  In this paper we propose Aleph, a leaderless, fully asynchronous, Byzantine
fault tolerant consensus protocol for ordering messages exchanged among
processes. It is based on a distributed construction of a partially ordered set
and the algorithm for reaching a consensus on its extension to a total order.
To achieve the consensus, the processes perform computations based only on a
local copy of the data structure, however, they are bound to end with the same
results. Our algorithm uses a dual-threshold coin-tossing scheme as a
randomization strategy and establishes the agreement in an expected constant
number of rounds. In addition, we introduce a fast way of validating messages
that can occur prior to determining the total ordering.
  This version of the protocol is deprecated. For current version see
arXiv:1908.05156.
