Theoretical results of consensus protocol in primary-backup distributed system

Question

I am picking up knowledge of consensus protocols in a distributed system. Such a distributed system does primary-backup on databases.

I learned that "every consensus protocol can loop forever." from Leader election for paxos-based replicated key value store

Where is the information source of "every consensus protocol can loop forever"?

Status update: question answered. The same information source was provided by rystsov and another person of another post.

Could more theoretical results and the corresponding information source be shared?

Florist

Answer 1

The "every consensus protocol can loop forever" statement is known as the FLP impossibility result which is described in the Impossibility of Distributed Consensus with One Faulty Process paper.

Botts

Could you please double check? The paper does not show that "every consensus protocol can loop forever". – Florist

LEMMA 2 "P has a bivalent initial configuration" is not proved right. For P, "initial states ... the output register starts with value b, " and "the states in which the output register has value 0 or 1 are distinguished as being decision states". For bivalent, "let V be the set of decision values of configurations reachable from C. C is bivalent if |V| = 2." All decision states are output registers started with value b, so |V| != 2. When |V| != 2, P does not have a bivalent initial configuration. When LEMMA 2 is not proved right, THEOREM 1 is not proved right. – Florist

THEOREM 2 is not proved right. THEOREM 2 depends on "a node k is in an initial clique iff k is itself an ancestor of every node j that is an ancestor of k", and "there can be only one initial clique; it has cardinality at least L." A counterexample: 5 nodes A, B, C, D, and E. Let B => A mean B sends a message to A. In the 1st stage, B => A, C => A; C => B, D => B; D => C, E => C; E => D, A => D; A => E, B => E. In the 2nd stage, all nodes receive the boardcast messages from all other nodes, so all nodes know the graph nodes and edges. There is 0 initial clique with cardinality at least 3. – Florist

When the only 2 theorems THEOREM 1 and THEOREM 2 are not proved right, the paper does not prove any results. – Florist

@rystsov could you please double check if the "every consensus protocol can loop forever" statement is related to the Impossibility of Distributed Consensus with One Faulty Process paper? – Florist

@rystsov I got another person from another post telling me the same information source of "every consensus protocol can loop forever". I asked you about double checking but you do not have to do so. – Florist

@PatrickChan In the abstract of the paper it is explicitly written: "The problem is for the reliable processes to agree on a binary value. In this paper, it is shown that every protocol for this problem has the possibility of nontermination, even with only one faulty process" which basically means that "every consensus protocol can loop forever". If you're questioning the correctness of the proof then try cs.stackexchange.com since SO isn't the best place to do so. – Botts

@Botts thanks for telling me why you told me where the information source was. It was nice to get help from you. I didn't know about cs.stackexchange.com. – Florist