Distributed systems ranging from small local area networks to large wide area networks like the Internet composed of static and/or mobile users have become increasingly popular. A desirable property for any distributed service is fault-tolerance, which means the service remains uninterrupted even if some components in the network fail. This dissertation considers weak distributed models to find either algorithms to solve certain problems or impossibility proofs to show that a problem is unsolvable. These are the main contributions of this dissertation:
• Failure detectors are used as a service to solve consensus (agreement among nodes) which is otherwise impossible in failure-prone asynchronous systems. We find an algorithm for crash-failure detection that uses bounded size messages in an arbitrary, partitionable network composed of badly- behaved channels that can lose and reorder messages.
• Registers are a fundamental building block for shared memory emulations on top of message passing systems. The problem has been extensively studied in static systems. However, register emulation in dynamic systems with faulty nodes is still quite hard and there are impossibility proofs that point out scenarios where change in the system composition due to nodes entering and leaving (also called churn) makes the problem unsolvable.
We propose the first emulation of a crash-fault tolerant register in a system with continuous churn where consensus is unsolvable, the size of the system can grow without bound and at most a constant fraction of the number of nodes in the system can fail by crashing. We prove a lower bound that states that fault-tolerance for dynamic systems with churn is inherently lower than in static systems.
• We then extend the results in the crash-fault tolerant case to a dynamic system with continuous churn and nodes that can be Byzantine faulty. It is the first emulation of an atomic register in a system that can withstand nodes continually entering and leaving, imposes no upper bound on the system size and can tolerate Byzantine nodes. However, the number of Byzantine faulty nodes that can be tolerated is upper bounded by a constant number. Although the algorithm requires that there be a constant known upper bound on the number of Byzantine nodes, this restriction is unavoidable, as we show that it is impossible to emulate an atomic register if the system size and maximum number of servers that can be Byzantine in the system is unknown
