Visibly pushdown languages

Rajeev Alur, P. Madhusudan

Research output: Contribution to journalConference articlepeer-review


We propose the class of visibly pushdown languages as embeddings of context-free languages that is rich enough to model program analysis questions and yet is tractable and robust like the class of regular languages. In our definition, the input symbol determines when the pushdown automaton can push or pop, and thus the stack depth at every position. We show that the resulting class VPL of languages is closed under union, intersection, complementation, renaming, concatenation, and Kleene-*, and problems such as inclusion that are undecidable for context-free languages are EXPTIME-complete for visibly pushdown automata. Our framework explains, unifies, and generalizes many of the decision procedures in the program analysis literature, and allows algorithmic verification of recursive programs with respect to many context-free properties including access control properties via stack inspection and correctness of procedures with respect to pre and post conditions. We demonstrate that the class VPL is robust by giving two alternative characterizations: a logical characterization using the monadic second order (MSO) theory over words augmented with a binary matching predicate, and a correspondence to regular tree languages. We also consider visibly pushdown languages of infinite words and show that the closure properties, MSO-characterization and the characterization in terms of regular trees carry over. The main difference with respect to the case of finite words turns out to be determinizability: nondeterministic Büchi visibly pushdown automata are strictly more expressive than deterministic Muller visibly pushdown automata.

Original languageEnglish (US)
Pages (from-to)202-211
Number of pages10
JournalConference Proceedings of the Annual ACM Symposium on Theory of Computing
StatePublished - 2004
Externally publishedYes
EventProceedings of the 36th Annual ACM Symposium on Theory of Computing - Chicago, IL, United States
Duration: Jun 13 2004Jun 15 2004


  • Context-free languages
  • Logic
  • Pushdown automata
  • Regular tree languages
  • Verification
  • ω-languages

ASJC Scopus subject areas

  • Software


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