  Natural forking in blockchain refers to a phenomenon that there are a set of
blocks at one block height at the same time, implying that various nodes have
different perspectives of the main chain. Natural forking might give rise to
multiple adverse impacts on blockchain, jeopardizing the performance and
security of the system consequently. However, the ongoing literature in
analyzing natural forking is mainly from the macro point of view, which is not
sufficient to incisively understand this phenomenon. In this paper, we fill
this gap through leveraging the large deviation theory to conduct a microscopic
study of natural forking, which resorts to investigating the instantaneous
difference between block generation and dissemination in blockchain. Our work
is derived comprehensively and complementarily via a three-step process, where
both the natural forking probability and its decay rate are presented. Through
solid theoretical derivation and extensive numerical simulations, we find 1)
the probability of the mismatch between block generation and dissemination
exceeding a given threshold dwindles exponentially with the increase of natural
forking robustness related parameter or the difference between the block
dissemination rate and block creation rate; 2) the natural forking robustness
related parameter may emphasize a more dominant effect on accelerating the
abortion of natural forking in some cases; 3) when the self-correlated block
generation rate is depicted as the stationary autoregressive process with a
scaling parameter, it is found that setting a lower scaling parameter may speed
up the failure of natural forking. These findings are valuable since they offer
a fresh theoretical basis to engineer optimal countermeasures for thwarting
natural forking and thereby enlivening the blockchain network.
