Solving Numerical NP-Complete Problems with Spiking Neural P Systems

Abstract

Starting from an extended nondeterministic spiking neural P system that solves the Subset Sum problem in a constant number of computation steps, recently proposed in a previous paper, we investigate how different properties of spiking neural P systems affect the capability to solve numerical NP–complete problems. In particular, we show that by using maximal parallelism we can convert any given integer number from the usual binary notation to the unary form, and thus we can initialize the above P system with the required (exponential) number of spikes in polynomial time. On the other hand, we prove that this conversion cannot be performed in polynomial time if the use of maximal parallelism is forbidden. Finally, we show that if we can choose whether each neuron works in the nondeterministic vs. deterministic and/or in the maximal parallel vs. sequential way, then there exists a uniform family of spiking neural P systems that solves the Subset Sum problem.