On the Complexity of Membership and Counting in Height-Deterministic Pushdown Automata

Abstract. While visibly pushdown languages properly generalise regular languages and are properly contained in deterministic context-free languages, the complexity of their membership problem is equivalent to that of regular languages. However, the corresponding counting problem could be harder than counting paths in a non-deterministic finite automaton: it is only known to be in LogDCFL. We investigate the membership and counting problems for generalisations of visibly pushdown automata, defined using the notion of heightdeterminism. We show that, when the stack-height of a given PDA can be computed using a finite transducer, both problems have the same complexity as for visibly pushdown languages. We also show that when allowing pushdown transducers instead of finite-state ones, both problems become LogDCFL-complete; this uses the fact that pushdown transducers are sufficient to compute the stack heights of all real-time heightdeterministic pushdown automata, and yields a candidate a...

• Type: Conference
• Year: 2008
• Where: CSR
• Authors: Nutan Limaye, Meena Mahajan, Antoine Meyer
• Keywords: CSR 2008, Pushdown, Pushdown Automata, Pushdown Transducers, Theoretical Computer Science