A Graph-Based Classical and Quantum Approach to Deterministic L-System Inference

TL;DR

This paper presents a novel method to automatically infer deterministic L-systems from data using a graph-based approach, translating the problem into MIS and SAT, and introduces both classical and quantum algorithms for solution.

Contribution

It introduces the characteristic graph for L-system inference and develops classical and quantum algorithms, enabling polynomial-time inference from data.

Findings

Classical exact algorithm for D0L-system inference.

Approximate quantum algorithm for the same problem.

Polynomial-time translation of inference into MIS and SAT problems.

Abstract

L-systems can be made to model and create simulations of many biological processes, such as plant development. Finding an L-system for a given process is typically solved by hand, by experts, in a massively time-consuming process. It would be significant if this could be done automatically from data, such as from sequences of images. In this paper, we are interested in inferring a particular type of L-system, deterministic context-free L-system (D0L-system) from a sequence of strings. We introduce the characteristic graph of a sequence of strings, which we then utilize to translate our problem (inferring D0L-systems) in polynomial time into the maximum independent set problem (MIS) and the SAT problem. After that, we offer a classical exact algorithm and an approximate quantum algorithm for the problem.