Forbidden-Context & Ordered Grammar Systems

TL;DR

This paper explores the integration of forbidden random context and ordered grammars into cooperating distributed grammar systems, clarifying their generative capacities and resolving open problems in regulated rewriting.

Contribution

It introduces new combinations of grammar ideas within CDGS, providing a comprehensive classification and solving longstanding open questions.

Findings

Identified five key classes of languages from the combinations.

Clarified the relationships among these language classes.

Resolved several open problems in the literature.

Abstract

In this paper, we consider combining the ideas of forbidden random context grammars as well as of ordered grammars with cooperating distributed grammar systems (CDGS). We focus on investigating their generative capacities. Both ideas can be added to CDGS in two ways: either having (e.g.) a strict order of the rules in each component, or having a strict order on the components. This leads to four different scenarios, only some of them have been addressed in the literature before. While in the area of CDGS, many inclusions among language classes have been %are still open questions for decades, the proposed addition of forbidden random context and ordered regulation variants leads to a clear picture which allows us to get down to only five different classes of languages well known from classical regulated rewriting. This way, we also solve some open problems from the literature.