Impossibility results in the presence of multiple faulty processes

Gadi Taubenfeld, Shumel Katz, Shlomo Moran

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationFoundations of Software Technology and Theoretical Computer Science - 9th Conference, Proceedings
EditorsC.E. Veni Madhavan
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783540520481
StatePublished - 1989
Externally publishedYes
Event9th Conference on Foundations of software Technology and Theoretical Computer Science, FST and TCS 1989 - Bangalore, India
Duration: 19 Dec 198921 Dec 1989

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume405 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th Conference on Foundations of software Technology and Theoretical Computer Science, FST and TCS 1989

Bibliographical note

Publisher Copyright:
© 1989, Springer-Verlag.


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