  Distributed automata are finite-state machines that operate on finite
directed graphs. Acting as synchronous distributed algorithms, they use their
input graph as a network in which identical processors communicate for a
possibly infinite number of synchronous rounds. For the local variant of those
automata, where the number of rounds is bounded by a constant, Hella et al.
(2012, 2015) have established a logical characterization in terms of basic
modal logic. In this thesis, we provide similar logical characterizations for
two more expressive classes of distributed automata.
  The first class extends local automata with a global acceptance condition and
the ability to alternate between nondeterministic and parallel computations. We
show that it is equivalent to monadic second-order logic on graphs. By
restricting transitions to be nondeterministic or deterministic, we also obtain
two strictly weaker variants for which the emptiness problem is decidable.
  Our second class transfers the standard notion of asynchronous algorithm to
the setting of nonlocal distributed automata. The resulting machines are shown
to be equivalent to a small fragment of least fixpoint logic, and more
specifically, to a restricted variant of the modal {\mu}-calculus that allows
least fixpoints but forbids greatest fixpoints. Exploiting the connection with
logic, we additionally prove that the expressive power of those asynchronous
automata is independent of whether or not messages can be lost.
