Reachability problems in BioAmbients

BioAmbients (BA) is a powerful model for representing various aspects of living cells. The model provides a rich set of operations for the movement and interaction of molecules. The richness of the language motivates the study of fragments of the full model and the comparison with other computational models. In this paper, we investigate the impact of the merge capability, used for fusing the contents of two sibling ambients, on the decidability of two reachability problems called Target and Spatial reachability. By enhancing techniques —based on the theory of Petri nets— already used in the context of Mobile Ambients, we prove that both Target and Spatial reachability are decidable for a Turing-complete fragment of BA without merge. Then we extend this fragment with a limited form of merge, that does not reduce the total number of ambients: in this fragment Target reachability is no longer decidable, but by resorting to the theory of Petri nets with transfer arcs we prove that at least Spatial reachability is still decidable. Finally, we show that if we consider the standard merge capability then both reachability problems turn out to be undecidable. Besides characterizing the power of merge, the proof techniques that we use also establish an interesting connection between BA and other computational models like standard Petri nets, their extension with transfer arcs, and Two Counter Machines (a Turing complete formalism based on registers).