Atomic Gliders and CA as Language Generators (Extended Version)

TL;DR

This paper formalizes cellular automata as language generators, introducing a glider-based semantics that reveals their ability to produce complex, non-regular languages from simple local rules, with implications for analyzing multi-agent systems.

Contribution

It develops a formal framework for CA as language generators and introduces a novel glider-based semantics to analyze their structured dynamics and computational complexity.

Findings

CA-generated languages can be non-regular and non-context-free.

Regular initial configurations can lead to complex language structures.

The framework links CA dynamics to formal language theory and MAS analysis.

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.