Sequential P Systems with Unit Rules and Energy Assigned to Membranes

We introduce a new variant of membrane systems where the rules are directly assigned to membranes (and not to the regions as this is usually observed in the area of membrane systems) and, moreover, every membrane carries an energy value that can be changed during a computation by objects passing through the membrane. For the application of rules leading from one configuration of the system to the succeeding configuration we consider a sequential derivation mode and do not use the mode of maximal parallelism. The result of a successful computation is considered to be the distribution of energy values carried by the membranes. We show that for such systems using a kind of priority relation on the rules we already obtain universal computational power. When omitting the priority relation, we obtain a characterization of the family of Parikh sets generated by context-free matrix grammars (with lambda-rules).