Very Special Languages and Representations of Recursively Enumerable Languages via Computation Histories

A method of encoding the computation histories of a wide class of machines is introduced and used to derive several representation theorems for the class of recursively enumerable languages. In particular it is demonstrated that any recursively enumerable language K ⊂ Σ* can be represented as K = Φ Σ ( R ∩ D 1 ⋮ D 2 ), where D 1 and D 2 are fixed semi-Dyck languages, 〈 is the shuffle operation, R is a regular language depending on K and Φ Σ is a weak identity homomorphism. This result is the natural analog for the recursively enumerable languages of the Chomsky-Shutzenberger representation of the context-free languages.