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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.

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

Spiking neural P systems (SN P systems for short) are a class of neural-like computing models in the framework of membrane computing. Inspired by the neurophysiological structure of the brain, SN P systems have been extended in various ways. P–Lingua is a standard language for the definition of P systems, where pLinguaCore library provides particular implementations of parsers and simulators for the models specified in P–Lingua. A support for simulating SN P systems in P–Lingua was introduced recently and soon expanded to cover further features of these systems. In this paper, we present an extension of P–Lingua related to asynchronous SN P systems, in order to incorporate simulation capabilities for limited asynchronous SN P systems and asynchronous SN P systems with local synchronization.

Spiking neural P systems (SN P systems, for short) with rules on synapses are a new variant of SN P systems, where the spiking and forgetting rules are placed on synapses instead of in neurons. Recent studies illustrated that this variant of SN P systems is universal working in the way that the synapses starting from the same neuron work in parallel (i.e., all synapses starting from the same neuron should apply their rules if they have rules to be applied). In this work, we consider SN P systems with rules on synapses working in another way: the synapses starting from the same neuron are restricted to work in a sequential way (i.e., at each step at most one synapse starting from the same neuron applies its rule). It is proved that the computational power of SN P systems with rules on synapses working in this way is reduced; specifically, they can only generate finite sets of numbers. Such SN P systems with rules on synapses are proved to be universal, if synapses are allowed to have weight at most 2 (if a rule which can generate n spikes is applied on a synapse with weight k, then the neuron linking to this synapse will receive totally nk spikes). Two small universal SN P systems with rules on synapses for computing functions are also constructed: a universal system with 26 neurons when using extended rules and each synapse having weight at most 2, and a universal system with 26 neurons when using standard rules and each synapse having weight at most 12. These results illustrate that the weight is an important feature for the computational power of SN P systems.

In a biological system, if a long enough time interval is given, an enabled chemical reaction will finish its reaction in the given time interval. With this motivation, it is natural to impose a bound on the time interval when an enabled spiking rule in a spiking neural P system (SN P system, for short) remains unused. In this work, a new working mode of SN P systems is defined, which is called limited asynchronous mode. In an SN P system working in limited asynchronous mode, if a rule is enabled at some step, this rule is not obligatorily used. From this step on, if the unused rule may be used later, it should be used in the given time interval. If further spikes make the rule non-applicable, then the computation continues in the new circumstances. The computation result of a computation in an SN P system working in limited asynchronous mode is defined as the total number of spikes sent into the environment by the system. It is proved that limited asynchronous SN P systems with standard spiking rules are universal. If the number of spikes present in each neuron of a limited asynchronous SN P system with standard spiking rules is bounded during a computation, then the power of a limited asynchronous SN P system with standard spiking rules falls drastically, and we get a characterization of semilinear sets of numbers.

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

Spiking neural P systems are a class of distributed parallel computing models inspired from the way the neurons communicate with each other by means of electrical impulses (called "spikes"). In this paper, we consider a restricted variant of spiking neural P systems, called homogeneous spiking neural P systems, where each neuron has the same set of rules. The universality of homogeneous spiking neural P systems is investigated. One of universality results is that it is sufficient for homogeneous spiking neural P system to have only one neuron that behaves nondeterministically in order to achieve Turing completeness.