In this paper, we obtain some refinement of representation theorems for context-free languages by using Dyck languages, insertion systems, strictly locally testable languages, and morphisms. For instance, we improved the Chomsky-Schiitzenberger representation theorem and show that each context-free language L can be represented in the form L = h(D ∩ R), where D is a Dyck language, R is a strictly 3-testable language, and ft is a morphism. A similar representation for context-free languages can be obtained, using insertion systems of weight (3,0) and strictly 4-testable languages.
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