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Tissue P systems with evolutional communication rules and cell division (TPec, for short) are a class of bio-inspired parallel computational models, which can solve NP-complete problems in a feasible time. In this work, a variant of TPec, called $k$-distributed tissue P systems with evolutional communication and cell division ($k\text{-}\Delta_{TP_{ec}}$, for short) is proposed. A uniform solution to the SAT problem by $k\text{-}\Delta_{TP_{ec}}$ under balanced fixed-partition is presented. The solution provides not only the precise satisfying truth assignments for all Boolean formulas, but also a precise amount of possible such satisfying truth assignments. It is shown that the communication resource for one-way and two-way uniform $k$-P protocols are increased with respect to $k$; while a single communication is shown to be possible for bi-directional uniform $k$-P protocols for any $k$. We further show that if the number of clauses is at least equal to the square of the number of variables of the given boolean formula, then $k\text{-}\Delta_{TP_{ec}}$ for solving the SAT problem are more efficient than TPec as show in \cite{bosheng2017}; if the number of clauses is equal to the number of variables, then $k\text{-}\Delta_{TP_{ec}}$ for solving the SAT problem work no much faster than TPec.

Numerical P systems (for short, NP systems) are distributed and parallel computing models inspired both from the structure of living cells and from the economic reality, where the values of variables evolve by programs that are composed by production functions and repartition protocols: the value of a production function is distributed to variables according to the corresponding repartition protocol. In this work, we introduce a new method of using evolution programs into NP systems, where thresholds are associated with production functions. The computation power of NP systems with production thresholds is investigated. Specifically, we prove that NP systems with lower-thresholds (the production function value can be distributed only when it is not smaller than a given constant), with one membrane working both in the all-parallel mode and in the sequential mode, are universal. The universal results of NP systems with lower-thresholds are extended to NP systems with upper-thresholds (the production function value can be distributed only when it is not greater than a given constant) by simulating the former with the latter. These universality results show that NP systems with production thresholds have the potential to implement any computer program or robot behavior.

Tissue P systems with symport/antiport rules are a class of distributed parallel computing models inspired by the cell intercommunication in tissues, where objects are never modified in the process of communication, just changing their place within the system. In this work, a variant of tissue P systems, called tissue P systems with evolutional symport/antiport rules is introduced, where objects are moved from one region to another region and may be evolved during this process. The computational power of such P systems is studied. Specifically, it is proved that such P systems with one cell and using evolutional symport rules of length at most 3 or using evolutional antiport rules of length at most 4 are Turing universal (only the family of all finite sets of positive integers can be generated by such P systems if standard symport/antiport rules are used). Moreover, cell division rules are considered in tissue P systems with evolutional symport/antiport rules, and a limit on the efficiency of such P systems is provided with evolutional communication rules of length at most 2. The computational efficiency of this kind of models is shown when using evolutional communication rules of length at most 4.

In search of the borderline between universality and non-universality of purely catalytic P systems, we prove that purely catalytic P systems with one catalyst are universal when inhibitors plus promoters or a priority relation among the rules plus promoters are used. The universality is also obtained for purely catalytic cooperating P systems with two catalysts (without any control on the use of rules). Some related open problems are also formulated.

The operation of splicing on words was introduced by Tom Head while proposing a theoretical model of DNA recombination. Subsequent investigations on splicing on linear and circular strings of symbols have resulted in a number of theoretical properties. A different kind of splicing on two words, referred to as flat splicing, has been considered recently. This operation is extended to flat splicing on picture arrays, thus defining a new model of generation of digitized pictures, which is called as array flat splicing system (AFS). Results on the generative power of AFS in comparison with certain well-known picture array defining models and certain non-closure results are obtained.

In spite of the fact that many ways of using the evolution rules in a P system were already investigated, there is still a case, which we call the flat maximal parallelism, which appeared in several papers, but which deserves a more careful attention: in each step, in each membrane, a maximal set of applicable rules is chosen and each rule in the set is applied exactly once. In this work, flat maximal parallelism is studied for non-cooperating P systems with promoters. Specifically, we prove that non-cooperating P systems with at most one promoter associated with any rule, working in the flat maximally parallel way, are Turing universal (the Turing universality of such P systems is open if they work in the maximally parallel way). Moreover, a uniform solution to the SAT problem is provided by using non-cooperating P systems with promoters and membrane division, working in the flat maximal parallel way.

A control strategy on the computations in a one-catalyst P system is provided: the rules are assumed "colored" and in each step only rules of the same "color" are used. Such control leads to Turing universality for one-catalyst P systems with one membrane. Turing universality is also reached for purely catalytic P systems with two catalysts, and for purely catalytic P systems with only one catalyst and cooperating rules working in the so-called terminal mode.

Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired by spiking neurons. SN P systems with anti-spikes (ASN P systems) are a variant of SN P systems, which were inspired by inhibitory impulses/spikes or inhibitory synapses. In this work, we consider ASN P systems with the restrictions: (1) systems are simple in the sense that each neuron has only one rule; (2) at each step the neuron(s) with the maximum number of spikes among the neurons that are active (can spike) will fire; (3) the feature of delays and forgetting rules are not used. These restrictions make the systems working in a sequential way. We investigate the computational power of ASN P systems under these restrictions. Specifically, we prove that such systems with spiking rules of categories ( a , a ) and ( a , a ? ) are universal as both number generating and accepting devices. We also prove that ASN P systems with inhibitory synapses using spiking rules of category ( a , a ) are universal as both generating and accepting devices. These results show that ASN P systems are still powerful working with these restrictions.

Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired from the way neurons process information and communicate by means of spikes, where neurons are different in the sense that they can have different sets of spiking rules. In this work, we consider a variant of SN P systems with two restrictions: (1) all neurons contain only spikes (neurons are homogeneous in this case, since they can be considered as containers of spikes), while the spiking rules are moved on the synapses; (2) all synapses are homogeneous in the sense that each synapse has the same set of rules. These restrictions correspond to the fact that the SN P system consists of only one kind of neurons and one kind of synapses. The computational power of SN P systems with homogeneous neurons and synapses is investigated. Specifically, it is proved that such systems are Turing universal as both number generating and number accepting devices.

Axon P systems are computing models with a linear structure in the sense that all nodes (i.e., computing units) are arranged one by one along the axon. Such models have a good biological motivation: an axon in a nervous system is a complex information processor of impulse signals. Because the structure of axon P systems is linear, the computational power of such systems has been proved to be greatly restricted; in particular, axon P systems are not universal as language generators. It remains open whether axon P systems are universal as number generators. In this paper, we prove that axon P systems are universal as both number generators and function computing devices, and investigate the number of nodes needed to construct a universal axon P system. It is proved that four nodes (respectively, nine nodes) are enough for axon P systems to achieve universality as number generators (respectively, function computing devices). These results illustrate that the simple linear structure is enough for axon P systems to achieve a desired computational power.

Numerical P systems (for short, NP systems) are distributed and parallel computing models inspired from the structure of living cells and economics. Enzymatic numerical P systems (for short, ENP systems) are a variant of NP systems, which have been successfully applied in designing and implementing controllers for mobile robots. Since ENP systems were proved to be Turing universal, there has been much work to simplify the universal systems, where the complexity parameters considered are the number of membranes, the degrees of polynomial production functions or the number of variables used in the systems. Yet the number of enzymatic variables, which is essential for ENP systems to reach universality, has not been investigated. Here we consider the problem of searching for the smallest number of enzymatic variables needed for universal ENP systems. We prove that for ENP systems as number acceptors working in the all-parallel or one-parallel mode, one enzymatic variable is sufficient to reach universality; while for the one-parallel ENP systems as number generators, two enzymatic variables are sufficient to reach universality. These results improve the best known results that the numbers of enzymatic variables are $13$ and $52$ for the all-parallel and one-parallel systems, respectively.

Inspired by mitosis process and membrane fission processes, cell-like P systems with symport/antiport rules and membrane division rules or membrane separation rules have been introduced, respectively. These computation systems have two key features: the ability to have infinite copies of some objects (within an active environment) and to generate an exponential workspace in polynomial time. In this work, we extend the P-Lingua framework for simulating that kind of P systems taking into account these two features. Consequently, a new simulator has been developed and included in pLinguaCore library. The functioning of the simulator has been checked by simulating efficient solutions to SAT problem using a family of cell-like P systems with symport/antiport rules and membrane division rules or membrane separation rules. The corresponding MeCoSim based application is also provided. ∗Address for correspondence: Huazhong University of Science and Technology, Wuhan 430074, Hubei, China. Received February 2015; revised April 2015. 212 L.F. Macias-Ramos et al. / P–Lingua Simulator for P Systems with Symport/Antiport Rules

Tissue P systems are a class of bio-inspired computing models motivated by biochemical interactions between cells in a tissue-like arrangement. Tissue P systems with cell division offer a theoretical device to generate an exponentially growing structure in order to solve computationally hard problems efficiently with the assumption that there exists a global clock to mark the time for the system, the execution of each rule is completed in exactly one time unit. Actually, the execution time of different biochemical reactions in cells depends on many uncertain factors. In this work, with this biological inspiration, we remove the restriction on the execution time of each rule, and the computational efficiency of tissue P systems with cell division is investigated. Specifically, we solve subset sum problem by tissue P systems with cell division in a time-free manner in the sense that the correctness of the solution to the problem does not depend on the execution time of the involved rules.

P systems are a class of computational models inspired by the structure and the functioning of a living cell. In the semantics of P systems, there exists a global clock, which marks the time for the system, and the execution time of each rule takes exactly one time unit. However, in living cells, the execution time of different biochemical reactions is dependent on many uncontrollable factors, and it is hard to know precisely the specific execution time of a reaction. In this work, with this biological inspiration, we consider the class of P systems with active membranes that are "robust" against the execution time of rules. Specifically, we give a time-free uniform solution to the SAT problem using P systems with active membranes, where the constructed P system can solve a family of instances with an arbitrarily given size, and the execution time of the involved rules has no influence on the correctness of the solution. We also prove that any Turing computable set of numbers can be generated by a time-free P system with active membranes in the sense that the set of numbers generated by the given P system with active membranes does not depend on the execution time of rules.

P systems are a class of distributed and parallel computing models inspired by the structure and the functioning of a single cell and complexes of cells. The computational efficiency of P systems with active membranes has been investigated widely with the assumption that the application of rules is completed in exactly one time unit. However, in biological facts, different biological processes may take different times to complete, and the execution time of certain biological process could vary because of external uncontrollable conditions. With this biological motivation, in this work, we solve SAT problem by a family of P systems with active membranes in a time-free manner in the sense that the correctness of the solution does not depend on the precise timing of the involved rules. In such a solution, standard cell division rules for elementary membranes are applied: the newly generated membranes have the same label with their parent membrane. This result answers an open problem formulated in Song et al. (Theor Comput Sci 529:61---68, 2014).

Spiking neural P (SN P) systems are a class of parallel computation models inspired by neurons, where the firing condition of a neuron is described by a regular expression associated with spiking rules. However, it is NP-complete to decide whether the number of spikes is in the length set of the language associated with the regular expression. In this paper, in order to avoid using regular expressions, two major and rather natural modifications in their form and functioning are proposed: the spiking rules no longer check the number of spikes in a neuron, but, in exchange, a polarization is associated with neurons and rules, one of the three electrical charges −, 0,+. Surprisingly enough, the computing devices obtained are still computationally complete, which are able to compute all Turing computable sets of natural numbers. On this basis, the number of neurons in a universal SN P system with polarizations is estimated. Several research directions are mentioned at the end of this paper.

In evolutionary many-objective optimization, diversity maintenance plays an important role in pushing the population towards the Pareto optimal front. Existing many-objective evolutionary algorithms mainly focus on convergence enhancement, but pay less attention to diversity enhancement, which may fail to obtain uniformly distributed solutions or fall into local optima. This paper proposes a radial space division based evolutionary algorithm for many-objective optimization, where the solutions in high-dimensional objective space are projected into the grid divided 2-dimensional radial space for diversity maintenance and convergence enhancement. Specifically, the diversity of the population is emphasized by selecting solutions from different grids, where an adaptive penalty based approach is proposed to select a better converged solution from the grid with multiple solutions for convergence enhancement. The proposed algorithm is compared with five state-of-the-art many-objective evolutionary algorithms on a variety of benchmark test problems. Experimental results demonstrate the competitiveness of the proposed algorithm in terms of both convergence enhancement and diversity maintenance.

Tissue P systems are a class of distributed and parallel models of computation inspired by the way of communication among living cells or between cells and their environment. In this work, we investigate the computational power of tissue P systems, where each rule is assigned either with a label chosen from an alphabet or with the empty label λ . The sequence of labels of rules applied during a halting computation is defined as the result of the computation, and the set of all results computed by a given tissue P system is called a control language. We prove that tissue P systems with antiport rules of weight one and without symport rules characterize regular languages; tissue P systems with antiport rules of weight at most two (resp., symport rules of weight at most two) without symport rules (resp., antiport rules) are universal. Tissue P systems with antiport rules of weight one and symport rules of weight one are also proved to be universal. These results show that the rule complexity is crucial for tissue P systems to achieve a desired computational power.

Spiking neural P systems (SN P systems) are a class of distributed parallel computing devices inspired by the way neurons communicate by means of spikes; neurons work in parallel in the sense that each neuron that can fire should fire, but the work in each neuron is sequential in the sense that at most one rule can be applied at each computation step. In this work, with biological inspiration, we consider SN P systems with the restriction that at each step, one of the neurons (i.e., sequential mode) or all neurons (i.e., pseudo-sequential mode) with the maximum (or minimum) number of spikes among the neurons that are active (can spike) will fire. If an active neuron has more than one enabled rule, it nondeterministically chooses one of the enabled rules to be applied, and the chosen rule is applied in an exhaustive manner (a kind of local parallelism): the rule is used as many times as possible. This strategy makes the system sequential or pseudo-sequential from the global view of the whole network and locally parallel at the level of neurons. We obtain four types of SN P systems: maximum/minimum spike number induced sequential/pseudo-sequential SN P systems with exhaustive use of rules. We prove that SN P systems of these four types are all Turing universal as number-generating computation devices. These results illustrate that the restriction of sequentiality may have little effect on the computation power of SN P systems.

Spiking neural P systems (SN P systems, for short) are a class of membrane systems inspired from the way the neurons process information and communicate by means of spikes. In this paper, we introduce and investigate a new class of SN P systems, with spiking rules placed on synapses. The computational completeness is first proved, then two small universal SN P systems with rules on synapses for computing functions are constructed. Specifically, when using standard spiking rules, we obtain a universal system with 39 neurons, while when using extended spiking rules on synapses, a universal SN P system with 30 neurons is constructed.

P systems are a class of distributed and parallel computation models inspired by the structure and the functioning of living cells. P systems have been used to solve computation hard problems, where the execution of each rule is completed in unit time (a global clock is assumed for timing and synchronizing the execution of rules). The assumption that the execution of each rule takes exactly one time unit plays an vital role to make a system working synchronously, and it has also been used to characterize the computational efficiency and time complexity of a system. In this work, we investigate the computation power of P systems without such time assumption. Specifically, we give a time-free solution to SAT problem using P systems with active membranes in the sense that the correctness of the solution does not depend on the precise timing of the involved rules.

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. 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 working in the sequential way, where the sequentiality is induced by the minimum number of spikes: at each step, one (resp. all) of the neurons with the minimum number of spikes among the neurons that are active (can fire) will fire, called min-sequentiality (resp. min-pseudo-sequentiality). We prove that SN P systems working in min-sequentiality or min-pseudo-sequentiality are universal as both number generating and accepting devices, where the computation results are encoded by the time elapsed between the first two spikes of the output neuron. The results give positive answers to two open problems formulated in [O.H. Ibarra, A. Paun, A. Rodriguez-Paton, Sequential SNP systems based on min/max spike number, Theoretical Computer Science 410 (30-32) (2009) 2982-2991].

Spiking neural P systems SN P systems, for short are a class of distributed parallel computing devices inspired by the way neurons communicate by means of spikes, where neurons work in parallel in the sense that each neuron that can fire should fire at each computation step, and neurons can be different in the sense that they can have different sets of spiking rules. In this work, we consider SN P systems with the restrictions: 1 all neurons are homogeneous in the sense that each neuron has the same set of rules; 2 at each step the neuron with the maximum number of spikes among the neurons that are active can spike will fire. These restrictions correspond to the fact that the system consists of only one kind of neurons and a global view of the whole network makes the system sequential. The computation power of homogeneous SN P systems working in the sequential mode induced by the maximum spike number is investigated. Specifically, it is proved that such systems are universal as both generating and accepting devices.

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

Tissue P systems are a class of distributed parallel computing devices inspired by biochemical interactions between cells in a tissue-like arrangement, where objects can be exchanged by means of communication channels. In this work, inspired by the biological facts that the movement of most objects through communication channels is controlled by proteins and proteins can move through lipid bilayers between cells (if these cells are fused), we present a new class of variant tissue P systems, called tissue P systems with protein on cells, where multisets of objects (maybe empty), together with proteins between cells are exchanged. The computational power of such P systems is studied. Specifically, an efficient (uniform) solution to the SAT problem by using such P systems with cell division is presented. We also prove that any Turing computable set of numbers can be generated by a tissue P system with protein on cells. Both of these two results are obtained by such P systems with communication rules of length at most 4 (the length of a communication rule is the total number of objects and proteins involved in that rule). Ministerio de Economía y Competitividad TIN2012-37434

Membrane fission is a process by which a biological membrane is split into two new ones in the manner that the content of the initial membrane is separated and distributed between the new membranes. Inspired by this biological phenomenon, membrane separation rules were considered in membrane computing. In this work, we investigate cell-like P systems with symport/antiport rules and membrane separation rules from a computational complexity perspective. Specifically, we establish a limit on the efficiency of such P systems which use communication rules of length at most two, and we prove the computational efficiency of this kind of models when using communication rules of length at most three. Hence, a sharp borderline between tractability and NP–hardness is provided in terms of the length of communication rules. Ministerio de Economía y Competitividad TIN2012-37434

The notion of time-free solution to decision problem by P systems with proteins on membranes, in the sense that the correctness of the solution is irrelevant to the times associated with the involved rules, is defined.A time-free uniform solution to the SAT problem by P systems with proteins on membranes is given. P systems with proteins on membranes are a class of bio-inspired computing models, where the execution of each rule completes in exactly one time unit. However, in living cells, the execution time of biochemical reactions is difficult to know precisely because of various uncontrollable factors. In this work, we present a time-free uniform solution to SAT problem by P systems with proteins on membranes in the sense that the correctness of the solution is irrelevant to the times associated with the involved rules, and the P systems are constructed from the sizes of instances.

Cell-like P systems with symport/antiport rules are inspired by the structure of a cell and the way of communicating substances through membrane channels between neighboring regions. In this work, channel states are introduced into cell-like P systems with symport/antiport rules, and we call this variant of communication P systems as cell-like P systems with channel states and symport/antiport rules. In such P systems, at most one channel is established between neighboring regions, each channel associates with one state in order to control communication at each step, and rules are used in a sequential manner: on each channel at most one rule can be used at each step. The computational power of such P systems is investigated. Specifically, we show that cell-like P systems with two states and using uniport rules, or with any number of states and using antiport rules of length two, are able to compute only finite sets of non-negative integers.We further prove that cell-like P systems with two membranes are as powerful as Turing machines when channel states and symport/antiport rules are suitably combined. The results show that channel states are a feature that can increase the computational power of cell-like P systems with symport/antiport rules. Ministerio de Economía y Competitividad TIN2012-37434

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 neurons work in parallel in the sense that each neuron that can fire should fire, but the work in each neuron is sequential in the sense that at most one rule can be applied at each computation step. In this work, we consider SN P systems with the restriction that at most one neuron can fire at each step, and each neuron works in an exhaustive manner (a kind of local parallelism – an applicable rule in a neuron is used as many times as possible). Such SN P systems are called sequential SN P systems with exhaustive use of rules. The computation power of sequential SN P systems with exhaustive use of rules is investigated. Specifically, characterizations of Turing computability and of semilinear sets of numbers are obtained, as well as a strict superclass of semilinear sets is generated. The results show that the computation power of sequential SN P systems with exhaustive use of rules is closely related with the types of spiking rules in neurons.

Spiking neural P systems are a class of distributed parallel computing models inspired from the way neurons communicate with each other by means of electrical impulses, where there is a synapse between each pair of connected neurons. However, in a biological system, there can be several synapses for each pair of connected neurons. In this study, inspired by this biological observation, synapses in a spiking neural P system are endowed with integer weight denoting the number of synapses for each pair of connected neurons. With the price of weight on synapses, quite small universal spiking neural P systems can be constructed. Specifically, a universal spiking neural P system with standard rules and weight having 38 neurons is produced as device of computing functions; as generator of sets of numbers, we find a universal system with standard rules and weight having 36 neurons.

Different biological processes take different times to be completed, which can also be influenced by many environmental factors. In this work, a realistic definition of nonsynchronized spiking neural P systems (SN P systems, for short) is considered: during the work of an SN P system, the execution times of spiking rules cannot be known exactly (i.e., they are arbitrary). In order to establish robust systems against the environmental factors, a special class of SN P systems, called time-free SN P systems, is introduced, which always produce the same computation result independent of the execution times of the rules. The universality of time-free SN P systems is investigated. It is proved that these P systems with extended rules (several spikes can be produced by a rule) are equivalent to register machines. However, if the number of spikes present in the system is bounded, then the power of time-free SN P systems falls, and in this case, a characterization of semilinear sets of natural numbers is obtained.

Tissue P systems are distributed parallel and non-deterministic computing models in the framework of membrane computing, which are inspired by intercellular communication and cooperation between neurons. Recently, cell separation is introduced into tissue P systems, which enables systems to generate an exponential workspace in a polynomial time. In this work, the computational power of tissue P systems with cell separation is investigated. Specifically, a uniform family of tissue P systems with cell separation is constructed for efficiently solving a well-known NP-complete problem, the partition problem.

A tissue P system with cell division is a computing model which has two basic features: intercellular communication and the ability of cell division. The ability of cell division allows us to obtain an exponential amount of cells in linear time and to design cellular solutions to computationally hard problems in polynomial time. In this work we present an efficient solution to the tripartite matching problem by a family of such devices. This solution leads to an interesting open problem whether tissue P systems with cell division and communication rules of length 2 can solve NP-complete problems. An answer to this open problem will provide a borderline between efficiency and non-efficiency in terms of the lengths of communication rules Ministerio de Educación y Ciencia TIN2009-13192 Junta de Andalucía P08-TIC-04200

In this paper we continue previous studies on the computational effciency of spiking neural P systems, under the assumption that some pre-computed resources of exponential size are given in advance. Specifically, we give a deterministic solution for each of two well known PSPACE-complete problems: QSAT and Q3SAT. In the case of QSAT, the answer to any instance of the problem is computed in a time which is linear with respect to both the number n of Boolean variables and the number m of clauses that compose the instance. As for Q3SAT, the answer is computed in a time which is at most cubic in the number n of Boolean variables.

Spiking neural P systems (in short, SN P systems) are computing devices based on the way the neurons communicate through electrical impulses (spikes). These systems involve various ingredients; among them, we mention forgetting rules and the delay in firing rules. However, it is known that the universality can be obtained without using these two features. In this paper we improve this result in two respects: (i) each neuron contains at most two rules (which is optimal for systems used in the generative mode), and (ii) the rules in the neurons using two rules have the same regular expression which controls their firing. This result answers a problem left open in the literature, and, in this context, an incompleteness in some previous proofs related to the elimination of forgetting rules is removed. Moreover, this result shows a somewhat surprising uniformity of the neurons in the SN P systems able to simulate Turing machines, which is both of a theoretical interest and it seems to correspond to a biological reality. When a bound is imposed on the number of spikes present in a neuron at any step of a computation (such SN P systems are called finite), two surprising results are obtained. First, a characterization of finite sets of numbers is obtained in the generative case (this contrasts the case of other classes of SN P systems, where characterizations of semilinear sets of numbers are obtained for finite SN P systems). Second, the accepting case is strictly more powerful than the generative one: all finite sets and also certain arithmetical progressions can be accepted. A precise characterization of the power of accepting finite SN P systems without forgetting rules and delay remains to be found.

In this paper, we investigate the languages generated by asynchronous spiking neural P systems. Characterizations of finite languages and recursively enumerable languages are obtained by asynchronous spiking neural P systems with extended rules. The relationships of the languages generated by asynchronous spiking neural P systems with regular and non-semilinear languages are also investigated.

For given graphs G"1,G"2,G"3, the three-color Ramsey number R(G"1,G"2,G"3) is defined to be the least positive integer n such that every 3-coloring of the edges of complete graph K"n contains a monochromatic copy of G"i colored with i, for some [email protected][email protected]?3. In this paper, we prove that R(P"4,P"5,C"3)=11, R(P"4,P"5,C"4)=7, R(P"4,P"5,C"5)=11, R(P"4,P"5,C"7)=11, R(P"4,P"5,C"k)=k+2 for k>=23; R(P"4,P"6,C"4)=8, R(P"4,P"6,C"3)=R(P"4,P"6,C"5)=R(P"4,P"6,C"7)=13, R(P"4,P"6,C"k)=k+3 for k>=18.

The design of DNA sequences is one of the most practical and important research topics in DNA computing. We adopt taboo search algorithm and improve the method for the systematic design of equal-length DNA sequences, which can satisfy certain combinatorial and thermodynamic constraints. Using taboo search algorithm, our method can avoid trapping into local optimization and can find a set of good DNA sequences satisfying required constraints.

We continue the study of (extended) spiking neural P systems with exhaustive use of rules by considering these computing devices as language generators. Specifically, a step is associated with a symbol according to the number of spikes emitted by the output neuron and the sequence of these symbols associated with a halting computation constitutes a string. Two cases are considered: one of them interprets a step when no spike is emitted as a specified symbol, the other interprets such a step as the empty string. In both cases, it is proved that finite and recursively enumerable languages are characterized by extended spiking neural P systems working in the exhaustive mode. The relationships with regular languages are also investigated.

Simulated annealing technique has mostly been used to solve various optimization and learning problems, and it is well known that the maximum clique problem is one of the most studied NP-hard optimization problems owing to its numerous applications. In this note, a simple simulated annealing algorithm for the maximum clique problem is proposed and tested on all 80 DIMACS maximum clique instances. Although it is simple, the proposed simulated annealing algorithm is efficient on most of the DIMACS maximum clique instances. The simulation results show that the proposed simulated annealing algorithm outperforms a recent efficient simulated annealing algorithm proposed by Xu and Ma, and the solutions obtained by the proposed simulated annealing algorithm have the equal quality with those obtained by a recent trust region heuristic algorithm of Stanislav Busygin.

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.

P systems are computing models inspired by some basic features of biological membranes. In this work, membrane division, which provides a way to obtain an exponential workspace in linear time, is introduced into (cell-like) P systems with communication (symport/antiport) rules, where objects are never modified but they just change their places. The computational efficiency of this kind of P systems is studied. Specifically, we present a (uniform) linear time solution to the NP-complete problem, Subset Sum by using division rules for elementary membranes and communication rules of length at most 3. We further prove that such P system allowing division rules for non-elementary membranes can efficiently solve the PSPACE-complete problem, QSAT in a uniform way. Ministerio de Economía y Competitividad TIN2012-37434

The bio-inspired operations of linear and circular splicing respectively on linear and circular strings of symbols have been extensively investigated by many researchers for their theoretical properties. Recently, another kind of splicing of two words, referred to as flat splicing on strings, has been considered. We here extend this operation to flat splicing on picture arrays, thus defining a new model of picture generation, which we call as array flat splicing system (AFS) and obtain some results on the generative power of AFS in comparison with certain well-known picture array defining models.

The P systems (or membrane systems) are a class of distributed parallel computing devices of a biochemical type, where membrane division is the frequently investigated way for obtaining an exponential working space in a linear time, and on this basis solving hard problems, typically NP-complete problems, in polynomial (often, linear) time. In this paper, using another way to obtain exponential working space --- membrane separation, it was shown that Satisfiability Problem and Hamiltonian Path Problem can be deterministically solved in linear or polynomial time by a uniform family of P systems with separation rules, where separation rules are not changing labels, but polarizations are used. Some related open problems are mentioned.

This paper addresses the problem of removing the polarization of membranes from P systems with active membranes - and this is achieved by allowing the change of membrane labels by means of communication rules or by membrane dividing rules. As consequences of these results, we obtain the universality of P systems with active membranes which are allowed to change the labels of membranes, but do not use polarizations. Universality results are easily obtained also by direct proofs. By direct constructions, we also prove that SAT can be solved in linear time by systems without polarizations and with label changing possibilities. If non-elementary membranes can be divided, then SAT can be solved in linear time without using polarizations and label changing. Several open problems are also formulated.

The P systems are a class of distributed parallel computing devices of a biochemical type. In this note, we show that by using membrane separation to obtain exponential workspace, SAT problem can be solved in linear time in a uniform and con°uent way by active P systems without polarizations. This improves some results already obtained by A. Alhazov, Ts. Ishdorj. A universality result related to membrane separation is also obtained.

DNA computing has the potential to tackle computationally difficult problems that have real-world implications. The parallel search capabilities of DNA make it a valuable tool for approaching intractable computational problems, for which conventional computers have limited potentials. Up to now, many accomplishments have been achieved to improve its performance and increase its reliability. In this paper, the coloring problem has been solved by means of molecular biology techniques. The coloring problem is a well-known NP-complete problem. This work represents further evidence for the ability of DNA computing to solve NP-complete problems.

The graph-theoretic parameter that has probably received the most attention over the years is the chromatic number. As is well-known, the coloring problem is an NP-Complete problem. In this paper, it has been solved by means of molecular biology techniques. The algorithm is highly parallel and has satisfactory fidelity. This work shows further evidence for the ability of DNA computing to solve NP-Complete problems.

Spiking neural P systems (SN P systems) are a class of distributed parallel computing devices inspired by spiking neurons, where the spiking rules are usually used in a sequential way (an applicable rule is applied one time at a step) or an exhaustive way (an applicable rule is applied as many times as possible at a step). In this letter, we consider a generalized way of using spiking rules by “combining” the sequential way and the exhaustive way: if a rule is used at some step, then at that step, it can be applied any possible number of times, nondeterministically chosen. The computational power of SN P systems with a generalized use of rules is investigated. Specifically, we prove that SN P systems with a generalized use of rules consisting of one neuron can characterize finite sets of numbers. If the systems consist of two neurons, then the computational power of such systems can be greatly improved, but not beyond generating semilinear sets of numbers. SN P systems with a generalized use of rules consisting of three neurons are proved to generate at least a non-semilinear set of numbers. In the case of allowing enough neurons, SN P systems with a generalized use of rules are computationally complete. These results show that the number of neurons is crucial for SN P systems with a generalized use of rules to achieve a desired computational power.