Matrix representations of spiking neural P systems: Revisited

In the 2010, matrix representation of SN P system without delay was presented while in the case of SN P systems with delay, matrix representation was suggested in the 2017. These representations brought about series of simulation of SN P systems using computer software and hardware technology. In this work, we revisit these representation and provide some observations on the behavior of the computations of SN P systems. The concept of reachability of configuration is considered in both SN P systems with and without delays. A better computation of next configuration is proposed in the case of SN P system with delay.Comment: In: Gheorghe Paun (Ed) Proceedings of the 20th International Conference on Membrane Computing (CMC20), Editura Bibliostar, Ramnicu Valcea (2019) pp 227-24

An Improved GPU Simulator For Spiking Neural P Systems

Spiking Neural P (SNP) systems, variants of Psystems (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.Ministerio de Ciencia e Innovación TIN2009–13192Junta de Andalucía P08-TIC-0420

A Spiking Neural P System Simulator Based on CUDA

In this paper we present a Spiking Neural P system (SNP system) simulator based on graphics processing units (GPUs). In particular we implement the simulator using NVIDIA CUDA enabled GPUs. The massively parallel architecture of current GPUs is very suitable for the maximally parallel computations of SNP systems. We simulate a wider variety of SNP systems, after presenting a previous work on SNP system matrix representation which led to their simulation in GPUs, and the simulation algorithm included here. Finally, we compare and present the performance speedups of the CPU-GPU based simulator over the CPU only simulator.Ministerio de Ciencia e Innovación TIN2009–13192Junta de Andalucía P08-TIC-0420

On Communication Complexity in Evolution-Communication P Systems

Looking for a theory of communication complexity for P systems, we consider here so-called evolution-communication (EC for short) P systems, where objects evolve by multiset rewriting rules without target commands and pass through membranes by means of symport/antiport rules. (Actually, in most cases below we use only symport rules.) We first propose a way to measure the communication costs by means of “quanta of energy” (produced by evolution rules and) consumed by communication rules. EC P systems with such costs are proved to be Turing complete in all three cases with respect to the relation between evolution and communication operations: priority of communication, mixing the rules without priority for any type, priority of evolution (with the cost of communication increasing in this ordering in the universality proofs). More appropriate measures of communication complexity are then defined, as dynamical parameters, counting the communication steps or the number (and the weight) of communication rules used during a computation. Such parameters can be used in three ways: as properties of P systems (considering the families of sets of numbers generated by systems with a given communication complexity), as conditions to be imposed on computations (accepting only those computations with a communication complexity bounded by a given threshold), and as standard complexity measures (defining the class of problems which can be solved by P systems with a bounded complexity). Because we ignore the evolution steps, in all three cases it makes sense to consider hierarchies starting with finite complexity thresholds. We only give some preliminary results about these hierarchies (for instance, proving that already their lower levels contain complex – e.g., non-semilinear – sets), and we leave open many problems and research issues.Junta de Andalucía P08 – TIC 0420

Online Algorithms with Advice for the -search Problem

In the online search problem, a seller seeks to find the maximum price from a sequence of prices p1, p2,…, pn that is revealed in a piece-wise manner. The bound for all prices is well known in advance with m ≤ pί ≤ M. In the online k-search problem, the seller seeks to find the k maximum out of the n prices. In this paper, we present a tight bound of [Formula Presented] on the advice complexity of optimal online algorithms for online k-search. We also provide online algorithms with advice that use less than the required number of bits and compute the performance guarantee. Although it is natural to expect improvement due to the additional power of advice, we are interested to identify the relationship of additional information with respect to the improvement. We show that with 1 bit of advice, we can already surpass the quality of the best possible deterministic algorithm for online 2-search. We also provide a set of online algorithms, ALGί, that utilizes [Formula Presented] advice bits with a competitive ratio of (formula presented). We show that increasing the amount of advice improves the solution quality of the algorithm. Moreover, we compare the power of advice and randomization. We show that for some identified minimum number of advice bits, the lower bound on the competitive ratio of online algorithms with advice is better than any deterministic and randomized algorithm for online k-search

When Matrices Meet Brains

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. In this work, a discrete structure representation of SN P systems is proposed. Specifically, matrices are used to represent SN P systems. In order to represent the computations of SN P systems by matrices, configuration vectors are defined to monitor the number of spikes in each neuron at any given configuration; transition net gain vectors are also introduced to quantify the total amount of spikes consumed and produced after the chosen rules are applied. Nondeterminism of the systems is assured by a set of spiking transition vectors that could be used at any given time during the computation. With such matrix representation, it is quite convenient to determine the next configuration from a given configuration, since it involves only multiplying vectors to a matrix and adding vectors

Asynchronous Spiking Neural P Systems with Structural Plasticity

Spiking neural P (in short, SNP) systems are computing devices inspired by biological spiking neurons. In this work we consider SNP systems with structural plasticity (in short, SNPSP systems) working in the asynchronous (in short, asyn mode). SNPSP systems represent a class of SNP systems that have dynamic synapses, i.e. neurons can use plasticity rules to create or remove synapses. We prove that for asyn mode, bounded SNPSP systems (where any neuron produces at most one spike each step) are not universal, while unbounded SNPSP systems with weighted synapses (a weight associated with each synapse allows a neuron to produce more than one spike each step) are universal. The latter systems are similar to SNP systems with extended rules in asyn mode (known to be universal) while the former are similar to SNP systems with standard rules only in asyn mode (conjectured not to be universal). Our results thus provide support to the conjecture of the still open problem.Ministerio de Economía y Competitividad TIN2012-3743

Approximation and Computational Complexity of Some Hammock Variations of the Poset Cover Problem

The Hammock(⏟, , … , / )-Poset Cover Problem is a variation of the Poset Cover Problem with the same input – set {, , … , } of linear orders over the set {, , … ,}, but the solution is restricted to a set of simple hammock(⏟, , … , / ) posets. The problem is NP-Hard when ≥ but is in when = . The computational complexity of the problem when = is not yet known. In this paper, we determine the approximation complexity of the cases that have been shown to be NP-Hard. We show that the Hammock(⏟, , … , / )-Poset Cover Problem is in APX and, in particular, ( + / )-approximable, for ≥ . On the other hand, we also explore the computational complexity for the case where = [Hammock(2,2)-Poset Cover Problem]. We show that it is in when the transposition graph of the input set of linear orders is rectangula