Nancy A. Lynch

Brewer's conjecture and the feasibility of consistent, available, partition-tolerant web services

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.

Consensus in the presence of partial synchrony

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 &PHgr; on the relative speeds of different processors. In an asynchronous system no fixed upper bounds Δ and &PHgr; exist. In one version of partial synchrony, fixed bounds Δ and &PHgr; 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 &PHgr;. 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.

Hierarchical correctness proofs for distributed algorithms

This thesis introduces a new model for distributed computation in asynchronous networks, the input-output automaton. This simple, powerful model captures in a novel way the game-theoretical interaction between a system and its environment, and allows fundamental properties of distributed computation such as fair computation to be naturally expressed. Furthermore, this model can be used to construct modular, hierarchical correctness proofs of distributed algorithms. This thesis defines the input-output automaton model, and presents an interesting example of how this model can be used to construct such proofs.

A comparison of polynomial time reducibilities

Abstract Various forms of polynomial time reducibility are compared. Among the forms examined are many-one, bounded truth table, truth table and Turing reducibility. The effect of introducing nondeterminism into reduction procedures is also examined.

Reaching approximate agreement in the presence of faults

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.

Forward and backward simulations I.: untimed systems

A unified, comprehensive presentation of simulation techniques for verification of concurrent systems is given, in terms of a simple untimed automaton model. In particular, (1) refinements, (2) forward and backward simulations, (3) hybrid forward-backward and backward-forward simulations, and (4) history and prophecy relations are defined. History and prophecy relations are abstract versions of the history and prophecy variables of Abadi and Lamport, as well as the auxiliary variables of Owicki and Gries. Relationships between the different types of simulations, as well as soundness and completeness results, are stated and proved. Finally, it is shown how invariants can be incorporated into all the simulations. Even though many results are presented here for the first time, this paper can also be read as a survey ( in a simple setting ) of the research literature on simulation techniques. The development for untimed automata is designed to support a similar development for timed automata. Part II of this paper will show how the results of this paper can be carried over to the setting of timed automata.

Probabilistic Simulations for Probabilistic Processes

Several probabilistic simulation relations for probabilistic systems are defined and evaluated according to two criteria: compositionality and preservation of “interesting” properties. Here, the interesting properties of a system are identified with those that are expressible in an untimed version of the Timed Probabilistic concurrent Computation Tree Logic (TPCTL) of Hansson. The definitions are made, and the evaluations carried out, in terms of a general labeled transition system model for concurrent probabilistic computation. The results cover weak simulations, which abstract from internal computation, as well as strong simulations, which do not.

Distributed computation in dynamic networks

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 com- putable function of their initial inputs in O(n2) 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 + n2/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.

An upper and lower bound for clock synchronization

The problem of synchronizing clocks of processes in a fully connected network is considered. It is proved that, even if the clocks all run at the same rate as real time and there are no failures, an uncertainty of e in the message delivery time makes it impossible to synchronize the clocks of n processes any more closely than e(1−1/ n ). A simple algorithm is given that achieves this bound.

Cryptographic protocols

A cryptographic transformation is a mapping f from a set of cleartext messages, M, to a set of ciphertext messages. Since for m e M, f(m) should <underline>hide</underline> the contents of m from an enemy, f<supscrpt>-1</supscrpt> should, in a certain technical sense, be difficult to infer from f(m) and public knowledge about f. A <underline>cryptosystem</underline> is a model of computation and communication which permits the manipulation of messages by cryptographic transformations.