Tingfang Wu

Cell-like spiking neural P systems

With mathematical motivation, we consider a combination of basic features of multiset-rewriting P systems and of spiking neural P systems, that is, we consider cell-like P systems with spiking rules in their membranes (hence dealing with only one kind of objects, the spikes). The universality of these systems as number generating devices is proved for the two usual ways to define the output (internally or externally) and for various restrictions on the spiking rules. Several research topics are also pointed out.

On Languages Generated by Cell-Like Spiking Neural P Systems

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 Polarizations

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.

Numerical P systems with migrating variables

Abstract Numerical P systems are a class of P systems inspired both from the structure of living cells and from economics, where variables are associated with the membranes, and these associations are not changed during the computation. However, in the standard P systems, a crucial character for objects is that they can pass through membranes, between regions of the same cell, between cells, or between cells and their environment. We introduce this character also to numerical P systems, and call the new variant numerical P systems with migrating variables (MNP systems). The computational power of MNP systems is investigated both as number generators and as string generators, working in the one-parallel or the sequential modes. Specially, as number generators, MNP systems are proved to be universal working in the above two modes. As string generators, the generative capacity of such systems is investigated having as a reference the families of languages in the Chomsky hierarchy, and a characterization of recursively enumerable languages is obtained.

Cell-Like Spiking Neural P Systems With Request Rules

Cell-like spiking neural (cSN) P systems are a class of distributed and parallel computation models inspired by both the way in which neurons process information and communicate to each other by means of spikes and the compartmentalized structures of living cells. cSN P systems have been proved to be Turing universal if more spikes can be produced by consuming some spikes or spikes can be replicated. In this paper, in order to answer the open problem whether this functioning of producing more spikes and replicating spikes can be avoided by using some strategy without the loss of computation power, we introduce cSN P systems with request rules, which have classical spiking rules and forgetting rules, and also request rules in the skin membrane. The skin membrane can receive spikes from the environment by the application of request rules. cSN P systems with request rules are proved to be Turing universal. The results show that the decrease of computation power caused by removing the internal functioning of producing more spikes and replicating spikes can be compensated by request rules, which suggests that the communication between a cell and the environment is an essential ingredient of systems in terms of computation power.

Numerical P systems with production thresholds

Abstract 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.

Universal enzymatic numerical P systems with small number of enzymatic variables

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.

Spiking neural P systems with rules on synapses and anti-spikes

Abstract Spiking neural P systems with anti-spikes (in short, ASN P systems) are a variant of spiking neural P systems (in short, SN P systems), inspired by the way in which neurons process information and communicate to each other through both excitatory and inhibitory impulses. In this work, we consider ASN P systems with rules on synapses, where all neurons contain only spikes or anti-spikes, and the rules are placed on the synapses. The computational power of ASN P systems with rules on synapses is investigated with the restrictions: (1) systems are simple in the sense that each synapse has only one rule; (2) all spiking rules on synapses are bounded; (3) the delay feature and forgetting rules are not used. Specifically, we prove that ASN P systems with pure spiking rules of categories ( a , a ) and ( a , a ¯ ) on synapses are universal as number generating and accepting devices. The universality of ASN P systems with spiking rules of categories ( a , a ¯ ) and ( a ¯ , a ) on synapses as generating and accepting devices is obtained, where synapses can change spikes to anti-spikes or change anti-spikes to spikes. We also prove that ASN P systems with inhibitory synapses using spiking rules of category ( a , a ) on synapses are universal as both generating and accepting devices. These results illustrate that simple form of spiking rules is enough for ASN P systems with rules on synapses to achieve Turing universality.