A Reduction Theorem for Randomized Distributed Algorithms Under Weak Adversaries
Pages 219 - 239
Abstract
Weak adversaries are a way to model the uncertainty due to asynchrony in randomized distributed algorithms. They are a standard notion in correctness proofs for distributed algorithms, and express the property that the adversary (scheduler), which has to decide which messages to deliver to which process, has no means of inferring the outcome of random choices, and the content of the messages.In this paper, we introduce a model for randomized distributed algorithms that allows us to formalize the notion of weak adversaries. It applies to randomized distributed algorithms that proceed in rounds and are tolerant to process failures. For this wide class of algorithms, we prove that for verification purposes, the class of weak adversaries can be restricted to simple ones, so-called round-rigid adversaries, that keep the processes tightly synchronized. As recently a verification method for round-rigid adversaries has been introduced, our new reduction theorem paves the way to the parameterized verification of randomized distributed algorithms under the more realistic weak adversaries.
References
[1]
Aguilera M and Toueg S The correctness proof of Ben-Or’s randomized consensus algorithm Distrib. Comput. 2012 25 5 371-381
[2]
Aspnes J Randomized protocols for asynchronous consensus Distrib. Comput. 2003 16 2–3 165-175
[3]
Baier C and Katoen JP Principles of Model Checking 2008 Cambridge MIT Press
[4]
Ben-Or, M.: Another advantage of free choice: completely asynchronous agreement protocols (extended abstract). In: PODC, pp. 27–30 (1983)
[5]
Bertrand, N., Konnov, I., Lazic, M., Widder, J.: Verification of randomized consensus algorithms under round-rigid adversaries. In: CONCUR. LIPIcs, vol. 140, pp. 33:1–33:15 (2019)
[6]
Bouajjani, A., Enea, C., Ji, K., Qadeer, S.: On the completeness of verifying message passing programs under bounded asynchrony. In: CAV, pp. 372–391 (2018)
[7]
Bracha G Asynchronous Byzantine agreement protocols Inf. Comput. 1987 75 2 130-143
[8]
Chaouch-Saad M, Charron-Bost B, and Merz S Bournez O and Potapov I A reduction theorem for the verification of round-based distributed algorithms Reachability Problems 2009 Heidelberg Springer 93-106
[9]
Damian A, Drăgoi C, Militaru A, and Widder J Dillig I and Tasiran S Communication-closed asynchronous protocols Computer Aided Verification 2019 Cham Springer 344-363
[10]
Elrad T and Francez N Decomposition of distributed programs into communication-closed layers Sci. Comput. Program. 1982 2 3 155-173
[11]
Gleissenthall, K., Gökhan Kici, R., Bakst, A., Stefan, D., Jhala, R.: Pretend synchrony. In: POPL, pp. 59:1–59:30 (2019)
[12]
Konnov I, Lazic M, Veith H, and Widder J Para: Parameterized path reduction, acceleration, and SMT for reachability in threshold-guarded distributed algorithms Formal Methods Syst. Des. 2017 51 2 270-307
[13]
Konnov, I., Lazić, M., Veith, H., Widder, J.: A short counterexample property for safety and liveness verification of fault-tolerant distributed algorithms. In: POPL, pp. 719–734 (2017)
[14]
Konnov I and Widder J Margaria T and Steffen B ByMC: Byzantine model checker Leveraging Applications of Formal Methods, Verification and Validation. Distributed Systems 2018 Cham Springer 327-342
[15]
Kragl, B., Qadeer, S., Henzinger, T.A.: Synchronizing the asynchronous. In: CONCUR. LIPIcs, vol. 118, pp. 21:1–21:17 (2018)
[16]
Lipton RJ Reduction: a method of proving properties of parallel programs Commun. ACM 1975 18 12 717-721
[17]
Mostéfaoui A, Moumen H, and Raynal M Randomized k-set agreement in crash-prone and Byzantine asynchronous systems Theoretical Comput. Sci. 2018 709 80-97
[18]
Song YJ and van Renesse R Taubenfeld G Bosco: one-step Byzantine asynchronous consensus Distributed Computing 2008 Heidelberg Springer 438-450
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Information
Published In
Jan 2021
607 pages
ISBN:978-3-030-67066-5
DOI:10.1007/978-3-030-67067-2
- Editors:
- Fritz Henglein,
- Sharon Shoham,
- Yakir Vizel
© Springer Nature Switzerland AG 2021.
Publisher
Springer-Verlag
Berlin, Heidelberg
Publication History
Published: 17 January 2021
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