Iterated a-NGSM Maps and \Gamma Systems

The notion of an iterated Γ map, that is, a nondeterministic generalized sequential machine with accepting states, is introduced, which leads to the notions of Γ systems and languages. It is shown that the family of Γ languages is equal to the family of recursively enumerable languages. A detailed study is presented of the properties of subfamilies of the family of L languages and their relationship with the various families of L languages is investigated. An example result is that the family of e -free context—sensitive languages is equal to the family of languages generated by extensions of propagating deterministic Γ systems with at most three Γ maps.