### Early stopping in Byzantine agreementEarly stopping in Byzantine agreement

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 Author Dolev, Danny ♦ Reischuk, Ruediger ♦ Strong, H. Raymond Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1990 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract Two different kinds of Byzantine Agreement for distributed systems with processor faults are defined and compared. The first is required when coordinated actions may be performed by each participant at different times. This kind is called Simultaneous Byzantine Agreement (SBA).This paper deals with the number of rounds of message exchange required to reach Byzantine Agreement of either kind (BA). If an algorithm allows its participants to reach Byzantine agreement in every execution in which at most $\textit{t}$ participants are faulty, then the algorithm is said to tolerate $\textit{t}$ faults. It is well known that any BA algorithm that tolerates $\textit{t}$ faults (with $\textit{t}$ < $\textit{n}$ - 1 where $\textit{n}$ denotes the total number of processors) must run at least $\textit{t}$ + 1 rounds in some execution. However, it might be supposed that in executions where the number $\textit{f}$ of actual faults is small compared to $\textit{t},$ the number of rounds could be correspondingly small. A corollary of our first result states that (when $\textit{t}$ < $\textit{n}$ - 1) any algorithm for SBA must run $\textit{t}$ + 1 rounds in some execution where there are no faults. For EBA (with $\textit{t}$ < $\textit{n}$ - 1), a lower bound of $min(\textit{t}$ + $1,\textit{f}$ + 2) rounds is proved. Finally, an algorithm for EBA is presented that achieves the lower bound, provided that $\textit{t}$ is on the order of the square root of the total number of processors. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1990-10-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 37 Issue Number 4 Page Count 22 Starting Page 720 Ending Page 741

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Source: ACM Digital Library