Abstract:We introduce a normal form for context-free grammars, called Dyck normal form. This is a syntactical restriction of the Chomsky normal form, in which the two nonterminals occurring on the right-hand side of a rule are paired nonterminals. This pairwise property allows to define a homomorphism from Dyck words to words generated by a grammar in Dyck normal form. We prove that for each context-free language L, there exist an integer K and a homomorphism ϕ such that L = ϕ(D K ), where D K ⊆ D K , and D K is the on… Show more
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