Assembly in Directed Hypergraphs

2025-05-28

AI Summary

This work extends assembly theory to general chemical reaction systems, establishing a unified formal foundation linking it with rule-based double-pushout (DPO) graph rewriting and retrosynthetic analysis. Methodologically, it models assembly processes as the minimum B-hyperpath problem in directed hypergraphs, proving equivalence between assembly pathways and B-hyperpaths; introduces a generic assembly generalization framework that embeds assembly indices into a family of hyperpath cost metrics; and implements automated, efficient computation via integer linear programming (ILP). Key contributions are: (1) a unifying formalism integrating assembly theory, DPO graph rewriting, and retrosynthetic analysis; (2) a theoretical correspondence between assembly complexity and synthesis planning cost functions; and (3) a scalable computational framework enabling automatic generation and optimization of minimum-cost assembly pathways directly from reaction rule systems.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Assembly theory has received considerable attention in the recent past. Here we analyze the formal framework of this model and show that assembly pathways coincide with certain minimal hyperpaths in B-hypergraphs. This makes it possible to generalize the notion of assembly to general chemical reaction systems and to make explicit the connection to rule based models of chemistry, in particular DPO graph rewriting. We observe, furthermore, that assembly theory is closely related to retrosynthetic analysis in chemistry. The assembly index fits seamlessly into a large family of cost measures for directed hyperpath problems that also encompasses cost functions used in computational synthesis planning. This allows to devise a generic approach to compute complexity measures derived from minimal hyperpaths in rule-derived directed hypergraphs using integer linear programming.

Problem

• Generalize assembly theory to chemical reaction systems
• Connect assembly pathways to DPO graph rewriting
• Compute complexity measures via integer linear programming

Innovation

• Minimal hyperpaths in B-hypergraphs
• Connection to DPO graph rewriting
• Integer linear programming for complexity