# Optimal L-Systems for Stochastic L-system Inference Problems

arXiv: https://arxiv.org/abs/2409.02259 · HTML: https://mlsanity.com/paper/2409.02259/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 16 references that are in the map.
- First posted on arXiv 3 Sep 2024.

## Builds on (most cited first, 3 of 3)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Techniques for Inferring Context-Free Lindenmayer Systems With Genetic Algorithm](https://mlsanity.com/paper/1906.08860/) (2019)
- [Stochastic L-system Inference from Multiple String Sequence Inputs](https://mlsanity.com/paper/2001.10922/) (2020)

## Built on by (most cited first, 2 of 2)

- [A Graph-Based Classical and Quantum Approach to Deterministic L-System Inference](https://mlsanity.com/paper/2411.19906/) (2024)
- [FloraForge: LLM-Assisted Procedural Generation of Editable and Analysis-Ready 3D Plant Geometric Models For Agricultural Applications](https://mlsanity.com/paper/2512.11925/) (2025)

## Abstract (arXiv)

This paper presents two novel theorems that address two open problems in stochastic Lindenmayer-system (L-system) inference, specifically focusing on the construction of an optimal stochastic L-system capable of generating a given sequence of strings. The first theorem delineates a method for crafting a stochastic L-system that has the maximum probability of a derivation producing a given sequence of words through a single derivation (noting that multiple derivations may generate the same sequence). Furthermore, the second theorem determines the stochastic L-systems with the highest probability of producing a given sequence of words with multiple possible derivations. From these, we introduce an algorithm to infer an optimal stochastic L-system from a given sequence. This algorithm incorporates advanced optimization techniques, such as interior point methods, to ensure the creation of a stochastic L-system that maximizes the probability of generating the given sequence (allowing for multiple derivations). This allows for the use of stochastic L-systems as a model for machine learning using only positive data for training.