Closure properties of certain classes of languages under generalized morphic replication

In this paper a new language operator, a generalized morphic replication, is introduced. Let Ω be a finite set of morphisms and reversal morphisms from ∑* into Δ*, and ω be in Ω*. A morphic replicator is defined as follows: for each x in ∑* define ω(x) to be h₁(x) ... h_m(x), where |ω| = m and ω = h₁ ... h_m. A generalized morphic replication extends ω to languages by ω(L) = {ω(x): x is in L} and to sets W of morphic replicators, where W ⊆ Ω*, W(x) = {ω(x): ω is in W} and W(L) = UW(x), where the union is taken over all x in L.It is shown that the class of languages accepted in real time by a non-deterministic reversal-bounded multitape Turing machine, the class of NP, and the class of the recursively enumerable sets, are all closed under the generalized morphic replication when the morphisms and the reversal morphisms are, respectively, linear-erasing, polynomial-erasing, and arbitrary.