P versus B: P Systems as a Formal Framework for Controllability of Boolean Networks

TL;DR

This paper explores the use of P systems as a formal framework for analyzing the controllability of Boolean networks, bridging biological inspiration with computational modeling.

Contribution

It introduces Boolean P systems tailored for controlling Boolean networks and demonstrates their effectiveness in formal reasoning about controllability.

Findings

Boolean P systems successfully model sequential controllability.

The framework embeds controllability properties within P systems.

Technical challenges in modeling are addressed and overcome.

Abstract

Membrane computing and P systems are a paradigm of massively parallel natural computing introduced by Gheorghe P\u{a}un in 1999, inspired by the structure of the living cell and by its biochemical reactions. In spite of this explicit biological motivation, P systems have not been extensively used in modelling real-world systems. To confirm this intuition, we establish a state of the art investigation comparing the use of P systems to that of Boolean networks in this line of research. We then propose to use P systems as a tool for setting up formal frameworks to reason about other formalisms, and we introduce Boolean P systems, specifically tailored for capturing sequential controllability of Boolean networks. We show how to tackle some technical challenges and prove that sequential controllability properly embeds in the framework of Boolean P systems.