Computational Properties of Two P Systems Solving the 3-colouring Problem

Membrane computing, the research field initiated by Gheorghe Paun in 1998, defines computational models, called P systems, inspired by the behavior and structure of the living cell. Many variants of P systems have been introduced and also used as formal modeling and verification tools. Recently, kernel P systems were introduced as an unifying framework for P systems, which integrates many features of existing P system variants into an elegant and yet powerful modeling formalism. In this paper, we consider a tissue P system with active membranes and a simple kernel P system, both of them solving an NP-complete problem, the 3-colouring problem. In order to compare these two models, we determine, for both of them, the values of the variables corresponding to the colors in a number of particular cases using MeCoSim, a membrane computing simulator, and we deduce some of their nontrivial computational properties. The two models are also implemented in Event-B and properties are formally verified using the ProB model checker associated with the Rodin platform.