Two Generals' Problem

In computing, the Two Generals Problem is a thought experiment meant to illustrate the pitfalls and design challenges of attempting to coordinate an action by communicating over an unreliable link. It is related to the more general Byzantine Generals Problem (though published long before that later generalization) and appears often in introductory classes about computer networking (particularly with regard to the where it shows that TCP can't guarantee state consistency between endpoints and why), though it applies to any type of two party communication where failures of communication are possible. A key concept in epistemic logic, this problem highlights the importance of common knowledge. Some authors also refer to this as the Two Generals Paradox, the Two Armies Problem, or the Coordinated Attack Problem. The Two Generals Problem was the first computer communication problem to be proved to be unsolvable. An important consequence of this proof is that generalizations like the Byzantine Generals problem are also unsolvable in the face of arbitrary communication failures, thus providing a base of realistic expectations for any distributed consistency protocols.

Two armies, each led by a 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.

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