  We consider the (one-dimensional) array counterpart of contextual as well as
insertion and deletion string grammars and consider the operations of array
insertion and deletion in array grammars. First we show that the emptiness
problem for P systems with (one-dimensional) insertion rules is undecidable.
Then we show computational completeness of P systems using (one-dimensional)
array insertion and deletion rules even of norm one only. The main result of
the paper exhibits computational completeness of one-dimensional array grammars
using array insertion and deletion rules of norm at most two.

Formal Languages and Automata Theory