Computing Homology Groups in Binary 2D Imagery by Tissue-like P Systems

Abstract

We present a new solution for the Homology Groups of Binary 2D Image (HGB2I) Problem by using Membrane Computing techniques. This is a classical problem in Homology Theory which tries to calculate the number of connected components and the representative curves of the holes of these components from a given binary 2D image. To this aim, we present a family of P systems which solves all the instances of the problem in the framework of Tissue-like P systems with catalysts. This is a new framework which combines the membrane structure and symport-antiport communication rules of tissue- like P systems with the power of catalysts.