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It is well-known that RANDAO manipulation is possible in Ethereum if an adversary controls the proposers assigned to the last slots in an epoch. We provide a methodology to compute, for any fraction $\alpha$ of stake owned by an adversary, the maximum fraction $f(\alpha)$ of rounds that a strategic adversary can propose. We further implement our methodology and compute $f(\cdot)$ for all $\alpha$. For example, we conclude that an optimal strategic participant with $5\%$ of the stake can propose a $5.048\%$ fraction of rounds, $10\%$ of the stake can propose a $10.19\%$ fraction of rounds, and $20\%$ of the stake can propose a $20.68\%$ fraction of rounds., Comment: 28 pages, 7 figures, full version of the AFT 2024 paper

The increasing wireless communication capabilities of vehicles creates opportunities for more efficient intersection management strategies. One promising approach is the replacement of traffic lights with a system wherein vehicles run protocols among themselves to determine right of way. In this paper, we define the intersection problem to model this scenario abstractly, without any assumptions on the specific structure of the intersection or a bound on the number of vehicles. Protocols solving the intersection problem must guarantee safety (no collisions) and liveness (every vehicle eventually goes through). In addition, we would like these protocols to satisfy various optimality criteria, some of which turn out to be achievable only in a subset of the contexts. In particular, we show a partial equivalence between eliminating unnecessary waiting, a criterion of interest in the distributed mutual-exclusion literature, and a notion of optimality that we define called lexicographical optimality. We then introduce a framework to design protocols for the intersection problem by converting an intersection policy, which is based on a global view of the intersection, to a protocol that can be run by the vehicles through the use of knowledge-based programs. Our protocols are shown to guarantee safety and liveness while also being optimal under sufficient conditions on the context. Finally, we investigate protocols in the presence of faulty vehicles that experience communication failures and older vehicles with limited communication capabilities. We show that intersection protocols can be made safe, live and optimal even in the presence of faulty behavior., Comment: The full version of the DISC 2024 paper

Work on \emph{optimal} protocols for \emph{Eventual Byzantine Agreement} (EBA) -- protocols that, in a precise sense, decide as soon as possible in every run and guarantee that all nonfaulty agents decide on the same value -- has focused on emph{full-information protocols} (FIPs), where agents repeatedly send messages that completely describe their past observations to every other agent. While it can be shown that, without loss of generality, we can take an optimal protocol to be an FIP, full information exchange is impractical to implement for many applications due to the required message size. We separate protocols into two parts, the \emph{information-exchange protocol} and the \emph{action protocol}, so as to be able to examine the effects of more limited information exchange. We then define a notion of optimality with respect to an information-exchange protocol. Roughly speaking, an action protocol $P$ is optimal with respect to an information-exchange protocol $\mathcal{E}$ if, with $P$, agents decide as soon as possible among action protocols that exchange information according to $\mathcal{E}$. We present a knowledge-based EBA program for omission failures all of whose implementations are guaranteed to be correct and are optimal if the information exchange satisfies a certain safety condition. We then construct concrete programs that implement this knowledge-based program in two settings of interest that are shown to satisfy the safety condition. Finally, we show that a small modification of our program results in an FIP that is both optimal and efficiently implementable, settling an open problem posed by Halpern, Moses, and Waarts (SIAM J. Comput., 2001)., Comment: The full version of the PODC 2023 paper