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

Nutan Limaye (1) , Meena Mahajan (1) , Antoine Meyer (2)

1 IMSc - Institute of Mathematical Sciences [Chennai]
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

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 height-determinism. 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 height-deterministic pushdown automata, and yields a candidate arithmetization of LogDCFL that is no harder than LogDCFL (our main result).

Mots clés: pushdown automata; complexity; membership; counting

Domaines: Complexité [cs.CC]; Théorie et langage formel [cs.FL]

Nutan Limaye, Meena Mahajan, Antoine Meyer. On the Complexity of Membership and Counting in Height-Deterministic Pushdown Automata. Journal of Automata Languages and Combinatorics, 2009, 14 (3/4), p. 211-235. ⟨hal-00681253⟩