Under-approximating Cut Sets for Reachability in Large Scale Automata Networks

TL;DR

This paper introduces a new algorithm for efficiently identifying critical local states in large automata networks that are necessary for reachability, aiding analysis of complex biological systems.

Contribution

It presents a novel under-approximate method for computing cut sets in automata networks using a generalized Graph of Local Causality, scalable to large models.

Findings

Able to analyze networks with over 9000 components

Provides potential therapeutic targets in biological models

Enables tractable formal analysis of large-scale systems

Abstract

In the scope of discrete finite-state models of interacting components, we present a novel algorithm for identifying sets of local states of components whose activity is necessary for the reachability of a given local state. If all the local states from such a set are disabled in the model, the concerned reachability is impossible. Those sets are referred to as cut sets and are computed from a particular abstract causality structure, so-called Graph of Local Causality, inspired from previous work and generalised here to finite automata networks. The extracted sets of local states form an under-approximation of the complete minimal cut sets of the dynamics: there may exist smaller or additional cut sets for the given reachability. Applied to qualitative models of biological systems, such cut sets provide potential therapeutic targets that are proven to prevent molecules of interest to become active, up to the correctness of the model. Our new method makes tractable the formal analysis of very large scale networks, as illustrated by the computation of cut sets within a Boolean model of biological pathways interactions gathering more than 9000 components.