Collapsing Hierarchies of Parallel Rewriting P Systems without target conflicts

We continue the investigation of parallel rewriting P systems without target conflicts, a class of rewriting P systems with parallel application of evolution rules where the possible consistency problems for the communication of the resulting strings are eliminated by not allowing the application of conflicting rules. We refine and improve some of the previously known results about the generative power of these systems and point out the problems which are still open for investigation.