title: Spiking neural P systems with weights.
abstract: A variant of spiking neural P systems with positive or negative weights on synapses is introduced, where the rules of a neuron fire when the potential of that neuron equals a given value. The involved values-weights, firing thresholds, potential consumed by each rule-can be real (computable) numbers, rational numbers, integers, and natural numbers. The power of the obtained systems is investigated. For instance, it is proved that integers (very restricted: 1, -1 for weights, 1 and 2 for firing thresholds, and as parameters in the rules) suffice for computing all Turing computable sets of numbers in both the generative and the accepting modes. When only natural numbers are used, a characterization of the family of semilinear sets of numbers is obtained. It is shown that spiking neural P systems with weights can efficiently solve computationally hard problems in a nondeterministic way. Some open problems and suggestions for further research are formulated.
authors.affiliation: Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China. junwangjf@gmail.com
authors.forename: Jun
authors.initials: J
authors.lastname: Wang
authors.forename: Hendrik Jan
authors.initials: HJ
authors.lastname: Hoogeboom
authors.forename: Linqiang
authors.initials: L
authors.lastname: Pan
authors.forename: Gheorghe
authors.initials: G
authors.lastname: Păun
authors.forename: Mario J
authors.initials: MJ
authors.lastname: Pérez-Jiménez
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D000818:Animals; D001921:Brain / Q000502:physiology; D003198:Computer Simulation / Q000592:standards*; D006801:Humans; D009415:Nerve Net / Q000502:physiology; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D009435:Synaptic Transmission / Q000502:physiology*