Nondeterministic state complexity of nested word automata

We study the nondeterministic state complexity of Boolean operations on regular languages of nested words. For union and intersection we obtain matching upper and lower bounds. For complementation of a nondeterministic nested word automaton with n states we establish a lower bound that is significantly worse than the exponential lower bound for ordinary nondeterministic finite automata (NFA). We develop techniques to prove lower bounds for the size of nondeterministic nested word automata that extend the known techniques used for NFAs.