Verification of Randomized Consensus Algorithms Under Round-Rigid Adversaries

Authors Nathalie Bertrand , Igor Konnov , Marijana Lazić , Josef Widder

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Author Details

Nathalie Bertrand
  • Univ. Rennes, Inria, CNRS, IRISA, Rennes, France
Igor Konnov
  • University of Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
Marijana Lazić
  • TU München, 85748 Garching bei München, Germany
Josef Widder
  • TU Wien, 1040 Vienna, Austria
  • Interchain Foundation, 6340 Baar, Switzerland

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Nathalie Bertrand, Igor Konnov, Marijana Lazić, and Josef Widder. Verification of Randomized Consensus Algorithms Under Round-Rigid Adversaries. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 33:1-33:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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.

Subject Classification

ACM Subject Classification
  • Software and its engineering → Software verification
  • Software and its engineering → Software fault tolerance
  • Theory of computation → Logic and verification
  • threshold automata
  • counter systems
  • parameterized verification
  • randomized distributed algorithms
  • Byzantine faults


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