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In this note, we consider the problem of looking for small universal one-symbol tissue P systems with symport/antiport rules. It is proved that six cells suffice to generate any recursively enumerable set of natural numbers by such a one-symbol tissue P system with symport/antiport rules, under the restriction that only one channel is allowed between two cells or between a cell and the environment. As for the case of allowing two channels between a cell and the environment, it is shown that the computational completeness can be obtained by one-symbol tissue P systems with symport/antiport rules having at most five cells. These results partially answer an open problem formulated by Artiom Alhazov, Rudolf Freund and Marion Oswald. [ABSTRACT FROM AUTHOR]

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 → χ, where b,b' are spikes or anti-spikes. Therefore, the regular expressions which control the spiking are the simplest possible, 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. [ABSTRACT FROM AUTHOR]

Axon P systems are a class of spiking neural P systems. In this paper, the axon P systems are used as number generators and language generators. As a language generator, the relationships of the families of languages generated by axon P systems with finite and context-free languages are considered. As a number generator, a characterization of the family of finite sets can be obtained by axon P systems with only one node. The relationships of sets of numbers generated by axon P systems with semilinear sets of numbers are also investigated. This paper partially answers some open problems formulated by H. Chen, T.-O. Ishdorj and Gh. Păun. [ABSTRACT FROM AUTHOR]