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Spiking neural P systems (SN P systems) are a class of distributed and parallel neural-like computing models, inspired from the way neurons communicate by means of spikes. In this paper, a new variant of the systems, called SN P systems with learning functions, is introduced. Such systems can dynamically strengthen and weaken connections among neurons during the computation. A class of specific SN P systems with simple Hebbian learning function is constructed to recognize English letters. The experimental results show that the SN P systems achieve average accuracy rate 98.76% in the test case without noise. In the test cases with low, medium, and high noises, the SN P systems outperform back propagation neural networks and probabilistic neural networks. Moreover, comparing with spiking neural networks, SN P systems perform a little better in recognizing letters with noise. The result of this paper is promising in terms of the fact that it is the first attempt to use SN P systems in pattern recognition after many theoretical advancements of SN P systems, and SN P systems exhibit the feasibility for tackling pattern recognition problems.

Asynchronous tissue P systems with symport/antiport rules are a class of parallel computing models inspired by cell tissue working in a non-synchronized way, where the use of rules is not obligatory, that is, at a computation step, an enabled rule may or may not be applied. In this work, the notion of local synchronization is introduced at three levels: rules, channels, and cells. If a rule in a locally synchronous set of rules (resp., cells or channels) is used, then all enabled rules in the same locally synchronous set of rules (resp., whose involved channels or cells) should be applied in a maximally parallel manner and the implementation of these rules is finished in one computation step. The computational power of local synchronization on asynchronous tissue P systems with symport/antiport rules at the three levels is investigated. It is shown that asynchronous tissue P systems with symport/antiport rules and with locally synchronous sets of rules, channels, or cells are all Turing universal. By comparing the computational power of asynchronous tissue P systems with or without local synchronization, it can be found that the local synchronization is a useful tool to achieve a desired computational power.

Cell-like spiking neural P systems are a variant of standard spiking neural P systems, which have a cell-like instead of neural-like architecture. It has been proved that cell-like spiking neural P systems can generate Turing computable sets of numbers. In this work, the computational power of cell-like spiking neural P systems as language generators is investigated. Characterization of finite languages is obtained with cell-like spiking neural P systems when the number of spikes produced is less than the number of spikes consumed, and characterization of recursively enumerable languages is obtained by cell-like spiking neural P systems when there is no restriction on the number of produced spikes. The relationships of the languages generated by cell-like spiking neural P systems with regular, non-context-free and non-semilinear languages are also investigated.

Spiking neural P systems with rules on synapses are a new variant of spiking neural P systems. In the systems, the neuron contains only spikes, while the spiking/forgetting rules are moved on the synapses. It was obtained that such system with 30 neurons (using extended spiking rules) or with 39 neurons (using standard spiking rules) is Turing universal. In this work, this number is improved to 6. Specifically, we construct a Turing universal spiking neural P system with rules on synapses having 6 neurons, which can generate any set of Turing computable natural numbers. As well, it is obtained that spiking neural P system with rules on synapses having less than two neurons are not Turing universal: i) such systems having one neuron can characterize the family of finite sets of natural numbers; ii) the family of sets of numbers generated by the systems having two neurons is included in the family of semi-linear sets of natural numbers.

Recently, Gutiérrez-Naranjo and Leporati considered performing basic arithmetic operations on a new class of bio-inspired computing devices-spiking neural P systems (for short, SN P systems). However, the binary encoding mechanism used in their research looks like the encoding approach in electronic circuits, instead of the style of spiking neurons (in usual SN P systems, information is encoded as the time interval between spikes). In this work, four SN P systems are constructed as adder, subtracter, multiplier, and divider, respectively. In these systems, a number is inputted to the system as the interval of time elapsed between two spikes received by input neuron, the result of a computation is the time between the moments when the output neuron spikes.

issue 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). Ministerio de Economía y Competitividad TIN2012-37434

Spiking neural P systems (called SN P systems for short) are a class of parallel and distributed neural-like computation models inspired by the way the neurons process information and communicate with each other by means of impulses or spikes. In this work, we introduce a new variant of SN P systems, called SN P systems with rules on synapses working in maximum spiking strategy, and investigate the computation power of the systems as both number and vector generators. Specifically, we prove that i) if no limit is imposed on the number of spikes in any neuron during any computation, such systems can generate the sets of Turing computable natural numbers and the sets of vectors of positive integers computed by $k$ -output register machine; ii) if an upper bound is imposed on the number of spikes in each neuron during any computation, such systems can characterize semi-linear sets of natural numbers as number generating devices; as vector generating devices, such systems can only characterize the family of sets of vectors computed by sequential monotonic counter machine, which is strictly included in family of semi-linear sets of vectors. This gives a positive answer to the problem formulated in Song et al., Theor. Comput. Sci., vol. 529, pp. 82–95, 2014.

Spiking neural P systems (SN P systems, for short) are a class of parallel and distributed computation models inspired from the way the neurons process and communicate information by means of spikes. In this paper, we consider a new variant of SN P systems, where each synapse instead of neuron has a set of spiking rules, and the neurons contain only spikes; when the number of spikes in a given neuron is “recognized” by a rule on a synapse leaving from it, the rule is enabled; at a computation step, at most one enabled spiking rule is applied on a synapse, and $k$ spikes are removed from a neuron if the maximum number of spikes that the applied spiking rules on the synapses starting from this neuron consume is $k$ . The computation power of this variant of SN P systems is investigated. Specifically, we prove that such SN P systems can generate or accept any set of Turing computable natural numbers. This result gives an answer to an open problem formulated in Theor. Comput. Sci., vol. 529, pp. 82–95, 2014.

Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired from the way neurons communicate by means of spikes, where each neuron can have several spiking rules and forgetting rules and neurons work in parallel in the sense that each neuron that can fire should fire at each computation step. In this work, we consider SN P systems with the restrictions: 1) systems are simple (resp. almost simple) in the sense that each neuron has only one rule (resp. except for one neuron); 2) at each step the neuron(s) with the maximum number of spikes among the neurons that can spike will fire. These restrictions correspond to that the systems are simple or almost simple and a global view of the whole network makes the systems sequential. The computation power of simple SN P systems and almost simple SN P systems working in the sequential mode induced by maximum spike number is investigated. Specifically, we prove that such systems are Turing universal as both number generating and accepting devices. The results improve the corresponding ones in Theor. Comput. Sci., 410 (2009), 2982-2991.

The solution space exponential explosion caused by the enumeration of the candidate solutions maybe is the biggest obstacle in DNA computing. In the paper, a new unenumerative DNA computing model for graph vertex coloring problem is presented based on two techniques: 1) ordering the vertex sequence for a given graph in such a way that any two consecutive labeled vertices i and i+1 should be adjacent in the graph as much as possible; 2) reducing the number of encodings representing colors according to the construture of the given graph. A graph with 12 vertices without triangles is solved and its initial solution space includes only 283 DNA strands, which is 0.0532 of 3(12) (the worst complexity).

Spiking neural P systems are a class of distributed parallel computing devices inspired from the way neurons communicate by means of spikes. In this paper, the problem of looking for small universal computing devices is investigated in the framework of spiking neural P systems. A new approach is introduced to simulate register machines by spiking neural P systems, where only one neuron is used for all instructions of the simulated register machine; in this way, less neurons are used to construct universal spiking neural P systems working in exhaustive mode. Specifically, a universal spiking neural P system with 36 neurons is constructed, which works in exhaustive mode. This significantly improves the already known result, where 125 neurons are used.