# Concurrency in Boolean networks

## TL;DR

This paper uses Read Petri Nets to analyze Boolean networks, revealing that traditional update modes may overlook plausible behaviors, and proposes an encoding that captures more accurate dynamics of biological systems.

## Contribution

It introduces a novel encoding of Boolean networks using Read Petri Nets, improving the accuracy of behavioral predictions in biological modeling.

## Key findings

- Traditional updating modes can miss plausible behaviors.
- The proposed encoding captures more behaviors than asynchronous updating.
- The encoding provides a correct abstraction of multivalued refinements.

## Abstract

Boolean networks (BNs) are widely used to model the qualitative dynamics of biological systems. Besides the logical rules determining the evolution of each component with respect to the state of its regulators, the scheduling of component updates can have a dramatic impact on the predicted behaviours. In this paper, we explore the use of Read (contextual) Petri Nets (RPNs) to study dynamics of BNs from a concurrency theory perspective. After showing bi-directional translations between RPNs and BNs and analogies between results on synchronism sensitivity, we illustrate that usual updating modes for BNs can miss plausible behaviours, i.e., incorrectly conclude on the absence/impossibility of reaching specific configurations. We propose an encoding of BNs capitalizing on the RPN semantics enabling more behaviour than the generalized asynchronous updating mode. The proposed encoding ensures a correct abstraction of any multivalued refinement, as one may expect to achieve when modelling biological systems with no assumption on its time features.