Boolean language operations on nondeterministic automata with a pushdown of constant height

We study the cost of Boolean operations on constant height nondeterministic pushdown automata, i.e., on the ordinary pushdown automata with a limit on the size of the pushdown. For intersection, we show an exponential simulation and prove that the exponential blow-up is necessary in the worst case. 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. The same gaps for Boolean operations with regular languages have been shown for traditional nondeterministic automata with unrestricted pushdown.