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Wait-Free Consensus

Wait-Free Consensus. CPSC 661 Fall 2003 Supervised by: Lisa Higham Presented by: Wei Wei Zheng Nuha Kamaluddeen. Outline. Deterministic Wait-Free Consensus Problem FLP vs. Herlihy Impossibility and Universality Randomized Wait-Free. Deterministic Wait-Free.

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Wait-Free Consensus

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  1. Wait-Free Consensus CPSC 661 Fall 2003 Supervised by: Lisa Higham Presented by: Wei Wei Zheng Nuha Kamaluddeen

  2. Outline • Deterministic Wait-Free • Consensus Problem • FLP vs. Herlihy • Impossibility and Universality • Randomized Wait-Free

  3. Deterministic Wait-Free • Wait-Free Implementation is the one which guarantees that any process can complete any operation in a finite number of steps of that process • Given twoconcurrent objects Xand Y • Q: Does there exist a wait-free implementation of X by Y? • FLP and Herlihy’s papers answered this question

  4. Consensus Problem • A system of n processes that communicate through m shared objects • Each process starts with an input value from domain D • Communicates with one another by applying operations to the shared objects • Eventually agree on a common input value and halt

  5. Consensus Problem • Requirements: • Agreement: all processes decide on one common value if they do decide • Validity: the common decision value is the input of some process • Wait-Freedom: each process decides after a finite number of steps

  6. Consensus Number • Consensus Number for an object X is the largestn for which X solves consensus problem for n processes • If no largest n exists, then the consensus number is said to be infinite

  7. FLP vs. Herlihy • FLP answered the question for a specific object, i.e., R/W register. • FLP provided a stronger result for this special case: no implementation of consensus problem of n>=2 processes using R/W registers, even for at most 1 stopping faulty process, and even for binary inputs • Herlihy gave a more generalized answer: Impossibility and Universality Hierarchy for wait-free implementation of any type of object

  8. Impossibility and Universality Hierarchy

  9. Impossibility and Universality • Impossibility • It is impossible to construct a wait-free implementation of an object with consensus number n from any number of objects with a lower consensus number

  10. Impossibility and Universality • Universality: an object is universal in a system of n (or fewer) processes if it can implement any object of consensus number n (i.e., if it can solve the consensus problem for up to n processes) • Any object with consensus number n is universal in a system of n (or fewer) processes

  11. Why Is It Important • Research done before was focusing onconstructing complex objects from atomic R/W registers • Atomic registers have few applications in constructing wait-free implementation of more complex data structure, e.g., queue and test&set • Turning Points: • Pay attention toother primitives: stronger thanR/W registers • Give up wait-free • Use randomizedwait-free

  12. Randomized Wait-Free • Deterministic Wait-Free: Any process can complete any operation in an finite number of steps of that process Randomized expected

  13. Importance of Randomization • We can construct a randomized wait-free implementation of Read-Modify-Write by atomic R/W operations • Read-Modify-Write is universal • So, atomic R/W operation is universal • Herlihy’s hierarchy collapses to 1 levelusing randomization

  14. References • M. Fischer, N. Lynch, and M. Paterson. Impossibility of Distributed Consensus with One Faulty Process. Journal of ACM, Vol. 32, No. 2, April 1985, pp. 374-382. • M. Herlihy. Wait-Free Synchronization. ACM Transactions on Programming Languages and Systems, 13(1): 124-149. January 1991. • M. Herlihy. Randomized Wait-Free Concurrent Objects. In proceedings of the 10th annual ACM Symposium on Principles of Distributed Computing, August 1991, Montreal Canada

  15. Questions?

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