Towards a P Systems Normal Form Preserving Step-by-step Behavior

Starting from a compositional operational semantics of transition P Systems we have previously defined, we face the problem of developing an axiomatization that is sound and complete with respect to some behavioural equivalence. To achieve this goal, we propose to transform the systems into a unique normal form which preserves the semantics. As a first step, we introduce axioms which allow the transformation of membrane structures with no dissolving rules into flat membranes. We discuss the problems which arise when dissolving rules are allowed and we suggest possible solutions. We leave as future work the further step that leads to the wanted normal form.