P systems with minimal insertion and deletion

In this paper, we consider insertion–deletion P systems with priority of deletion over insertion. We show that such systems with one-symbol context-free insertion and deletion rules are able to generate Parikh sets of all recursively enumerable languages (PsRE). If a one-symbol one-sided context is added to the insertion or deletion rules, then all recursively enumerable languages can be generated. The same result holds if a deletion of two symbols is permitted. We also show that the priority relation is very important, and in its absence the corresponding class of P systems is strictly included in the family of matrix languages (MAT).