On the Degree of Extension of Some Models Defining Non-Regular Languages

TL;DR

This paper surveys the degree of extension in models defining non-regular languages, including context-free grammars and automata over groups, and explores measures for automata with translucent letters.

Contribution

It compiles key results on non-regularity degrees of context-free grammars and automata over groups, and introduces preliminary findings on automata with translucent letters.

Findings

Main results on non-regularity degree of context-free grammars

Extension degree of automata over groups

Preliminary results on automata with translucent letters

Abstract

This work is a survey of the main results reported for the degree of extension of two models defining non-regular languages, namely the context-free grammar and the extended automaton over groups. More precisely, we recall the main results regarding the degree on non-regularity of a context-free grammar as well as the degree of extension of finite automata over groups. Finally, we consider a similar measure for the finite automata with translucent letters and present some preliminary results. This measure could be considered for many mechanisms that extend a less expressive one.