The consensus problem involves an asynchronous system of processes, some of which may be unreliable The problem ~9 for the reliable processes to agree on a binary value We show that every protocol for thus problem has the posslblhty of nontermmatlon, even with only one faulty process By way of contrast, solutions are known for the synchronous case, the "Byzantine Generals" problem

The concept of partial synchrony in a distributed system is introduced. Partial synchrony lies between the cases of a synchronous system and an asynchronous system. In a synchronous system, there is a known fixed upper bound Δ on the time required for a message to be sent from one processor to another and a known fixed upper bound Φ on the relative speeds of different processors. In an asynchronous system no fixed upper bounds Δ and Φ exist. In one version of partial synchrony, fixed bounds Δ and Φ exist, but they are not known a priori. The problem is to design protocols that work correctly in the partially synchronous system regardless of the actual values of the bounds Δ and Φ. In another version of partial synchrony, the bounds are known, but are only guaranteed to hold starting at some unknown time T , and protocols must be designed to work correctly regardless of when time T occurs. Fault-tolerant consensus protocols are given for various cases of partial synchrony and various fault models. Lower bounds that show in most cases that our protocols are optimal with respect to the number of faults tolerated are also given. Our consensus protocols for partially synchronous processors use new protocols for fault-tolerant “distributed clocks” that allow partially synchronous processors to reach some approximately common notion of time.

When designing distributed web services, there are three properties that are commonly desired: consistency, availability, and partition tolerance. It is impossible to achieve all three. In this note, we prove this conjecture in the asynchronous network model, and then discuss solutions to this dilemma in the partially synchronous model.

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In this paper we investigate distributed computation in dynamic networks in which the network topology changes from round to round. We consider a worst-case model in which the communication links for each round are chosen by an adversary, and nodes do not know who their neighbors for the current round are before they broadcast their messages. The model captures mobile networks and wireless networks, in which mobility and interference render communication unpredictable. In contrast to much of the existing work on dynamic networks, we do not assume that the network eventually stops changing; we require correctness and termination even in networks that change continually. We introduce a stability property called T -interval connectivity (for T ≥ 1), which stipulates that for every T consecutive rounds there exists a stable connected spanning subgraph. For T = 1 this means that the graph is connected in every round, but changes arbitrarily between rounds.We show that in 1-interval connected graphs it is possible for nodes to determine the size of the network and compute any computable function of their initial inputs in O(n 2 ) rounds using messages of size O(log n + d), where d is the size of the input to a single node. Further, if the graph is T -interval connected for T > 1, the computation can be sped up by a factor of T , and any function can be computed in O(n + n 2 /T ) rounds using messages of size O(log n + d). We also give two lower bounds on the token dissemination problem, which requires the nodes to disseminate k pieces of information to all the nodes in the network.The T-interval connected dynamic graph model is a novel model, which we believe opens new avenues for research in the theory of distributed computing in wireless, mobile and dynamic networks.

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This paper considers a variant of the Byzantine Generals problem, in which processes start with arbitrary real values rather than Boolean values or values from some bounded range, and in which approximate, rather than exact, agreement is the desired goal. Algorithms are presented to reach approximate agreement in asynchronous, as well as synchronous systems. The asynchronous agreement algorithm is an interesting contrast to a result of Fischer et al, who show that exact agreement with guaranteed termination is not attainable in an asynchronous system with as few as one faulty process. The algorithms work by successive approximation, with a provable convergence rate that depends on the ratio between the number of faulty processes and the total number of processes. Lower bounds on the convergence rate for algorithms of this form are proved, and the algorithms presented are shown to be optimal.

We i n troduce the input-output automaton, a simple but powerful model of computation in asynchronous distributed networks. With this model we are able to construct modular, hierarchical correctness proofs for distributed algorithms. We de ne this model, and give a n i n teresting example of how i t c a n be used to construct such proofs.