Spiking neural P systems (SN P systems) are models of computation inspired by biological spiking neurons. SN P systems have neurons as spike processors, which are placed on the nodes of a directed and static graph (the edges in the graph are the synapses). In this paper, we introduce a variant called SN P systems with scheduled synapses (SSN P systems). SSN P systems are inspired and motivated by the structural dynamism of biological synapses, while incorporating ideas from nonstatic (i.e., dynamic) graphs and networks. In particular, synapses in SSN P systems are available only at specific durations according to their schedules. The SSN P systems model is a response to the problem of introducing durations to synapses of SN P systems. Since SN P systems are in essence static graphs, it is natural to consider them for dynamic graphs also. We introduce local and global schedule types, also taking inspiration from the above-mentioned sources. We prove that SSN P systems are computationally universal as number generators and acceptors for both schedule types, under a normal form (i.e., a simplifying set of restrictions). The introduction of synapse schedules for either schedule type proves useful in programming the system, despite restrictions in the normal form.
Spiking neural P (SNP) systems are a class of parallel, distributed, and nondeterministic computing models inspired by the spiking of biological neurons. In this work, the biological feature known as structural plasticity is introduced in the framework of SNP systems. Structural plasticity refers to synapse creation and deletion, thus changing the synapse graph. The "programming" therefore of a brain-like model, the SNP system with structural plasticity (SNPSP system), is based on how neurons connect to each other. SNPSP systems are also a partial answer to an open question on SNP systems with dynamism only for synapses. For both the accepting and generative modes, we prove that SNPSP systems are universal. Modifying SNPSP systems semantics, we introduce the spike saving mode and prove that universality is maintained. In saving mode however, a deadlock state can arise, and we prove that reaching such a state is undecidable. Lastly, we provide one technique in order to use structural plasticity to solve a hard problem: a constant time, nondeterministic, and semi-uniform solution to the NP-complete problem Subset Sum.
Spiking Neural P system is a computing model inspired on how the neurons in a living being are interconnected and exchange information. As a model in embrane computing, it is a non-deterministic and massively-parallel system. The latter makes GPU a good candidate for accelerating the simulation of these models. A matrix representation for systems with and without delay have been previously designed, and algorithms for simulating them with deterministic systems was also developed. So far, non-determinism has been problematic for the design of parallel simulators. In this work, an algorithm for simulating non-deterministic spiking neural P system with delays is presented. In order to study how the simulations get accelerated on a GPU, this algorithm was implemented in CUDA and used to simulate non-uniform and uniform solutions to the Subset Sum problem as a case study. The analysis is completed with a comparison of time and space resources in the GPU of such simulations.
Spiking Neural P (SNP) systems, variants of P systems (under Membrane and Natural computing), are computing models that acquire abstraction and inspiration from the way neurons 'compute' or process information. Similar to other P system variants, SNP systems are Turing complete models that by nature compute non-deterministically and in a maximally parallel manner. P systems usually trade (often exponential) space for (polynomial to constant) time. Due to this nature, P system variants are currently limited to parallel simulations, and several variants have already been simulated in parallel devices. In this paper we present an improved SNP system simulator based on graphics processing units (GPUs). Among other reasons, current GPUs are architectured for massively parallel computations, thus making GPUs very suitable for SNP system simulation. The computing model, hardware/software considerations, and simulation algorithm are presented, as well as the comparisons of the CPU only and CPU-GPU based simulators.
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