Strictly Locally Testable and Resources Restricted Control Languages in Tree-Controlled Grammars

TL;DR

This paper explores the expressive power of tree-controlled grammars with control languages that are strictly locally testable or resource-restricted, analyzing their generative capacity and set relations among these language families.

Contribution

It introduces new insights into the generative capabilities of tree-controlled grammars with specific regular control languages and studies their set-theoretic relationships.

Findings

Characterization of generative capacity for strictly locally testable control languages

Analysis of resource-restricted control language families

Set inclusion relations among subregular language families

Abstract

Tree-controlled grammars are context-free grammars where the derivation process is controlled in such a way that every word on a level of the derivation tree must belong to a certain control language. We investigate the generative capacity of such tree-controlled grammars where the control languages are special regular sets, especially strictly locally testable languages or languages restricted by resources of the generation (number of non-terminal symbols or production rules) or acceptance (number of states). Furthermore, the set theoretic inclusion relations of these subregular language families themselves are studied.