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- W2113299156 abstract "In this paper, we show that the protocol complex of a Byzantine synchronous system can remain $(k - 1)$-connected for up to $lceil t/k rceil$ rounds, where $t$ is the maximum number of Byzantine processes, and $t ge k ge 1$. This topological property implies that $lceil t/k rceil + 1$ rounds are necessary to solve $k$-set agreement in Byzantine synchronous systems, compared to $lfloor t/k rfloor + 1$ rounds in synchronous crash-failure systems. We also show that our connectivity bound is tight as we indicate solutions to Byzantine $k$-set agreement in exactly $lceil t/k rceil + 1$ synchronous rounds, at least when $n$ is suitably large compared to $t$. In conclusion, we see how Byzantine failures can potentially require one extra round to solve $k$-set agreement, and, for $n$ suitably large compared to $t$, at most that." @default.
- W2113299156 created "2016-06-24" @default.
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- W2113299156 date "2015-05-16" @default.
- W2113299156 modified "2023-09-27" @default.
- W2113299156 title "Tight Bounds for Connectivity and Set Agreement in Byzantine Synchronous Systems" @default.
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