Q#$2$: Suppose there are five nodes, A$,$ B$,$ C$,$ D$,$ and E$,$ in a distributed system that uses the Paxos algorithm for consensus. The nodes have the following roles: $[5+10=15]$

$$ Node A is the proposer that initiates a new value to be agreed upon.

$$ Nodes B$,$ C$,$ and D are acceptors that accept or reject the proposed value.

$$ Node E is the learner that learns the agreed$-$upon value.

Initially, the nodes have the following states:

$$ Node A proposes the value "hello world".

$$ Nodes B$,$ C$,$ and D have no accepted value.

$$ Node E has no learned value.

In round $1$ of the Paxos algorithm, node A sends a prepare message to nodes B$,$ C$,$ and D with proposal number $1.$ Nodes B and C respond with a promise message indicating that they have not accepted any proposal with a higher proposal number. Node D$,$ however, responds with a nack message indicating that it has already accepted a proposal with a higher proposal number. Node A retries with proposal number $2.$

In round $2$ of the Paxos algorithm, node A sends a prepare message to nodes B$,$ C$,$ and D with proposal number $2.$ Nodes B and C respond with a promise message again. Node D$,$ however, does not respond.