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

Abstract

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.