On the Generative Capacity of Contextual Grammars with Strictly Locally Testable Selection Languages

TL;DR

This paper investigates the generative power of contextual grammars with strictly locally testable selection languages, comparing their language families to those based on various other subregular language classes.

Contribution

It extends the understanding of contextual grammars by analyzing their generative capacity when using strictly locally testable selection languages and compares these to other subregular classes.

Findings

Families generated by these grammars form well-defined language classes.

Strictly locally testable selection languages lead to distinct generative capacities.

Comparison with other subregular classes reveals differences in expressive power.

Abstract

We continue the research on the generative capacity of contextual grammars where contexts are adjoined around whole words (externally) or around subwords (internally) which belong to special regular selection languages. All languages generated by contextual grammars where all selection languages are elements of a certain subregular language family form again a language family. We investigate contextual grammars with strictly locally testable selection languages and compare those families to families which are based on finite, monoidal, nilpotent, combinational, definite, suffix-closed, ordered, commutative, circular, non-counting, power-separating, or union-free languages.