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This paper proves a necessary and sufficient condition for the existence of <i>iterative</i>, algorithms that achieve <i>approximate Byzantine consensus</i> in arbitrary directed graphs, where each directed edge represents a communication channel between a pair of nodes. The class of iterative algorithms considered in this paper ensures that, after each… (More)

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In this work, we consider a generalized fault model that can be used to represent a wide range of failure scenarios, including correlated failures and non-uniform node reliabilities. This fault model is general in the sense that fault models studied in prior related work, such as f-total and f-local models, are special cases of the generalized fault model.… (More)

Consider a point-to-point network in which nodes are connected by directed links. This paper proves tight necessary and sufficient conditions on the underlying communication graphs for solving the following fault-tolerant consensus problems: Exact crash-tolerant consensus in synchronous systems, Approximate crash-tolerant consensus in asynchronous systems,… (More)

We explore the correctness of the Certified Propagation Algorithm (CPA) [5, 1, 7, 4] in solving broadcast with locally bounded Byzantine faults. CPA allows the nodes to use only local information regarding the network topology. We provide a tight necessary and sufficient condition on the network topology for the correctness of CPA. We also present some… (More)

This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each directed link of the underlying communication graph represents a communication channel between a pair of nodes. We adopt the transient Byzantine link failure model [15, 16], where an omniscient adversary controls a subset of the directed… (More)

This paper defines a new consensus problem, <i>convex hull consensus</i>. The input at each process is a d-dimensional vector of reals (or, equivalently, a point in the d-dimensional Euclidean space), and the output at each process is a <i>convex polytope</i> contained within the convex hull of the inputs at the fault-free processes. We explore the convex… (More)

Much of the past work on asynchronous approximate Byzantine consensus has assumed scalar inputs at the nodes [4, 8]. Recent work has yielded approximate Byzantine consensus algorithms for the case when the input at each node is a d-dimensional vector, and the nodes must reach consensus on a vector in the convex hull of the input vectors at the fault-free… (More)

For synchronous point-to-point n-node networks of undirected links, it has been previously shown that, to achieve consensus in presence of up to f Byzantine faults, the following two conditions are together necessary and sufficient: (i) n ≥ 3f + 1 and (ii) network connectivity greater than 2f. The first condition, that is, n ≥ 3f + 1, is known to be… (More)

The CAP theorem is a fundamental result that applies to distributed storage systems. In this article, we first present and prove two CAP-like impossibility theorems. To state these theorems, we present probabilistic models to characterize the three important elements of the CAP theorem: consistency (C), availability or latency (A), and partition tolerance… (More)