Membership Testing: Removing Extra Stacks from Multi-stack Pushdown Automata

We show that fixed membership testing for many interesting subclasses of multi-pushdown machines is no harder than for pushdowns with single stack. The models we consider are MVPA, OVPA and MPDA, which have all been defined and studied in the past. Multi-stack pushdown automata, MPDA, have ordered stacks with pop access restricted to the stack-top of the first non-empty stack. The membership for MPDAs is known to be in NSPACE(n) and in P. We show that the P-time algorithm can be implemented in the complexity class LogCFL; thus membership for MPDAs is LogCFL-complete. It follows that membership testing for ordered visibly pushdown automata OVPA is also in LogCFL. The membership problem for multi-stack visibly pushdown automata, MVPA, is known to be NP-complete. However, many applications focus on MVPA with O(1) phases. We show that for MVPA with O(1) phases, membership reduces to that in MPDAs, and so is in LogCFL.