  We show that a constant number of self-attention layers can efficiently
simulate, and be simulated by, a constant number of communication rounds of
Massively Parallel Computation. As a consequence, we show that logarithmic
depth is sufficient for transformers to solve basic computational tasks that
cannot be efficiently solved by several other neural sequence models and
sub-quadratic transformer approximations. We thus establish parallelism as a
key distinguishing property of transformers.
