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Byzantine Lattice Agreement in Asynchronous Systems

We study the Byzantine lattice agreement (BLA) problem in asynchronous distributed message passing systems. In the BLA problem, each process proposes a value from a join semi-lattice and needs to output a value also in the lattice such that all output values of correct processes lie on a chain despite the presence of Byzantine processes. We present an algorithm for this problem with round complexity of $O(\log f)$ which tolerates $f < \frac{n}{5}$ Byzantine failures in the asynchronous setting without digital signatures, where $n$ is the number of processes. We also show how this algorithm can be modified to work in the authenticated setting (i.e., with digital signatures) to tolerate $f < \frac{n}{3}$ Byzantine failures.