
Departmental Papers (CIS)
Date of this Version
June 2004
Document Type
Conference Paper
Recommended Citation
Rajeev Alur and P. Madhusudan, "Visibly Pushdown Languages", Proceedings of the Thirty-Sixth Annual ACM Symposium on Theory of Computing (STOC '04) , 202-211. June 2004. http://dx.doi.org/10.1145/1007352.1007390
Abstract
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.
Subject Area
CPS Theory
Publication Source
Proceedings of the Thirty-Sixth Annual ACM Symposium on Theory of Computing (STOC '04)
Start Page
202
Last Page
211
DOI
10.1145/1007352.1007390
Copyright/Permission Statement
© ACM 2004. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in STOC '04, http://dx.doi.org/10.1007/10.1145/1007352.1007390.
Keywords
Context-free languages, pushdown automata, verification, logic, regular tree languages, omega-languages, algorithms
Date Posted: 07 November 2005
Comments
Postprint version. Copyright ACM, 2004. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Proceedings of the 36th Annual ACM Symposium on Theory of Computing 2004, pages 202-211.
Publisher URL: http://doi.acm.org/10.1145/1007352.1007390