Spiking neural P systems with extended rules: universality and languages

Abstract

We consider spiking neural P systems with rules allowed to introduce zero, one, or more spikes at the same time. The motivation comes both from constructing small universal systems and from generating strings; previous results from these areas are briefly recalled. Then, the computing power of the obtained systems is investigated, when considering them as number generating and as language generating devices. In the first case, a simpler proof of universality is obtained, while in the latter case we find characterizations of finite and recursively enumerable languages (without using any squeezing mechanism, as it was necessary in the case of standard rules). The relationships with regular languages are also investigated.

Asynchronous Spiking Neural P Systems: Decidability and Undecidability

“…A survey of results and the biological motivations for these systems can be found in [5] and [2]. In the meantime, two main research directions were particularly active in this area of membrane computing: looking for classes of systems with tractable (for instance, decidable) properties, and looking for the possibility of using SN P systems for efficiently solving computationally hard problems.…”

Solving Subset Sum Problems by Time-free Spiking Neural P Systems

“…The systems, shown in Figure 1, are constructed in a uniform way. The input neurons σ c i, 3 , i = 1, 2, . .…”

“…Having 3 spikes, neuron σ c i,1 fires by the rule a 3 → a 2 , sending 2 spikes to neuron σ d at certain step. In this case, no spike is emitted to neuron σ out from the neuron σ c i, 3 . Note that before neuron σ d is activated, the number of spikes in neuron σ out is always even (it can only receive even number of spikes in any step), so neuron σ out cannot fire until neuron σ d fires.…”

“…SN P systems were proved to be computationally complete, i.e., Turing universal, as number generators [5,11,12,13,14,15], language generators [3,21], and function computing devices [16]. SN P systems with cell division or budding can generate new neurons during the computation, thus provide a way to generate exponential working space in polynomial or linear time.…”

“…In the previous obtained SN P systems in [3,5,6,7,8,12,16,20], a global clock is generally assumed marking the time for the system. The systems work in a synchronized manner in the global level (all neurons apply their rules in a parallel manner), and for each neuron, only one of the enabled rules can be used on the tick of the clock.…”