Sequential P Systems with Active Membranes Working on Sets

We study variants of P systems that are working in the sequential mode. Usually, they are not computationally complete, but there are possible extensions that can increase the computation power. Extensions that implement a notion of zero-checking are often computationally complete. P systems with an ability to create new membranes are a rare exception as they are known to be computationally complete even in the sequential mode without using a dedicated zero-check operation. Using sets instead of multisets was inspired by Reaction systems and we show how to use this relaxation in the context of active membranes. We challenge the original definition of a membrane creation because possible multiplicity of labels of child membranes are in conflict with no multiplicity of objects in Reaction systems. We propose more suitable notions of membrane creation and prove computational completeness by simulating a register machine.