The size-cost of Boolean operations on constant height deterministic pushdown automata

We study the size-cost of Boolean operations on constant height deterministic pushdown automata, i.e., on the traditional pushdown automata with a built-in constant limit on the height of the pushdown. We design a simulation showing that a complement can be obtained with a polynomial tradeoff. For intersection and union, we show an exponential simulation, and prove that the exponential blow-up cannot be avoided.