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

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.