In a fully asynchronous system, in which at least one process can have a fall error, the famous result of FLP impossibility has shown that a deterministic algorithm is impossible to obtain by consensus. [5] This impossibility results from the most pessimistic planning scenarios that, in practice, are unlikely, except in conflicting situations such as an intelligent denial of service attacker on the network. In most normal situations, process planning has some degree of natural coincidence. [4] In a fully asynchronous system, there is no consensual solution that can tolerate one or more fall errors, even if only the property of non-triviality is required. [5] This result is sometimes referred to as FLP`s proof of impossibility, named after the authors Michael J. Fischer, Nancy Lynch and Mike Paterson, who received the Dijkstra Prize for this important work. FLP`s results were mechanically verified to reflect assumptions of fairness. [13] FlP does not say, however, that it will never be possible to reach a consensus: only, in the model`s assumptions, no algorithm can always reach consensus in a limited time. In practice, this is highly unlikely to happen. A fundamental problem with distributed and multi-agent computing systems is to achieve the overall reliability of the system in the presence of a number of defective processes. This often requires coordination of processes to reach consensus or to agree on a data value needed during the calculation. Examples of consensual applications include agreement on which transactions to transfer to a database, on the order and order in which the computer must be copied and sent to the atom. Practical applications that often require consensus are cloud computing, measurement synchronization, PageRank, opinion formation, smart grids, state estimation, drone control (and multiple robots/agents in general), load compensation, blockchain and others.

The problem of consensus can be taken into account in asynchronous or synchronous systems. Although real-world communication is often asynchronous in nature, it is more convenient and often easier to model synchronous systems[4] because asynchronous systems naturally pose more problems than synchronous systems. For systems using n`displaystyle n` processors, which f`displaystyle are Byzantine, it has been shown that there is no algorithm that solves the consensus problem for n ≤ 3 f `displaystyle n`leq 3f` in the oral message model. [12] The evidence is designed by first indicating the impossibility of the case at three nodes No. 3 “Displaystyle No. 3″ and using this result to discuss the CPU partitions. In the written message model, there are protocols that can tolerate “Displaystyle No. 1.” [2] In a process n in a partially synchronous system (the system changes between good and bad synchronization phases), each process chooses a private value. Processes communicate with each other through a trick to determine a public value and generate a consensus vector with the following requirements:[7] Leslie Lamport`s Paxos consensus algorithm and variants like Raft are widely used in widely distributed and cloud computing systems.