# A P Systems Variant for Reasoning about Sequential Controllability of Boolean Networks

## TL;DR

This paper introduces Boolean P systems, a new formalism tailored for reasoning about the sequential controllability of Boolean networks, establishing its computational complexity as PSPACE-complete.

## Contribution

The paper proposes a novel Boolean P systems formalism for analyzing Boolean networks and formalizes the sequential controllability problem within this framework.

## Key findings

- Proves that the sequential controllability problem is PSPACE-complete.
- Demonstrates how P systems can be adapted for specific reasoning tasks.
- Provides a formal foundation for future research in biological network control.

## Abstract

A Boolean network is a discrete dynamical system operating on vectors of Boolean variables. The action of a Boolean network can be conveniently expressed as a system of Boolean update functions, computing the new values for each component of the Boolean vector as a function of the other components. Boolean networks are widely used in modelling biological systems that can be seen as consisting of entities which can be activated or deactivated, expressed or inhibited, on or off. P systems on the other hand are classically introduced as a model of hierarchical multiset rewriting. However, over the years the community has proposed a wide range of P system variants including diverse ingredients suited for various needs. In this work, we propose a new variant -- Boolean P systems -- specifically designed for reasoning about sequential controllability of Boolean networks, and use it to first establish a crisp formalization of the problem, and then to prove that the problem of sequential controllability is PSPACE-complete. We further claim that Boolean P systems are a demonstration of how P systems can be used to construct ad hoc formalisms, custom-tailored for reasoning about specific problems, and providing new advantageous points of view.