Representation of Spiking Neural P Systems with Anti-spikes through Petri Nets

Design of logic gates using spiking neural P systems with homogeneous neurons and astrocytes-like control

Abstract: In biological nervous systems, the operation of interacting neurons depends largely on the regulation from astrocytes. Inspired by this biological phenomenon, spiking neural P systems, i.e. SN P systems, with astrocyte-like control were proposed and were proven to have "Turing completeness" as computing models. In this work, the application of such systems for creating logical operators is investigated. Specifically, it is obtained in a constructive way that SN P systems with astrocyte-like control can synthesize the operations of Boolean logic gates, i.e. AND, OR, NOT, NOR, XOR and NAND gates. The resulting systems are simple and homogeneous, which means only one type of neuron with a unique spiking rule is used. With these neural-like logic gates, more complex Boolean circuits with cascade connections can be constructed. As such, they can be used to implement finite computing devices, such as the finite transducers. These results demonstrate a novel method of constructing logic circuits that work in a neural-like manner, as well as shed some lights on potential directions of designing neural circuits theoretically.

Modelling and analysis of spiking neural P systems with anti-spikes using Pnet lab

Abstract: Petri Nets are promising methods for modelling and simulating biological systems. Spiking Neural P system with anti-spikes (SN PA systems) is a biologically inspired computing model that incorporates two types of objects called spikes and anti-spikes thus representing binary information in a natural way. In this paper, we propose a methodology to simulate SN PA systems using a Petri net tool called Pnet Lab. It provides a promising way for SN PA systems because of its parallel execution semantics and appropriateness to represent typical working processes of these systems. This enables us to verify system properties, system soundness and to simulate the dynamic behaviour.

Spiking Neural P Systems

Abstract: This paper proposes a way to incorporate the idea of spiking neurons into the area of membrane computing, and to this aim we introduce a class of neural-like P systems which we call spiking neural P systems (in short, SN P systems). In these devices, the time (when the neurons fire and/or spike) plays an essential role. For instance, the result of a computation is the time between the moments when a specified neuron spikes. Seen as number computing devices, SN P systems are shown to be computationally complete (both in the generating and accepting modes, in the latter case also when restricting to deterministic systems). If the number of spikes present in the system is bounded, then the power of SN P systems falls drastically, and we get a characterization of semilinear sets. A series of research topics and open problems are formulated.

Spiking Neural P Systems with Anti-Spikes

Abstract: 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 → lambda , where b,b′ are spikes or anti-spikes. Therefore, the regular expressions which control the spiking are the simplest possi- ble, 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.

A Brief Introduction to Coloured Petri Nets

Abstract: Coloured Petri Nets (CP-nets or CPN) is a graphical oriented language for design, specification, simulation and verification of systems. It is in particular well-suited for systems in which communication, synchronisation and resource sharing are important. Typical examples of application areas are communication protocols, distributed systems, imbedded systems, automated production systems, work flow analysis and VLSI chips.