Fast randomized consensus using shared memory
Journal of Algorithms
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
Proceedings of the nineteenth annual ACM symposium on Principles of distributed computing
Distributed Algorithms
Symbolic Model Checking of Probabilistic Processes Using MTBDDs and the Kronecker Representation
TACAS '00 Proceedings of the 6th International Conference on Tools and Algorithms for Construction and Analysis of Systems: Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS 2000
TACAS '00 Proceedings of the 6th International Conference on Tools and Algorithms for Construction and Analysis of Systems: Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS 2000
Verification of Infinite State Systems by Compositional Model Checking
CHARME '99 Proceedings of the 10th IFIP WG 10.5 Advanced Research Working Conference on Correct Hardware Design and Verification Methods
Model Checking of Probabalistic and Nondeterministic Systems
Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science
Verification of an Implementation of Tomasulo's Algorithm by Compositional Model Checking
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
Induction in Compositional Model Checking
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Verification of the randomized consensus algorithm of Aspnes and Herlihy: a case study
Distributed Computing
Model checking for a probabilistic branching time logic with fairness
Distributed Computing
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Verifying Randomized Byzantine Agreement
FORTE '02 Proceedings of the 22nd IFIP WG 6.1 International Conference Houston on Formal Techniques for Networked and Distributed Systems
Probabilistic Symbolic Model Checking with PRISM: A Hybrid Approach
TACAS '02 Proceedings of the 8th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
PRISM: Probabilistic Symbolic Model Checker
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
Using Bounded Model Checking to Verify Consensus Algorithms
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Synthesis for PCTL in parametric Markov decision processes
NFM'11 Proceedings of the Third international conference on NASA Formal methods
Symmetry reduction for probabilistic model checking
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Scaling probabilistic timing verification of hardware using abstractions in design source code
Proceedings of the International Conference on Formal Methods in Computer-Aided Design
Randomized wait-free consensus using an atomicity assumption
OPODIS'05 Proceedings of the 9th international conference on Principles of Distributed Systems
Assume-Guarantee verification for probabilistic systems
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Polynomial-Time verification of PCTL properties of MDPs with convex uncertainties
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Compositional probabilistic verification through multi-objective model checking
Information and Computation
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We consider the randomized consensus protocol of Aspnes and Herlihy for achieving agreement among N asynchronous processes that communicate via read/write shared registers. The algorithm guarantees termination in the presence of stopping failures within polynomial expected time. Processes proceed through possibly unboundedly many rounds; at each round, they read the status of all other processes and attempt to agree. Each attempt involves a distributed random walk: when processes disagree, a shared coin-flipping protocol is used to decide their next preferred value. Achieving polynomial expected time depends on the probability that all processes draw the same value being above an appropriate bound. For the non-probabilistic part of the algorithm, we use the proof assistant Cadence SMV to prove validity and agreement for all N and for all rounds. The coin-flipping protocol is verified using the probabilistic model checker PRISM. For a finite number of processes (up to 10) we automatically calculate the minimum probability of the processes drawing the same value. The correctness of the full protocol follows from the separately proved properties. This is the first time a complex randomized distributed algorithm has been mechanically verified.