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In this report, we investigate the multi-valued Byzantine consensus problem.We introduce two algorithms: the first one achieves traditional validityrequirement for consensus, and the second one achieves a stronger "q-validity"requirement. Both algorithms are more efficient than the ones introduces in ourrecent PODC 2011 paper titled "Error-Free Multi-Valued Consensus with ByzantineFailures".

New Efficient Error-Free Multi-Valued Consensus with Byzantine Failures