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 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 two concurrent objects X and Y Q: Does there exist a wait-free implementation of X by Y? FLP and Herlihy’s papers answered this question

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

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

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

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

Impossibility and Universality Hierarchy Consensus Number Object 1 R/W registers 2 Test&set, swap, fetch&add, queue, stack 2n - 2 n-register assignment Infinity Memory-to-memory move and swap, augmented queue, compare&swap, fetch&cons, sticky byte

Impossibility and Universality 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

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

Why Is It Important Research done before was focusing on constructing 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 to other primitives: stronger than R/W registers Give up wait-free Use randomized wait-free

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

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 level using randomization

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

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