In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. In the past, two independent hierarchies have been obtained for external and internal contextual grammars, one based on selection languages defined by structural properties (finite, monoidal, nilpotent, combinational, definite, ordered, non-counting, power-separating, suffix-closed, commutative, circular, or union-free languages), the other one based on selection languages defined by resources (number of non-terminal symbols, production rules, or states needed for generating or accepting them). In a previous paper, the language families of these hierarchies for external contextual grammars were compared and the hierarchies merged. In the present paper, we compare the language families of these hierarchies for internal contextual grammars and merge these hierarchies.
翻译:本文继续研究选择语言来自正则语言子族的上下文语法的能力。过去,针对外部和内部上下文语法分别得到了两个独立的层级:一个基于由结构特性定义的选择语言(有限、幺半群、幂零、组合、确定、有序、非计数、幂分离、后缀封闭、交换、圆形或无联合语言),另一个基于由资源定义的选择语言(生成或接受它们所需的非终结符号、产生式规则或状态的数量)。在先前的一篇论文中,比较了这些用于外部上下文语法的层级中的语言族并合并了层级。在本文中,我们比较了这些用于内部上下文语法的层级中的语言族,并合并了这些层级。