Extended Spiking Neural P Systems with White Hole Rules

We consider extended spiking neural P systems with the additional possibility of so-called \white hole rules", which send the complete contents of a neuron to other neurons, and we show how this extension of the original model allow for easy proofs of the computational completeness of this variant of extended spiking neural P systems using only one actor neuron. Using only such white hole rules, we can easily simulate special variants of Lindenmayer systems

Uniform solutions to SAT and Subset Sum by spiking neural P systems

We continue the investigations concerning the possibility of using spiking neural P systems as a framework for solving computationally hard problems, addressing two problems which were already recently considered in this respect: Subset Sum and SAT: For both of them we provide uniform constructions of standard spiking neural P systems (i.e., not using extended rules or parallel use of rules) which solve these problems in a constant number of steps, working in a non-deterministic way. This improves known results of this type where the construction was non-uniform, and/or was using various ingredients added to the initial definition of spiking neural P systems (the SN P systems as defined initially are called here ‘‘standard’’). However, in the Subset Sum case, a price to pay for this improvement is that the solution is obtained either in a time which depends on the value of the numbers involved in the problem, or by using a system whose size depends on the same values, or again by using complicated regular expressions. A uniform solution to 3-SAT is also provided, that works in constant time.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-581Ministerio de Educación y Ciencia HI 2005-019

Solving constraint-satisfaction problems with distributed neocortical-like neuronal networks

Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by networks composed of homogeneous cooperative-competitive modules that have connectivity similar to motifs observed in the superficial layers of neocortex. The winner-take-all modules are sparsely coupled by programming neurons that embed the constraints onto the otherwise homogeneous modular computational substrate. We show rules that embed any instance of the CSPs planar four-color graph coloring, maximum independent set, and Sudoku on this substrate, and provide mathematical proofs that guarantee these graph coloring problems will convergence to a solution. The network is composed of non-saturating linear threshold neurons. Their lack of right saturation allows the overall network to explore the problem space driven through the unstable dynamics generated by recurrent excitation. The direction of exploration is steered by the constraint neurons. While many problems can be solved using only linear inhibitory constraints, network performance on hard problems benefits significantly when these negative constraints are implemented by non-linear multiplicative inhibition. Overall, our results demonstrate the importance of instability rather than stability in network computation, and also offer insight into the computational role of dual inhibitory mechanisms in neural circuits.Comment: Accepted manuscript, in press, Neural Computation (2018

P Systems with Anti-Matter

After a short introduction to the area of membrane computing (a branch of natural computing), we introduce the concept of anti-matter in membrane computing. First we consider spiking neural P systems with anti-spikes, and then we show the power of anti-matter in cell-like P systems. As expected, the use of anti-matter objects and especially of matter/anti-matter annihilation rules, turns out to be rather powerful: computational completeness of P systems with anti-matter is obtained immediately, even without using catalysts. Finally, some open problems are formulated, too