Classical and Quantum Algorithms for the Deterministic L-system Inductive Inference Problem

2024-11-29

arXiv.org

AI Summary

Manual inference of D0L systems in biomorphological modeling is time-consuming and inefficient. Method: We propose the first feature-graph-based automated inference framework, reformulating D0L system identification—from string sequences—into a joint Maximum Independent Set (MIS) and Boolean Satisfiability (SAT) problem on feature graphs, enabling polynomial-time reduction. We introduce a novel feature-graph modeling paradigm and design a dual-track solver: a classical backtracking algorithm ensures exact decidability, while the Quantum Approximate Optimization Algorithm (QAOA) delivers substantial speedup for large-scale instances under polynomial resource constraints. Contribution/Results: Experiments demonstrate that our framework outperforms existing classical heuristic methods in both accuracy and efficiency, offering a scalable, verifiable pathway for automated L-system discovery.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Sampling/Simulation-based Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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-system) 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.

Problem

• D0L Systems
• Automated Image Recognition
• Biological Process Modeling

Innovation

• D0L-System Recognition
• Quantum Computing Approximation
• Feature Mapping