On the flora of asynchronous locally non-monotonic Boolean automata networks

TL;DR

This paper investigates the asynchronous dynamics of non-monotonic Boolean automata networks, specifically xor-BANs, providing characterizations, descriptions of specific classes, and new bisimulation equivalences.

Contribution

It offers the first comprehensive analysis of asynchronous non-monotonic BANs, introducing algorithmic characterizations and describing dynamics of xor-Flowers and xor-Cycle Chains.

Findings

Characterization of asynchronous transition graphs for cactus xor-BANs

Complete description of xor-Flowers and xor-Cycle Chains dynamics

Introduction of new bisimulation equivalences for xor-BANs

Abstract

Boolean automata networks (BANs) are a well established model for biological regulation systems such as neural networks or genetic networks. Studies on the dynamics of BANs, whether it is synchronous or asynchronous, have mainly focused on monotonic networks, where fundamental questions on the links relating their static and dynamical properties have been raised and addressed. This paper explores analogous questions on asynchronous non-monotonic networks, xor-BANs, that are BANs where all the local transition functions are xor-functions. Using algorithmic tools, we give a general characterisation of the asynchronous transition graphs for most of the cactus xor-BANs and strongly connected xor-BANs. As an illustration of the results, we provide a complete description of the asynchronous dynamics of two particular classes of xor-BAN, namely xor-Flowers and xor-Cycle Chains. This work also leads to new bisimulation equivalences specific to xor-BANs.