Unreliable Failure Detectors for Asynchronousdistributed

It is well-known that several fundamental problems of fault-tolerant distributed computing, such as Consensus and Atomic Broadcast, cannot be solved in asyn-chronous systems with crash failures. These impossibility results stem from the lack of reliable failure detection in such systems. To circumvent such impossibility results, we introduce the concept of unreliable failure detectors that can make mistakes, and study the problem of using them to solve Consensus (and Atomic Broadcast). It is easy to solve Consensus using a \perfect" failure detector (one that does not make mistakes). But is perfect failure detection necessary to solve Consensus? We show that Consensus is solvable with unreliable failure detectors, even if they make an innnite number of mistakes. This leads to the following question: What is the \weakest" failure detector for solving Consensus? We introduce a notion of algorithmic reducibility that allows us to compare seemingly incomparable failure detectors. Using this concept, we show that one of the failure detectors that we introduce here is indeed the weakest failure detector for solving Consensus in asynchronous systems with a majority of correct processes. We also show that Consensus and Atomic Broadcast are equivalent in asyn-chronous systems. Thus all our results regarding the solvability of Consensus using failure detectors, apply to Atomic Broadcast as well. spent his childhood in various cities in India: Bombay, Calcutta and nally Kanpur. After completing high school at the Doon school, he went on to do a Bachelor of iii This thesis is dedicated to my parents who taught me how to think. iv Acknowledgements A large number of people contributed either directly or indirectly to this thesis. I was extremely fortunate to have Sam Toueg as my advisor. Without his guidance, I would still be trying to shave oo deltas from broadcast algorithms; without his cooking knowledge, I would never have learnt to cook pasta sauce \a la putanesca". Sam has put in as much work|if not more|towards this thesis, as I have. I am indebted to Vassos Hadzilacos, my other co-author, for his invaluable contributions to this work. Without his help, Chapter 4 would not have happened. Further, his critical readings of the work presented in Chapter 3 have greatly innuenced the way it is presented. The idea of using unreliable failure detectors came from the many invaluable discussions I had with the Isis folks, in particular Aleta Ricciardi and Ken Bir-man (also see RB91]). Rod Downey taught …