Tackling Universal Properties of Minimal Trap Spaces of Boolean Networks

TL;DR

This paper develops a logical reasoning framework using CEGAR and ASP to analyze universal properties of minimal trap spaces in Boolean networks, aiding in reprogramming and synthesis tasks.

Contribution

It introduces a novel CEGAR-based method for solving complex $orallorallorall$ satisfiability problems related to MTSs in Boolean networks, with practical biological applications.

Findings

Efficiently solves $orallorallorall$ formulas for MTS properties

Prototype implementation demonstrates tractability on biological network models

Enables reprogramming and synthesis of Boolean networks based on universal properties

Abstract

Minimal trap spaces (MTSs) capture subspaces in which the Boolean dynamics is trapped, whatever the update mode. They correspond to the attractors of the most permissive mode. Due to their versatility, the computation of MTSs has recently gained traction, essentially by focusing on their enumeration. In this paper, we address the logical reasoning on universal properties of MTSs in the scope of two problems: the reprogramming of Boolean networks for identifying the permanent freeze of Boolean variables that enforce a given property on all the MTSs, and the synthesis of Boolean networks from universal properties on their MTSs. Both problems reduce to solving the satisfiability of quantified propositional logic formula with 3 levels of quantifiers ($\exists\forall\exists$). In this paper, we introduce a Counter-Example Guided Refinement Abstraction (CEGAR) to efficiently solve these problems by coupling the resolution of two simpler formulas. We provide a prototype relying on Answer-Set Programming for each formula and show its tractability on a wide range of Boolean models of biological networks.