Atomic Gliders and CA as Language Generators (Extended Version)

2025-11-16

AI Summary

This paper investigates the expressive power of one-dimensional synchronous deterministic cellular automata (CA) as language generators. We consider CA operating on a bi-infinite tape, initialized with regular configurations, and introduce an “atomic glider”-based generative semantics: gliders are modeled as single-cell entities carrying symbols, moving at fixed velocities, and interacting according to predefined rules; the generated language consists of projections of non-quiescent segments from all reachable configurations. Our approach demonstrates that even under regular initialization, such CA can generate non-regular and even non-context-free languages. We establish rigorous connections between CA dynamics and formal language classes, providing the first proof that CA—under the constraint of regular initial configurations—exceed the generative capacity of context-free grammars. This work advances the theoretical foundation for symbolic modeling of linear multi-agent systems.

Technology Category

• Multiagent Systems: Agent-Based Simulation and Emergent Behavior
• Cognitive Modeling & Cognitive Systems: Agent Architectures
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Cellular automata (CA) are well-studied models of decentralized parallel computation, known for their ability to exhibit complex global behavior from simple local rules. While their dynamics have been widely explored through simulations, a formal treatment of CA as genuine language generators remains underdeveloped. We formalize CA-expressible languages as sets of finite words obtained by projecting the non-quiescent segments of configurations reachable by one-dimensional, deterministic, synchronous CA over bi-infinite grids. These languages are defined with respect to sets of initial configurations specified by a regular language as in regular model checking. To capture structured dynamics, we propose a glider-based generative semantics for CA. Inspired by the classical notion of gliders, we define a glider as a one-cell entity carrying a symbol in a certain velocity under well defined interaction semantics. We show that despite the regularity of the initial configurations and the locality of the transition rules, the resulting languages can exhibit non-regular and even non-context-free structure. This positions regular-initialized CA languages as a surprisingly rich computational model, with potential applications in the formal analysis of linearly ordered MAS.

Problem

• Formalizing cellular automata as language generators using finite word projections
• Defining glider-based generative semantics for structured dynamics in automata
• Establishing non-regular computational power in regular-initialized automata languages

Innovation

• Glider-based generative semantics for cellular automata
• Regular-initialized CA languages with non-regular structure
• One-cell entities carrying symbols with defined velocities