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 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

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 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

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
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

9. 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

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 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

12. Randomized Wait-Free Randomized
Deterministic Wait-Free: Any process can complete any operation in an finite number of steps of that process
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 level using 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
M. Herlihy. Wait-Free Synchronization. ACM Transactions on Programming Languages and Systems, 13(1): 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?