We deal with a normal form for context-free grammars, called Dyck normal form. This normal form 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, along with several other terminal rewriting conditions, makes it possible 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 phi such that L=phi(D'_K), where D'_K is a subset of D_K and D_K is the one-sided Dyck language over K letters. As an application we give an alternative proof of the inclusion of the class of even linear languages in AC1.

翻译：我们研究上下文无关文法的一种范式，称为Dyck范式。这种范式是Chomsky范式的语法限制，其中规则右侧出现的两个非终结符是配对的非终结符。这种配对性质以及若干其他终结符重写条件，使得能够定义从Dyck词到由Dyck范式文法生成的词的同态。我们证明，对于每个上下文无关语言L，存在一个整数K和一个同态φ，使得L=φ(D'_K)，其中D'_K是D_K的子集，D_K是K个字母上的单边Dyck语言。作为一种应用，我们给出了偶数线性语言类包含于AC1的另一种证明。