Merging two Hierarchies of Internal Contextual Grammars with Subregular Selection

TL;DR

This paper explores the combination of two hierarchies of internal contextual grammars based on subregular language classes, advancing understanding of their computational power and relationships.

Contribution

It introduces a unified hierarchy for internal contextual grammars by merging two existing hierarchies based on structural properties and resource constraints.

Findings

Merged hierarchies for internal contextual grammars are established.

Comparison of language families shows the relationships between different subregular classes.

The research extends previous work on external grammars to internal grammars.

Abstract

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.