Alternative representations of P systems solutions to the graph colouring problem

Abstract

This paper first presents a simulation of the simple kernel P systems solution to the graph 3-colouring problem presented in a previous paper by Gheorghe et al., implemented in a programming style named Concurrent ML, which is based on the concept of synchronous communication between logical processing elements. This paper then presents and informally analyses an alternative compact single-cell solution to the same problem using P systems with compound objects (cP systems), which has the benefit of naturally adapting to the use of any number of colours greater than zero—only the specified colour symbols need to be changed. Successful and failing examples of the latter solution are also presented.