Summary. In this paper we consider insertion-deletion P systems with priority of deletion over the insertion. We show that such systems with one symbol context-free insertion and deletion rules are able to generate P sRE. If one-symbol one-sided context is added to insertion or deletion rules but no priority is considered, 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 MAT. 1

Summary. In this article we investigate insertion systems of small size in the framework of P systems. We consider P systems with insertion rules having one symbol context and we show that they have the computational power of matrix grammars. If contexts of length two are permitted, then any recursively enumerable language can be generated. In both cases an inverse morphism and a weak coding were applied to the output of the corresponding P systems. 1

Recent investigations show insertion-deletion systems of small size that are not complete and cannot generate all recursively enumerable languages. However, if additional computational distribution mechanisms like P systems are added, then the computational completeness is achieved in some cases. In this article we take two insertion-deletion systems that are not computationally complete, consider them in the framework of P systems and show that the computational power is strictly increased by proving that any recursively enumerable language can be generated. At the end some open problems are presented. 1