1 / 39

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 Impossibility Universality Randomized Wait-Free Robust weak shared coin Multi Consensus Game Use randomizes solution

elaina
Download Presentation

Wait-Free Consensus

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. Outline • Deterministic Wait-Free • Impossibility • Universality • Randomized Wait-Free • Robust weak shared coin • Multi Consensus Game • Use randomizes solution • Recycling counter • Conclusion

  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 • Giventwoconcurrent 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. Consensus Number 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 Hierarchy Object

  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 strictly smaller 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 • The n-consensus object is universal in a system of n (or fewer) processes

  11. FIFO Queue • Supports two operations: • enq(queue, val): appends a new element to the end of queue with the value val • deq(queue): reads and removes the first element of queue

  12. FIFO Queue has n >= 2 P: decide(input: value) returns(value) prefer[P] := input if deq(A) = 0 then return prefer[P] else return prefer[Q] endif end decide Prefer A 0 ┴ 1 ┴ Initially

  13. FIFO Queue has n = 2 • Impossible for n > 2 • Proof: • Initially: • Three processes P, Q and R • Each about to make decision step • P's operation x-valent • Q's operation y-valent • Cover all possible combinations of operations

  14. FIFO Queue has n = 2 (cont.) • Case 1: P and Q deq(A) A A C: bi-valent 1 1 Q deq(A) P deq(A) 2 2 3 3 x-valent y-valent T S P deq(A) Q deq(A) T' v S' v R S'~T'

  15. FIFO Queue has n = 2 (cont.) • Case 2: P enq(A, p) and Q deq(A) A Non-Empty Queue A C: bi-valent 1 1 Q deq(A) P enq(A, p) 2 2 3 3 y-valent T x-valent S P enq(A, p) Q deq(A) p T' p S' R S'~T'

  16. FIFO Queue has n = 2 (cont.) • Case 2: P enq(A, p) and Q deq(A) A Empty Queue A C bi-valent Q deq(A) p p P enq(A, p) y-valent T x-valent S P enq(A, p) T' R S~T’

  17. FIFO Queue has n = 2 (cont.) • Case 3: P and Q enq() A A C: bi-valent P enq(A, p) Q enq(A, q) 1 1 2 2 x-valent y-valent S T Q enq(A, q) P enq(A, p) S' T' p P-only until it deq q P-only until it deq p q q p P’s P’s T’’ S’’ Q’s Q-only until it deq q Q-only until it deq p Q’s R S’’’~T’’’ S’’’ T’’’

  18. Augmented Queue • Add one more operation to the FIFO queue: • Peek(): returns but does not remove the first item in the queue • See how the queue becomes POWERFULL

  19. Augmented Queue has n = infinity decide(input: value) enq(A, input) Return peek(q) end decide

  20. Universality • An object is UNIVERSAL if it implements any other object • Example: Object R implements object A Object A Invoke Invoke Pi Front-End Object R Respond Respond

  21. Universality Algorithm: Idea Consensus Object Input: (var, pref_val) Output: decides val to var Input: invoke invoke Universal Algorithm Output: respond respond

  22. Universality Algorithm: Idea • A linked list to represent the object • Each cell represents an invocation • Sequence of cells represent the sequence of applied operations • Sequence: unbounded integer size

  23. Universality Algorithm: Idea • When a process P makes an invocation • P creates a node with sequence = 0 and fill in its invocation • P tries to attach its node to the linked list • Attaching the node means performing its invocation • Once the node is attached, it will have a sequence and all of its entries will be filled

  24. Universality Algorithm: Idea • Apply (invoke, state, state, result) • May be non-deterministic • Apply (invoke, state) represents (new_state, result)

  25. Universality Algorithm: Node Seq: integer New: consensus object After: consensus object Inv: INVOKE state New result Before: * cell After: * cell

  26. Universality Algorithm: Linked-List Anchor before before before Seq = 1 Seq = 2 Seq = 3 Seq = 4 Inv2 Inv3 Inv4 State: S1 State: S2 State: S3 State: S4 Res: R2 Res: R3 Res: R4 after after after before after Example: Apply(Inv2, S1)  (S2, R2) Similarly: Apply(Inv3, S2)  (S3, R3) ……etc.

  27. P4 P1 P2 P3 P0 Universality Algorithm decide(var, val) Assigns a val to var Head Announce 0 1 2 3 4 0 1 2 3 4 Anchor Seq = 1 State: S1 Initially before after NULL NULL

  28. P4 P1 P2 P3 P0 Universality Algorithm decide(var, val) Assigns a val to var Head Announce 0 1 2 3 4 0 1 2 3 4 3 Anchor 3 Seq = 1 0 Inv State: S1 3 before after NULL NULL

  29. P4 P1 P2 P3 P0 Universality Algorithm decide(var, val) Assigns a val to var Head Announce 0 1 2 3 4 0 1 2 3 4 (S1, Inv) (S2, R2) Anchor Seq = 1 0 Seq = 2 Inv before State: S1 State: S2 Res: R2 before after after NULL NULL

  30. P4 P1 P2 P3 P0 Universality Algorithm Decide(var, val) Assignes a val to var Head Announce 0 1 2 3 4 0 1 2 3 4 Anchor Seq = 1 Seq = 2 before Inv State: S1 State: S2 Res: R2 before after after NULL NULL

  31. P4 P1 P2 P3 P0 Universality Algorithm decide(var, val) Assigns a val to var Head Announce 0 1 2 3 4 S2, Inv1 0 1 2 3 4 1 S2, Inv1 3 S2, Inv1 1 1 S3, R3 Anchor 1 S3, R3 Seq = 1 0 0 0 Seq = 2 Inv1 Inv3 before Inv4 1 Inv State: S1 State: S2 Res: R2 1 before S3, R3 after after NULL NULL

  32. P4 P1 P2 P3 P0 Universality Algorithm decide(var, val) Assigns a val to var Head Announce 0 1 2 3 4 0 1 2 3 4 Anchor Seq = 1 0 0 Seq = 2 Seq = 3 Inv3 before Inv4 before Inv Inv1 State: S1 State: S2 State: S3 Res: R2 Res: R3 before after after NULL NULL

  33. Universality Algorithm: Why Help • Beyond being nice • With help  wait-free • Without help  non-blocking

  34. Universal Algorithm create my_cell (use INV = INVOKE) Announce my_cell While my_cell is not attached to the linked-list Consult head to point to some process: help, and see if it needs help if yes prefer (help) elseprefer (my_cell) send my prefer to decide send my apply preference to decide fill fields of the attached cell return my new RESULT universal(what: INVOC) returns(RESULT) my_cell: cell := [seq:0, inv: what new: create(consensus_object) before: create(consensus_object) after: null] announce[P] := my_cell for each process Q do head[P] := max(head[P], head[Q]) while (announce[P].seq = 0]) c: *cell := head[P] help: *cell := announce[(c.seq mod n) + 1] if help.seq = 0 then prefer := help else prefer := announce[P] d := decide(c.after, prefer) decide(d.new, apply(d.inv, c.new.state)) d.before := c d.seq := c.seq + 1 head[P] := d head[P] := announce[P] return (announce[P].new.result) enduniversal

  35. Impossibility/Universality: Importance • Research done before was focusingonconstructing complex objects from atomic R/W registers • Atomic registers have few applicationsin constructing wait-free implementation of more complex data structure • Examples: • Sets, queues, stacks, priority queues, lists • Classical synchronization primitives: test&set, compare&swap, fetch&add • Simple memory-to-memory operation: move and swap

  36. Research Turning Points • Pay attention to other primitives: stronger than R/W registers • Give up wait-free • Use randomized wait-free

  37. Conclusion • Deterministic Wait-Free Consensus • Impossibility and universality Hierarchy • Universality algorithm

  38. References • M. Herlihy. Wait-Free Synchronization. ACM Transactions on Programming Languages and Systems, 13(1): 124-149. January 1991.

  39. Questions?

More Related