Descriptional complexity of unambiguous input-driven pushdown automata

It is known that a nondeterministic input-driven pushdown automaton (IDPDA) (a.k.a. visibly pushdown automaton; a.k.a. nested word automaton) of size n can be transformed to an equvalent deterministic automaton of size 2 2) (B. von Braunmühl, R. Verbeek, “Input-driven languages are recognized in log n space”, FCT 1983), and that this size is necessary in the worst case (R. Alur, P. Madhusudan, “Adding nesting structure to words”, J.ACM, 2009). This paper demonstrates that the same worst-case 2 2) size blow-up occurs when converting a nondeterministic IDPDA to an unambiguous one, and an unambiguous IDPDA to a deterministic one. In addition, the methods developed in this paper are used to demonstrate that the descriptional complexity of complementation for nondeterministic IDPDAs is 2 2), and that the descriptional complexity of homomorphisms for deterministic IDPDAs is 2 2) as well.