An agreement problem in which a group of generals, each commanding a portion of the Byzantine army, encircle a city. These generals wish to formulate a plan for attacking the city. In its simplest form, the generals must decide only whether to attack or retreat. Some generals may prefer to attack, while others prefer to retreat, but they must agree on a common decision or face defeat.

There are two further complications to the problem. First is the potential presence of traitorous generals, which might express their vote selectively; for instance, if nine generals are voting, four of whom support attacking while four others are in favor of retreat, the ninth general may send a vote of retreat to those generals in favor of retreat, and a vote of attack to the rest. Those who received a retreat vote from the ninth general will retreat, while the rest will attack (which may not go well for the attackers).

The second complication is that generals are separated, and therefore the messengers themselves can be intercepted by traitorous generals or forge false votes.

The Byzantine Generals’ Problem is the problem that consensus mechanisms are designed to solve