Probabilistic Analysis of Validator Lifecycle and Fork Resolution in Ethereum 2.0-Like PoS System

Ethereum 2.0 uses a Proof-of-Stake-based consensus which aims to minimize the impact of malicious validators by decentralizing the voting protocol. In this paper we investigate the lifecycle of a validator in a consensus protocol similar to Ethereum 2.0 but with simplifications introduced for tractability. In particular, the protocol operates with near-single slot finality and includes the impact of behaviors such as truthful and false voting, abstention from voting, voluntary exit from the validator committee, and return to the committee upon depositing the required stake. Using probabilistic techniques and a Markov chain model, we examine the impact of all those factors on consensus probability. Our results indicate that the probability of truthful voting has a predominant effect on consensus, although the interplay between probabilities of voluntary exit and waiting before returning to the committee also plays an important role. We also investigate the process of fork resolution and model the behavior of the blockchain in the presence of multiple tips, and we show that probability of truthful voting is equally important in this case as higher values accelerate fork resolution.