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We introduce a normal form for context-free grammars, called Dyck normalform. This is a syntactical restriction of the Chomsky normal form, in whichthe two nonterminals occurring on the right-hand side of a rule are pairednonterminals. This pairwise property allows to define a homomorphism from Dyckwords to words generated by a grammar in Dyck normal form. We prove that foreach context-free language L, there exist an integer K and a homomorphism hsuch that L=h(D'_K), where D'_K is a subset of the one-sided Dyck language overK letters. Through a transition-like diagram for a context-free grammar in Dycknormal form, we effectively build a regular language R that satisfies theChomsky-Schutzenberger theorem. Using graphical approaches we refine R suchthat the Chomsky-Schutzenberger theorem still holds. Based on this readjustmentwe sketch a transition diagram for a regular grammar that generates a regularsuperset approximation for the initial context-free language.

Around Context-Free Grammars -- a Normal Form, a Representation Theorem, and a Regular Approximation