On the Dynamics of PB Systems with Volatile Membranes

We investigate decision problems like reachability and boundedness for extensions of PB systems with volatile membranes. Specifically, we prove that reachability and boundedness are decidable for PB systems extended with rules for membrane dissolution. For PB systems extended with membrane creation, reachability is still decidable whereas boundedness becomes undecidable. Furthermore, we show that both problems are undecidable for PB systems extended with both dissolution and creation rules. Finally, we prove that reachability and boundedness become decidable for PB systems with dissolution rules and in which only one instance of each type of membrane can be created during a computation. Our work extends previous results obtained for PB systems by Dal Zilio and Formenti in a paper appeared in the proceedings