Two Generals problem

by Dmitry Kirsanov 27. July 2020 08:44

There is a logical problem, a thought experiment for emulating the communication over an unreliable link, called “the Two Generals’ Problem”. In case if, like most people, you never heard of it, here is the definition:

Two armies, each led by a different general, are preparing to attack a fortified city. The armies are encamped near the city, each in its own valley. A third valley separates the two hills, and the only way for the two generals to communicate is by sending messengers through the valley. Unfortunately, the valley is occupied by the city's defenders and there's a chance that any given messenger sent through the valley will be captured.

While the two generals have agreed that they will attack, they haven't agreed upon a time for attack. It is required that the two generals have their armies attack the city at the same time in order to succeed, else the lone attacker army will die trying. They must thus communicate with each other to decide on a time to attack and to agree to attack at that time, and each general must know that the other general knows that they have agreed to the attack plan. Because acknowledgement of message receipt can be lost as easily as the original message, a potentially infinite series of messages is required to come to consensus.

The thought experiment involves considering how they might go about coming to consensus. In its simplest form one general is known to be the leader, decides on the time of attack, and must communicate this time to the other general. The problem is to come up with algorithms that the generals can use, including sending messages and processing received messages, that can allow them to correctly conclude:

Yes, we will both attack at the agreed-upon time.

Allowing that it is quite simple for the generals to come to an agreement on the time to attack (i.e. one successful message with a successful acknowledgement), the subtlety of the Two Generals' Problem is in the impossibility of designing algorithms for the generals to use to safely agree to the above statement.

It’s even called a “paradox” for “inability to find a logical solution” to this problem. Because the proposed solution is to send confirmation for confirmation, and messenger could disappear.

If so many people are saying, that there is no solution, then perhaps there isn’t one, right? More...

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