A truely morphic characterization of recursively enumerable sets

Abstract

Continuing recent research of [3–9] et al. we study the composition of homomorphisms, inverse homomorphisms and twin-morphisms 〈g,h〉 and 〈g,h〉⁻¹, where 〈g,h〉 (w) = g(w) ∩ h(w) and 〈g,h〉⁻¹ (w) = g⁻¹(w) ∩ h⁻¹ (w). We investigate some properties of these morphic mappings and concentrate on a characterization of the recursively enumerable sets, which says: For every recursively enumerable set L there exist four homomorphisms such that L=f₁ ° <f₂, f₃> ° f ^-1₄ ({$}) and L=h₁ ° <h₂, h₃>^-1 ° h ^-1₄ ({$}), and four homomorphisms are minimal for such representations.