Insertion and deletion errors with a forbidden symbol

We study asymmetric insertion and deletion errors in q-ary strings where a fixed symbol, say 0, is forbidden for deletion and insertion. This error generalizes the classical insertion/deletion error and models of restricted deletions, such as deletion of only 0´s in run-length limited strings. We show that the size of an asymmetric insertion set is a constant for strings with fixed number of 0´s, sizes of asymmetric deletion sets obey a monotonicity, and exponentially large codes exist. We show the latter by finding bounds and expressions for sizes of asymmetric insertion and deletion sets and nonasymptotic upper and lower bounds on code sizes.