On the Robust Power of Morphogenetic Systems for Time Bounded Computation

The time appears ripe to enrich the original idea of membrane computing with principles of self-assembly in space. To this effect, a first step was taken with the introduction of a new such family of models M systems (for morphogenetic system) that own a number of basic macro-properties exhibited by higher living organisms (such as self-assembly, cell division akin to mitosis and self-healing), while still only leveraging local interactions of simple atomic components and explicit geometric constraints of their constituting elements. Here we further demonstrate that, experimentally in silico, M systems are in general also capable of demonstrating these properties robustly after being assembled from scratch from some atomic components and entering a homeostatic regime. The results are obtained through a series of experiments carried out with an M system simulator designed to implement this kind of model by researchers interested in exploring new capabilities. We further define probabilistic complexity classes for M systems and we show that the model is theoretically capable of solving NP-complete problems in P-time, despite apparent problems of an implementation, such as kinetic and concentration bottlenecks.