Sharing memory in distributed systems

We propose an algorithm for simulating atomic registers, test-and-set, fetch-and-add, and read-modify-write registers in a message passing system. The algorithm is fault tolerant and works correctly in presence of up to (N/2) -1 node failures where N is the number of processors in the system. The high resilience of the algorithm is obtained by using randomized consensus algorithms and a robust communication primitive. The use of this primitive allows a processor to exchange local information with a majority of processors in a consistent way, and therefore to take decisions safely. The simulator makes it possible to translate algorithms for the shared memory model to that for the message passing model. With some minor modifications the algorithm can be used to robustly simulate shared queues, shared stacks, etc. (Abstract shortened with permission of author.)

Impossibility results in the presence of multiple faulty processes

Abstract. We investigate the impossibility of solving certain problems in an unreliable distributed system where multiple processes may fail. We assume undetectable crash failures which means that a process may become faulty at any time during an execution and that no event can happen on a process after it fails. A sufficient condition is provided for the unsolvability of problems in the presence of multiple faulty processes. Several problems are shown to be solvable in the presence of t − 1 faulty processes but not in the presence of t faulty processes for any t. These problems are variants of problems which are unsolvable in the presence of a single faulty process (such as consensus, choosing a leader, ranking, matching). In order to prove the impossibility result a contradiction is shown among a set of axioms which characterize any fault-tolerant protocol solving the problems we treat. In the course of the proof, we present two results that appear to be of independent interest: first, we show that for any protocol there is a computation in which some process is a splitter. This process can split the possible outputs of the protocol to two disjoint sets. In case that the protocol is also fault-tolerant, then this splitter must be a decider, that can split its own output values into two different singletons. These results generalize and expand known results for asynchronous systems.