On the complexity of asynchronous agreement against powerful adversaries

We introduce new techniques for proving lower bounds on the running time of randomized algorithms for asynchronous agreement against powerful adversaries. In particular, we define a strongly adaptive adversary that is computationally unbounded and has a limited ability to corrupt a dynamic subset of...

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Veröffentlicht in:Distributed computing Jg. 28; H. 6; S. 377 - 389
Hauptverfasser: Lewko, Allison, Lewko, Mark
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2015
Springer Nature B.V
Schlagworte:
Adaptive algorithms
Algorithms
Computer Communication Networks
Computer Hardware
Computer Science
Computer Systems Organization and Communication Networks
Crashes
Expenses
Failure
Lower bounds
Processors
Running
Software Engineering/Programming and Operating Systems
Theory of Computation
Partial Execution
Byzantine Agreement
Faulty Processor
Crash Failure
Message Buffer
ISSN:0178-2770, 1432-0452
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Zusammenfassung:We introduce new techniques for proving lower bounds on the running time of randomized algorithms for asynchronous agreement against powerful adversaries. In particular, we define a strongly adaptive adversary that is computationally unbounded and has a limited ability to corrupt a dynamic subset of processors by erasing their memories. We demonstrate that the randomized agreement algorithms designed by Ben-Or and Bracha to tolerate crash or Byzantine failures in the asynchronous setting extend to defeat a strongly adaptive adversary. These algorithms have essentially perfect correctness and termination, but at the expense of exponential running time. In the case of the strongly adaptive adversary, we show that this dismally slow running time is inherent : we prove that any algorithm with essentially perfect correctness and termination against the strongly adaptive adversary must have exponential running time. We additionally interpret this result as yielding an enhanced understanding of the tools needed to simultaneously achieving perfect correctness and termination as well as fast running time for randomized algorithms tolerating crash or Byzantine failures.
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ISSN:0178-2770
1432-0452
DOI:10.1007/s00446-014-0224-5