# Interactions between Causal Structures in Graph Rewriting Systems

## TL;DR

This paper develops a formal framework to analyze how different causal mechanisms in graph rewriting systems interact, enabling verification of mutual influences and compliance with empirical data in complex molecular models.

## Contribution

It introduces a rigorous method to define and verify interference between mechanisms in graph rewriting systems, advancing understanding of molecular interactions.

## Key findings

- Framework for interference analysis between mechanisms
- Ability to verify if influences are realizable
- Potential to guide rule adjustments for empirical compliance

## Abstract

Graph rewrite formalisms are a powerful approach to modeling complex molecular systems. They capture the intrinsic concurrency of molecular interactions, thereby enabling a formal notion of mechanism (a partially ordered set of events) that explains how a system achieves a particular outcome given a set of rewrite rules. It is then useful to verify whether the mechanisms that emerge from a given model comply with empirical observations about their mutual interference. In this work, our objective is to determine whether a specific event in the mechanism for achieving X prevents or promotes the occurrence of a specific event in the mechanism for achieving Y. Such checks might also be used to hypothesize rules that would bring model mechanisms in compliance with observations. We define a rigorous framework for defining the concept of interference (positive or negative) between mechanisms induced by a system of graph-rewrite rules and for establishing whether an asserted influence can be realized given two mechanisms as an input.