Nondeterministic State Complexity of Positional Addition

Consider nondeterministic finite automata recognizing base-k positional notation of numbers. Assume that numbers are read starting from their least significant digits. It is proved that if two sets of numbers S and T are represented by nondeterministic automata of m and n states, respectively, then their sum {s +t | s G S, t G T} is represented by a nondeterministic automaton with 2mn + 2m + 2n +1 states. Moreover, this number of states is necessary in the worst case for all k > 9.