Yes, but those aren't Byzantine failures. Byzantine failures present with incorrect values, not simply the absence of a value (as seen by a total hardware failu

Yes, but those aren't Byzantine failures. Byzantine failures present with incorrect values, not simply the absence of a value (as seen by a total hardware failure). See the abstract in Lamport's original paper introducing the Byzantine generals problem [0]. We also see a similar issue in error correction -- an introductory undergrad course might teach this via Lagrange interpolation [1], where you need only n+k of the coefficients in the presence of erasure errors, but n+2k in the general case (where n is the size of the actual message, and k is the maximum number of errors to correct). [0] https://www.microsoft.com/en-us/research/wp-content/uploads/2016/12/The-Byzantine-Generals-Problem.pdf https://www.microsoft.com/en-us/research/wp-content/uploads/... [1] https://inst.eecs.berkeley.edu/~cs70/fa14/notes/n8.pdf https://inst.eecs.berkeley.edu/~cs70/fa14/notes/n8.pdf