Spiking Neural P Systems with Anti-Spikes

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 ! b0 or bc ! ¸, where b; b0 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.Junta de Andalucía P08 – TIC 0420

New Normal Forms for Spiking Neural P Systems

We consider a natural restriction in the architecture of a spiking neural P system, namely, to have neurons of a small number of types (i.e., using a small number of sets of rules), and we prove that three types of neurons are su±cient in order to generate each recursively enumerable set of numbers as the distance between the first two spikes emitted by the system or as the number of spikes in a specified neuron, in the halting configuration. The case we investigate is that of spiking neural P systems with standard rules, with delays, but without using forgetting rules; similar normal forms remain to be found for other types of systems.Junta de Andalucía P08 – TIC 0420

On Parallel Array P Systems

We further investigate the parallel array P systems recently introduced by K.G. Subramanian, P. Isawasan, I. Venkat, and L. Pan. We rst make explicit several classes of parallel array P systems (with one or more axioms, with total or maximal parallelism, with rules of various types). In this context, some results from the above mentioned paper by Subramanian et al. are improved. A series of open problems are formulated

P Systems with Active Membranes and Separation Rules

The P systems are a class of distributed parallel computing devices of a biochemical type. In this paper, a new de¯nition of separation rules in P systems with active membranes is given. Under the new de¯nition, the e±ciency and universality of P systems with active membranes and separation rules instead of division are investigated

Solving Multidimensional 0-1 Knapsack Problem by P Systems with Input and Active Membranes

P systems are parallel molecular computing models based on pro- cessing multisets of objects in cell-like membrane structures. In this paper we give a membrane algorithm to multidimensional 0-1 knapsack problem in lin- ear time by recognizer P systems with input and with active membranes using 2-division. This algorithm can also be modi¯ed to solve general 0-1 integer programming problem

About the Efficiency of Spiking Neural P Systems

Spiking neural P systems were proved to be Turing complete as function computing or number generating devices. Moreover, it has been considered in several papers that spiking neural P systems are also computationally efficient devices working in a non-deterministic way or with exponential pre-computed resources. In this paper, neuron budding rules are introduced in the framework of spiking neural P systems, which is biologically inspired by the growth of dendritic tree of neuron. Using neuron budding rules in SN P systems is a way to trade space for time to solve computational intractable problems. The approach is examined here with a deterministic and polynomial time solution to sat problem without using exponential pre-computed resources

Asynchronous Spiking Neural P Systems with Local Synchronization

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. Asynchronous SN P systems are non-synchronized systems, where the use of spik- ing rules (even if they are enabled by the contents of neurons) is not obligatory. In this paper, with a biological inspiration (in order to achieve some speci c biological func- tioning, neurons from the same functioning motif or community work synchronously to cooperate with each other), we introduce the notion of local synchronization into asyn- chronous SN P systems. The computation power of asynchronous SN P systems with local synchronization is investigated. Such systems consisting of general neurons (resp. unbounded neurons) and using standard spiking rules are proved to be universal. Asyn- chronous SN P systems with local synchronization consisting of bounded neurons and using standard spiking rules characterize the semilinear sets of natural numbers. These results show that the local synchronization is useful, it provides some \programming capacity" useful for achieving a desired computational power.Junta de Andalucía P08 – TIC 0420

Asynchronous Spiking Neural P Systems with Local Synchronization

Summary. 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. Asynchronous SN P systems are non-synchronized systems, where the use of spiking rules (even if they are enabled by the contents of neurons) is not obligatory. In this paper, with a biological inspiration (in order to achieve some specific biological functioning, neurons from the same functioning motif or community work synchronously to cooperate with each other), we introduce the notion of local synchronization into asynchronous SN P systems. The computation power of asynchronous SN P systems with local synchronization is investigated. Such systems consisting of general neurons (resp. unbounded neurons) and using standard spiking rules are proved to be universal. Asynchronous SN P systems with local synchronization consisting of bounded neurons and using standard spiking rules characterize the semilinear sets of natural numbers. These results show that the local synchronization is useful, it provides some “programming capacity ” useful for achieving a desired computational power.