1. Failure Detectors & Consensus

2. Agenda Unreliable Failure Detectors (CHANDRA TOUEG) Reducibility ◊S≥◊W, ◊W≥◊S Solving Consensus using ◊S (MOSTEFAOUI RAYNAL)

3. Unreliable Failure Detectors A distributed failure detector D consists of a local failure detector module D p at each process p When D p suspects a process j to have crashed it adds j to suspects p, if later on D p realizes it made a mistake it can remove j from suspects p Failure detectors are defined in terms of abstract properties. Namely, two classes of competence and four classes of accuracy.

4. Completeness Classes Strong Completeness  Eventually, every process that crashes is permanently suspected by every correct process Weak Completeness  Eventually, every process that crashes is permanently suspected by some correct process

5. Accuracy Classes Strong Accuracy  No process is suspected before it crashes Weak Accuracy  Some correct process is never suspected Eventual Strong Accuracy  There is a time after which correct processes are not suspected by any correct process Eventual Weak Accuracy  There is a time after which some correct process is never suspected by any correct process.

6. Failure Detectors Classes Strong Weak StrongWeakEventual StrongEventual Weak Accuracy Completeness Perfect P Q Strong S Weak W Eventually Perfect ◊P ◊Q◊Q Eventually Strong ◊S Eventually Weak ◊W

7. Reducibility A Distributed Algorithm T D→D’ transforms a failure detector D into a failure detector D’ if it maintains a variable output p at every process p which emulates the output of D’ T D→D’ is called a reduction algorithm and D’ is reducible to D, denoted D ≥ D’ (D’ is “weaker”) A simple T ◊S → ◊W ?

8. From Weak Completeness to Strong Completeness T ◊W → ◊S Code for process p output p ← Φ Task 1: repeat forever suspects p ← ◊W p send(p, suspects p ) to all Task 2: upon receiving (q, suspects q ) for some q output p ← (output p U suspects q ) – {q} ◊S≥◊W && ◊W≥◊S → ◊W=◊S

9. Consensus In the Consensus problem every process p i proposes a value v i and all correct processes have to decide on some value v, in relation to the set of proposed values. More formally, a distributed consensus algorithm must satisfy:  Termination: Every correct process eventually decides on some value.  Validity: If a process decides v, then v was proposed by some process (non triviality)  Agreement: No two correct processes decide differently It is impossible to solve consensus in asynchronous system even if only one process might crash [FLP]

10. Solving Consensus using ◊S Code for process p i 1 ≤ i ≤ n Task 1: r i ← 0; est i ← v i ; 1. while didn’t decide do 2. c ← (r i mod n) + 1; est_from_c i ← ∟; r i ← r i + 1 3. if (i = c) then est_from_c i ← est i 4. else wait until is received from p c or c is suspected 5. if received then est_from_c i ← v 6. send to all 7. wait until collected from a majority of processes 8. rec i ← {est_from_c | was received} 9. if rec i = {v} then decide v and send to all 10. if rec i = {v, ∟} then est i ← v Task 2: 1. Upon reception of decide v and send to all