Spiking Neural P Systems with Structural Plasticity: Attacking the Subset Sum Problem

Spiking neural P systems with structural plasticity (in short, SNPSP systems) are models of computations inspired by the function and structure of biological neurons. In SNPSP systems, neurons can create or delete synapses using plasticity rules. We report two families of solutions: a non-uniform and a uniform one, to the NP-complete problem Subset Sum using SNPSP systems. Instead of the usual rule-level nondeterminism (choosing which rule to apply) we use synapse-level nondeterminism (choosing which synapses to create or delete). The nondeterminism due to plasticity rules have the following improvements from a previous solution: in our non-uniform solution, plasticity rules allowed for a normal form to be used (i.e. without forgetting rules or rules with delays, system is simple, only synapse-level nondeterminism); in our uniform solution the number of neurons and the computation steps are reduced.Ministerio de Economía y Competitividad TIN2012-3743

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

On Complexity Classes of Spiking Neural P Systems

A sequence of papers have been recently published, pointing out various intractable problems which may be solved in certain fashions within the framework of spiking neural (SN) P systems. On the other hand, there are also results demonstrating limitations of SN P systems. In this paper we define recognizer SN P systems providing a general platform for this type of results. We intend to give a more systematic characterization of computational power of variants of SN P systems, and establish their relation to standard complexity classes

Frontiers of Membrane Computing: Open Problems and Research Topics

This is a list of open problems and research topics collected after the Twelfth Conference on Membrane Computing, CMC 2012 (Fontainebleau, France (23 - 26 August 2011), meant initially to be a working material for Tenth Brainstorming Week on Membrane Computing, Sevilla, Spain (January 30 - February 3, 2012). The result was circulated in several versions before the brainstorming and then modified according to the discussions held in Sevilla and according to the progresses made during the meeting. In the present form, the list gives an image about key research directions currently active in membrane computing

A Model of an Oscillatory Neural Network with Multilevel Neurons for Pattern Recognition and Computing

The current study uses a novel method of multilevel neurons and high order synchronization effects described by a family of special metrics, for pattern recognition in an oscillatory neural network (ONN). The output oscillator (neuron) of the network has multilevel variations in its synchronization value with the reference oscillator, and allows classification of an input pattern into a set of classes. The ONN model is implemented on thermally-coupled vanadium dioxide oscillators. The ONN is trained by the simulated annealing algorithm for selection of the network parameters. The results demonstrate that ONN is capable of classifying 512 visual patterns (as a cell array 3 * 3, distributed by symmetry into 102 classes) into a set of classes with a maximum number of elements up to fourteen. The classification capability of the network depends on the interior noise level and synchronization effectiveness parameter. The model allows for designing multilevel output cascades of neural networks with high net data throughput. The presented method can be applied in ONNs with various coupling mechanisms and oscillator topology.Comment: 26 pages, 24 figure

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Solving the Partition Problem by Using Tissue-like P Systems with Cell Division

Tissue-like P systems with cell division is a computing model in the framework of Membrane Computing that shares with the spiking neural P system model a similar biological inspiration. Namely, both models are based on the intercellular communication and cooperation between neurons, respectively. Due to this fact, in both models the devices have the same structure: a network of elementary units (cells in a tissue and interconnected neurons, respectively). Nonetheless, the two models are quite different. One of the differences is the ability of tissue-like P systems with cell division for increasing the number of cells during the computation. In this paper we exploit this ability and present a polynomial-time solution for the (NP-complete) Partition problem via a uniform family of such P systems.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58