It can be shown that the variations in these problems are equivalent to the extent that the solution to a problem in one type of model may be the solution to another problem in another type of model. For example, a solution to the problem of the “Low Byzantine General” in a synchronized authenticated message transmission model can help find a solution to low interactive coherence. [8] An interactive coherence algorithm can solve the consensus problem by choosing majority value in its consensual vector as a consensual value. [9] However, some simultaneous objects are universal, which means they can resolve the consensus between any number of processes and simulate all other objects. The ability to simulate other objects with universal objects is to create an operation sequence with that simultaneous object. [38] 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] According to the hierarchy, reading/writing registers also cannot resolve consensus in the two-process system.

The structure of data such as the battery, the queue, etc., can only resolve the consensus between two processes. Why can`t these objects solve the consensus between more processes? An effective way to prove this is to enjoy the benefits of bivalence. Suppose the output is binary, a state is bivalent if both outputs are possible, and if the output reached by the state is only 0/1, the state is called 0-valent/1-valent. The basic idea is to make a contradiction by performing certain operations to get a state of both 0-valent and 1-valent. 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] The problem of consensus is a fundamental problem in the control of multi-agent systems. One approach to consensus is for all processes (agents) to agree on a majority value. In this context, a majority requires at least half of the votes available (each process being voted). However, one or more defective processes can distort the result, so that a consensus cannot be reached or cannot be reached incorrectly. Therefore, a consensual protocol that tolerates Byzantine errors must be resilient to any potential error. In the case of synchronous systems, all communication is supposed to be done in rounds. In a turn, a process can send all the messages it needs while it receives all messages from other processes. In this way, no message from a turn can affect stagnant messages sent in the same turn. There are two types of errors that a process can undergo, a fall error or a Byzantine error.

A crash error occurs when a process ends abruptly and does not continue. Byzantine failures are failures for which no conditions are laid. They can. B produce by malicious acts of an opponent. A process in which a Byzantine failure occurs may send conflicting or contradictory data to other processes, or it may sleep and resume activities after a longer delay. Of the two types of errors, Byzantine failures are much more disruptive. Some cryptocurrencies, such as Ripple, use a node validation system to validate the Ledger.