Performance of Ethereum 2.0-Like Consensus Under Single-Slot Finality

Implementing a consensus protocol in a Proof-of-Stake context requires a delicate tradeoff between different system parameters. Ethereum 2.0, probably the most popular PoS system today, uses a large number of validators to achieve decentralization, but long time windows, during which both blocks and attestations for those blocks are considered valid, open up the possibility for a number of attacks that target the process of consensus. A possible remedy would be to try to achieve single-slot finality similar to that obtained in Practical Byzantine Fault Tolerance (PBFT). In this paper, we develop a Markov chain model of validator lifecycle in an Ethereum 2.0-like system with single-slot finality which includes penalties and rewards, as well as the possibility of voluntary exit and waiting to rejoin the validator pool. Using the model, we obtain the probability of achieving consensus as the function of probabilities of different events, most notably the probability of truthful voting by the validator. Our results indicate that consensus is rather sensitive to false voting, and that low probability of waiting and low probability of voluntary exit help improve the probability of consensus.