Lindenmayer graph languages, first-order theories and expanders

TL;DR

This paper explores the connection between Lindenmayer graph languages, first-order theories, and expanders, demonstrating how these can be unified within a parallel graph grammar framework and analyzed through automatic structures.

Contribution

It introduces a formalism that unifies combinatorial generation of expanders and Lindenmayer models using parallel graph grammars and automatic structures.

Findings

Unified framework for expanders and Lindenmayer models

First-order properties can be checked via automatic structures

Parallel graph grammar formalism is effective for these models

Abstract

Combinatorial generation of expander families and Lindenmayer-style development models are both parallel in nature. Both can be handled within proposed parallel graph grammar formalism. Their first-order properties can then be checked by encompassing the generated graph language into an appropriate automatic structure.