P systems with symport/antiport rules: The traces of objects

We continue here the study of those P systems where the computation is performed by the communication of objects, that is, systems with symport and antiport rules. Instead of the (number of) objects collected in a specified membrane, as the result of a computation we consider the itineraries of a certain object through membranes, during a halting computation, written as a coding of the string of labels of the visited membranes. The family of languages generated in this way is investigated with respect to its place in the Chomsky hierarchy. When the (symport and antiport) rules are applied in a conditional manner, promoted or inhibited by certain objects which should be present in the membrane where a rule is applied, then a characterization of recursively enumerable languages is obtained; the power of systems with the rules applied freely is only partially described.