Spiking Neural P Systems with Communication on Request.

Spiking Neural [Formula: see text] Systems are Neural System models characterized by the fact that each neuron mimics a biological cell and the communication between neurons is based on spikes. In the Spiking Neural [Formula: see text] systems investigated so far, the application of evolution rules depends on the contents of a neuron (checked by means of a regular expression). In these [Formula: see text] systems, a specified number of spikes are consumed and a specified number of spikes are produced, and then sent to each of the neurons linked by a synapse to the evolving neuron. [Formula: see text]In the present work, a novel communication strategy among neurons of Spiking Neural [Formula: see text] Systems is proposed. In the resulting models, called Spiking Neural [Formula: see text] Systems with Communication on Request, the spikes are requested from neighboring neurons, depending on the contents of the neuron (still checked by means of a regular expression). Unlike the traditional Spiking Neural [Formula: see text] systems, no spikes are consumed or created: the spikes are only moved along synapses and replicated (when two or more neurons request the contents of the same neuron). [Formula: see text]The Spiking Neural [Formula: see text] Systems with Communication on Request are proved to be computationally universal, that is, equivalent with Turing machines as long as two types of spikes are used. Following this work, further research questions are listed to be open problems.

Tissue P Systems With Channel States Working in the Flat Maximally Parallel Way.

Tissue P systems with channel states are a class of bio-inspired parallel computational models, where rules are used in a sequential manner (on each channel, at most one rule can be used at each step). In this work, tissue P systems with channel states working in a flat maximally parallel way are considered, where at each step, on each channel, a maximal set of applicable rules that pass from a given state to a unique next state, is chosen and each rule in the set is applied once. The computational power of such P systems is investigated. Specifically, it is proved that tissue P systems with channel states and antiport rules of length two are able to compute Parikh sets of finite languages, and such P systems with one cell and noncooperative symport rules can compute at least all Parikh sets of matrix languages. Some Turing universality results are also provided. Moreover, the NP-complete problem SAT is solved by tissue P systems with channel states, cell division and noncooperative symport rules working in the flat maximally parallel way; nevertheless, if channel states are not used, then such P systems working in the flat maximally parallel way can solve only tractable problems. These results show that channel states provide a frontier of tractability between efficiency and non-efficiency in the framework of tissue P systems with cell division (assuming P ≠ NP ).

Spiking neural P systems with weights.

A variant of spiking neural P systems with positive or negative weights on synapses is introduced, where the rules of a neuron fire when the potential of that neuron equals a given value. The involved values-weights, firing thresholds, potential consumed by each rule-can be real (computable) numbers, rational numbers, integers, and natural numbers. The power of the obtained systems is investigated. For instance, it is proved that integers (very restricted: 1, -1 for weights, 1 and 2 for firing thresholds, and as parameters in the rules) suffice for computing all Turing computable sets of numbers in both the generative and the accepting modes. When only natural numbers are used, a characterization of the family of semilinear sets of numbers is obtained. It is shown that spiking neural P systems with weights can efficiently solve computationally hard problems in a nondeterministic way. Some open problems and suggestions for further research are formulated.

Small universal spiking neural P systems.

In search for small universal computing devices of various types, we consider here the case of spiking neural P systems (SN P systems), in two variants: as devices that compute functions and as devices that generate sets of numbers. We start with the first case and we produce a universal spiking neural P system with 84 neurons. If a slight generalization of the used rules is adopted, namely, we allow rules for producing simultaneously several spikes, then a considerable reduction, to 49 neurons, is obtained. For SN P systems used as generators of sets of numbers, we find a universal system with restricted rules having 76 neurons and one with extended rules having 50 neurons.

Membrane computing: brief introduction, recent results and applications.

The internal organization and functioning of living cells, as well as their cooperation in tissues and higher order structures, can be a rich source of inspiration for computer science, not fully exploited at the present date. Membrane computing is an answer to this challenge, well developed at the theoretical (mathematical and computability theory) level, already having several applications (via usual computers), but without having yet a bio-lab implementation. After briefly discussing some general issues related to natural computing, this paper provides an informal introduction to membrane computing, focused on the main ideas, the main classes of results and of applications. Then, three recent achievements, of three different types, are briefly presented, with emphasis on the usefulness of membrane computing as a framework for devising models of interest for biological and medical research.

Bio-steps beyond Turing.

Are there 'biologically computing agents' capable to compute Turing uncomputable functions? It is perhaps tempting to dismiss this question with a negative answer. Quite the opposite, for the first time in the literature on molecular computing we contend that the answer is not theoretically negative. Our results will be formulated in the language of membrane computing (P systems). Some mathematical results presented here are interesting in themselves. In contrast with most speed-up methods which are based on non-determinism, our results rest upon some universality results proved for deterministic P systems. These results will be used for building "accelerated P systems". In contrast with the case of Turing machines, acceleration is a part of the hardware (not a quality of the environment) and it is realised either by decreasing the size of "reactors" or by speeding-up the communication channels. Consequently, two acceleration postulates of biological inspiration are introduced; each of them poses specific questions to biology. Finally, in a more speculative part of the paper, we will deal with Turing non-computability activity of the brain and possible forms of (extraterrestrial) intelligence.

(In search of) probabilistic P systems.

The aim of this paper is to (preliminarily) discuss various ways of introducing probabilities in membrane systems. We briefly present both ideas already circulated in the literature and new proposals, trying to have a systematic overview of possibilities of associating probabilities with the ingredients of a membrane system: with (localization of) single objects, with multiplicities of objects (hence with the multisets), with the rules (depending or not on the previous applied rule), with the communication targets. For a certain mode of using the probabilities associated with the evolution rules (in string-object P systems) we obtain the computational universality.