Technical Report CS0586

TR#:CS0586
Class:CS
Title: Impossibility Results in The Presence of Mpltiple Faulty Processes
Authors: G. Taubenfeld, S. Katz, and S. Moran
PDFCS0586.pdf
Abstract: We investigate the impossibility of solving certain problems in an unreliable distributed system where multiple processes may fail. We assume undetectable crash(fail-stop) failures, which means that a process may become faulty at any time during an execution and that no event c,an occur 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 are variants of problems unsolvable in the presence of a single faulty process (such as consensus, choosing a leader, ranking, or matching). In order to prove the impossibility result a contradiction is shown among a set of axioms that characterize any faulttolerant protocol solving the problems we treat: In the course of the proof, we present two results of independent interest: first, we show that for any protocol there is a computation in which some procesS is a splitter, i.e., it can split the possible dutputs of the protocol to two disjoint sets. If the protocol is also fault-tolerant, then this splitter must be a decider, i.e., it can split its own output values into two different singletons. These results generalize and extend previously known results for completely asynchronous systems.
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