Power of controlled insertion and deletion
The paper investigates classes of languages obtained as the closure of certain atomic languages under some insertion and deletion operations. Each of the classes studied is closed under an insertion operation, a deletion operation and an iterative insertion one. The operations are controlled and have been chosen as stated in order to allow an increase as well as a decrease of the length of the words in the operands. The iterative operation has been included in each class to provide an infinite growth of the strings.