Boolean Language Operations on Nondeterministic Automata with a Pushdown of Constant Height

We study the size-cost of Boolean operations on constant height nondeterministic pushdown automata, i.e. on pushdown automata with a constant limit on the size of the pushdown. For intersection, we show an exponential simulation and prove that the exponential blowup is necessary. For union, instead, we provide a linear trade-off while, for complement, we show a double-exponential simulation and prove a single-exponential lower bound.