  Motivated by work on bio-operations on DNA strings, we consider an
outfix-guided insertion operation that can be viewed as a generalization of the
overlap assembly operation on strings studied previously. As the main result we
construct a finite language $L$ such that the outfix-guided insertion closure
of $L$ is non-regular. We consider also the closure properties of regular and
(deterministic) context-free languages under the outfix-guided insertion
operation and decision problems related to outfix-guided insertion. Deciding
whether a language recognized by a deterministic finite automaton is closed
under outfix-guided insertion can be done in polynomial time. The complexity of
the corresponding question for nondeterministic finite automata remains open.
