  Input-driven pushdown automata (also known as visibly pushdown automata and
as nested word automata) are a subclass of deterministic pushdown automata and
a superclass of the parenthesis languages. Nguyen and Ogawa ("Event-clock
visibly pushdown automata", SOFSEM 2009) defined a timed extension of these
automata under the event-clock model, and showed that this model can be
determinized using the method of region construction. This paper defines a
further extension of this model with the event clock on the call-return
operations, and proposes a new, direct determinization procedure for these
automata: an $n$-state nondeterministic automaton with $k$ different clock
constraints is transformed to a deterministic automaton with $2^{n^2}$ states,
$2^{n^2+k}$ stack symbols and the same clock constraints as in the original
automaton. The construction is shown to be asymptotically optimal with respect
to both the number of states and the number of stack symbols.

Formal Languages and Automata Theory