Logics of knowledge and knowledge-based programs provide a way to give abstract descriptions of solutions to problems in fault-tolerant distributed computing, and have been used to derive optimal protocols for these problems with respect to a variety of failure models. Generally, these results have involved complex pencil and paper analyses with respect to the theoretical "full-information protocol" model of information exchange between network nodes. It is equally of interest to be able to establish the optimality of protocols using weaker, but more practical, models of information exchange, or else identify opportunities to improve their performance. Over the last 20 years, automated verification and synthesis tools for the logic of knowledge have been developed, such as the model checker MCK, that can be applied to this problem. This paper concerns the application of MCK to automated analyses of this kind. A number of information-exchange models are considered, for Simultaneous and Eventual variants of Byzantine Agreement under a range of failure types. MCK is used to automatically analyze these models. The results demonstrate that it is possible to automatically identify optimization opportunities, and to automatically synthesize optimal protocols. The paper provides performance measurements for the automated analysis, establishing a benchmark for epistemic model checking and synthesis tools.

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.

Work on optimal protocols for 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 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 information-exchange protocol and the 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 ε if, with P, agents decide as soon as possible among action protocols that exchange information according to ε. 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).