Forbidden-Context & Ordered Grammar Systems

2026-04-21

AI Summary

This study addresses a long-standing open problem concerning language class inclusions in cooperative distributed grammar systems (CDGS) by systematically integrating two regulatory mechanisms—forbidding random context and ordered rules—into the CDGS framework for the first time. The authors construct four novel model variants that operate along two dimensions: rule ordering within components and execution ordering across components. Employing formal language-theoretic methods, they precisely characterize the generative power of these models, establishing exact equivalences with five well-known classes of controlled rewriting languages. This work not only resolves several previously unsettled inclusion relationships reported in the literature but also clarifies the formerly ambiguous hierarchy of language classes and substantially streamlines the theoretical foundation of CDGS.

Technology Category

Constraint Satisfaction and Optimization: Distributed CSP/OptimizationCognitive Modeling & Cognitive Systems: Computational CreativityKnowledge Representation and Reasoning: Knowledge Representation Languages

Application Category

Web Mining and Content Analysis: Models for Web evolutionSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semanticsGraph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

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.

Problem

• cooperating distributed grammar systems
• forbidden random context grammars
• ordered grammars
• generative capacity
• language classes

Innovation

• forbidden random context
• ordered grammar
• cooperating distributed grammar systems
• regulated rewriting
• generative capacity