most five symbols. Between these extreme cases of one symbol and one cell, respectively, there seems to be a trade-off between the number of cells and the number of symbols, e.g., for the case of tissue P systems with two channels between a cell and the environment we show that computational completeness can be obtained with two cells and three symbols as well as with three cells and two symbols, respectively.

Marion Oswald

Papers

Computationally universal P systems without priorities: two catalysts are sufficient

A Short Note on Analysing P Systems with Antiport Rules.

P Systems with Activated/Prohibited Membrane Channels

GP Systems with Forbidding Context

Tissue P systems with Antiport rules and small numbers of symbols and cells