We present some high-level open problems in the complexity theory of membrane systems, related to the actual computing power of confluence vs determinism, semi-uniformity vs uniformity, deep vs shallow membrane structures, membrane division vs internal evolution of membranes. For each of these problems we present some reasonable approaches that are, however, unable to be employed “as-is” to provide a complete solution. This will hopefully sparkle new ideas that will allow tackling these open problems.
