The object of Byzantine fault tolerance is to be able to defend against a Byzantine failure, in which a component of some system not only behaves erroneously, but also fails to behave consistently when interacting with multiple other components. Correctly functioning components of a Byzantine fault tolerant system will be able to reach the same group decisions assuming there aren't too many Byzantine faulty components.
These arbitrary failures may be loosely categorized as follows:
For example, if the output of one function is the input of another, then small round-off errors in the first function can produce much larger errors in the second. If the second function were fed into a third, the problem could grow even larger, until the values produced are worthless. Another example is in compiling source code. One minor syntactical error early on in the code can produce large numbers of perceived errors later, as the compiler gets out-of-phase with the lexical and syntactic information in the source program.
Steps are taken by processes, the abstractions that execute the algorithms. A faulty process is one that at some point exhibits one of the above failures. A process that is not faulty is correct.
The Byzantine failure assumption models real-world environments in which computers and networks may behave in unexpected ways due to hardware failures, network congestion and disconnection, as well as malicious attacks. Byzantine failure-tolerant algorithms must cope with such failures and still satisfy the specifications of the problems they are designed to solve. Such algorithms are commonly characterized by their resilience t, the number of faulty processes with which an algorithm can cope.
Many classic agreement problems, such as the Byzantine Generals' Problem, have no solution unless t < n / 3, where n is the number of processes in the system.
The Two Generals' Problem is a specific case which assumes that processes are reliable but communication between processes is not reliable.
Byzantine fault tolerance can be achieved if the loyal (non-faulty) generals have a unanimous agreement on their strategy. Note that if the source general is correct, all loyal generals must agree upon that value. Otherwise, the choice of strategy agreed upon is irrelevant.
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