Reachability in Pushdown Register Automata

We investigate reachability in pushdown automata over infinite alphabets: machines with finite control, a finite collection of registers and pushdown stack. First we show that, despite the stack’s unbounded storage capacity, in terms of reachability/emptiness these machines can be faithfully represented by using only 3r elements of the infinite alphabet, where r is the number of registers. Moreover, this bound is tight. Next we settle the complexity of the associated reachability/emptiness problems. In contrast to register automata, where differences in register storage policies gave rise to differing complexity bounds, the emptiness problem for pushdown register automata is EXPTIME-complete in all cases. We also provide a solution to the global reachability problem, based on representing pushdown configurations with a special register automaton. Finally, we examine extensions of pushdown storage to higher orders and show that reachability is undecidable already at order 2, unlike in the finite alphabet case.