List-Decoding for the Arbitrarily Varying Channel Under State Constraints

List-decoding for arbitrarily varying channels (AVCs) under state constraints is investigated. It is shown that rates within of the randomized coding capacity of AVCs with input-dependent state can be achieved under maximal error with list-decoding using lists of size O(1/epsilon). Under the average error criterion, an achievable rate and converse bound are given for lists of size L. These bounds are based on two different notions of symmetrizability and do not coincide in general. An example is given which shows that for list size L, the capacity may be positive but strictly smaller than the randomized coding capacity, in contrast to the situation without constraints.