Local generation of languages: the monotonic binary sequences

2026-01-09

arXiv.org

AI Summary

This study investigates how monotone binary sequence languages can be generated through constrained local communication mechanisms modeled by simplicial complexes. It formalizes the language generation problem for the first time within a simplicial-complex-based local communication framework, bridging algebraic topology and formal language theory to systematically establish connections between generative capacity and the topological structure of the underlying complex. The main contributions include proving several general results and providing a complete characterization of multiple classes of minimal simplicial complexes capable of generating such languages, thereby revealing how topological constraints fundamentally influence computational expressiveness.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Natural Language Processing: Generation
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

In a previous article, we have introduced the problem of local generation of languages, where the communication underlying the generation procedure is captured by a simplicial complex. We study in details this problem for the language of binary monotonic sequences. We prove general results and identify several classes of minimal simplicial complexes generating this language.

Problem

• local generation
• monotonic binary sequences
• simplicial complex
• formal languages

Innovation

• local generation
• monotonic binary sequences
• simplicial complex
• formal languages
• minimal complexes