Verification of randomized consensus algorithms under round-rigid adversaries

Randomized fault-tolerant distributed algorithms pose a number of challenges for automated verification: (i) parameterization in the number of processes and faults, (ii) randomized choices and probabilistic properties, and (iii) an unbounded number of asynchronous rounds. This combination makes veri...

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Bibliographic Details
Published in:International journal on software tools for technology transfer Vol. 23; no. 5; pp. 797 - 821
Main Authors: Bertrand, Nathalie, Konnov, Igor, Lazić, Marijana, Widder, Josef
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2021
Springer Nature B.V
Springer Verlag
Subjects:
Algorithms
Computer Science
Crashes
Fault tolerance
Faults
Parameterization
Schedules
Software Engineering
Software Engineering/Programming and Operating Systems
Theory of Computation
Verification
Fault tolerance
Parameterized
Verification
Distributed algorithms
Probabilistic
ISSN:1433-2779, 1433-2787
Online Access:Get full text
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Summary:Randomized fault-tolerant distributed algorithms pose a number of challenges for automated verification: (i) parameterization in the number of processes and faults, (ii) randomized choices and probabilistic properties, and (iii) an unbounded number of asynchronous rounds. This combination makes verification hard. Challenge (i) was recently addressed in the framework of threshold automata. We extend threshold automata to model randomized consensus algorithms that perform an unbounded number of asynchronous rounds. For non-probabilistic properties, we show that it is necessary and sufficient to verify these properties under round-rigid schedules, that is, schedules where processes enter round  r only after all processes finished round r - 1 . For almost-sure termination, we analyze these algorithms under round-rigid adversaries, that is, fair adversaries that only generate round-rigid schedules. This allows us to do compositional and inductive reasoning that reduces verification of the asynchronous multi-round algorithms to model checking of a one-round threshold automaton. We apply this framework and automatically verify the following classic algorithms: Ben-Or’s and Bracha’s seminal consensus algorithms for crashes and Byzantine faults, 2-set agreement for crash faults, and RS-Bosco for the Byzantine case.
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ISSN:1433-2779
1433-2787
DOI:10.1007/s10009-020-00603-x