On the complexity of membership and counting in height-deterministic pushdown automata

  • Authors:

  • Nutan Limaye;Meena Mahajan;Antoine Meyer

  • Affiliations:

  • The Institute of Mathematical Sciences, Chennai, India;The Institute of Mathematical Sciences, Chennai, India;LIAFA, Université Paris Diderot-Paris 7, Paris Cedex 13, France

  • Venue:
  • CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
  • Year:
  • 2008

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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 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).