Abstract
In this paper, we prove new upper bounds on the complexity of the certified write-all problem with respect to an adaptive adversary. Our strongest result is that for any $\epsilon > 0$, there exists an $O(p^{1+\epsilon})$ work algorithm for the p-processor p-memory cell write-all. We also give a randomized $O(p^2\log p)$ work algorithm for a p-processor $p^2$-memory cell write-all.
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