Unreliable Failure Detectors for Reliable Distributed Systems

238 T. D. CHANDRA AND S. TOUEGEvery process p executes the followingTo execute R-broadcast(m):send m to all (including p)R-deliver(m) occurs as fo]lows:when receive m for the first timeif sender(m) # p then send m to aflR-deliver(m)FIG.4. Reliable Broadcast by message diffusion.Since Q satisfies weak completeness, by Lemma 3.1, 53’ satisfies strong completeness.We now show that ~ and $23’have the same accuracy property. If 9 is in Qor W, this follows from Lemma 3.2. If !3 is in 0S2 or OW, this follows fromLemma 3.3. •lBy Theorem 3.4 and Observation 2.6.1, we have:COROLLARY3.5. 9 = Q, Y’= W, OQ?= 03, and OY = OW.The relations given in Corollary 3.5 are sufficient for the purposes of thispaper. A complete enumeration of the relations between the eight failuredetectors classes defined in Figure 1 is given in Section 8.4. Reliable BroadcastWe now define Reliable Broadcast, a communication primitive for asynchronoussystems that we use in our algorithm.13 Informally, Reliable Broadcast guaranteesthat (1) all correct processes deliver the same set of messages, (2) allmessages broadcast by correct processes are delivered, and (3) no spuriousmessages are ever delivered. Formally, Reliable Broadcast is defined in terms oftwo primitives, R-broadcasr(m ) and R-deliver(m) where m is a message drawnfrom a set of possible messages. When a process executes R-broadcast(m), wesay that it R-broadcasts m, and when a process executes R-deliver(m), we saythat it R-delivers m. We assume that every message m includes a field denotedsender(m) that contains the identity of the sender, and a field with a sequencenumber; these two fields make every message unique. Reliable Broadcastsatisfies the following properties [Hadzilacos and Toueg 1994]:Validity. If a correct process R-broadcasts a message m, then it eventuallyR-delivers m.Agreement. If a correct process R-delivers a message m, then all correctprocesses eventually R-deliver m.Uniform tnte~”ty. For any message m, every process R-delivers m at mostonce, and only if m was previously R-broadcast by sender(m).In Figure 4, we give a simple Reliable Broadcast algorithm for asynchronoussystems. Informally, when a process receives a message for the first time, it relaysthe message to all processes and then R-delivers it, This algorithm satisfies1~This is a ~rash.failureToueg [1985] for “Byzantine” failures.version of the asynchronous broadcast primitive defined in Bracha and