  We characterize the capacity for the discrete-time arbitrarily varying
channel with discrete inputs, outputs, and states when (a) the encoder and
decoder do not share common randomness, (b) the input and state are subject to
cost constraints, (c) the transition matrix of the channel is deterministic
given the state, and (d) at each time step the adversary can only observe the
current and past channel inputs when choosing the state at that time. The
achievable strategy involves stochastic encoding together with list decoding
and a disambiguation step. The converse uses a two-phase "babble-and-push"
strategy where the adversary chooses the state randomly in the first phase,
list decodes the output, and then chooses state inputs to symmetrize the
channel in the second phase. These results generalize prior work on specific
channels models (additive, erasure) to general discrete alphabets and models.
