Departmental Papers (CIS)
Date of this Version
August 2006
Document Type
Book Chapter
Recommended Citation
Rajeev Alur, Swarat Chaudhuri, and P. Madhusudan, "Languages of Nested Trees", Lecture Notes in Computer Science: Computer Aided Verification 4144, 329-342. August 2006. http://dx.doi.org/10.1007/11817963_31
Abstract
We study languages of nested trees—structures obtained by augmenting trees with sets of nested jump-edges. These graphs can naturally model branching behaviors of pushdown programs, so that the problem of branching-time software model checking may be phrased as a membership question for such languages. We define finite-state automata accepting such languages—these automata can pass states along jump-edges as well as tree edges. We find that the model-checking problem for these automata on pushdown systems is EXPTIME-complete, and that their alternating versions are expressively equivalent to NT-μ, a recently proposed temporal logic for nested trees that can express a variety of branching-time, "context-free" requirements. We also show that monadic second order logic (MSO) cannot exploit the structure: MSO on nested trees is too strong in the sense that it has an undecidable model checking problem, and seems too weak to capture NT-μ.
Subject Area
CPS Theory
Publication Source
Lecture Notes in Computer Science: Computer Aided Verification
Volume
4144
Start Page
329
Last Page
342
DOI
10.1007/11817963_31
Copyright/Permission Statement
The original publication is available at www.springerlink.com
Date Posted: 08 December 2006
This document has been peer reviewed.
Comments
From the 18th International Conference, CAV 2006, Seattle, WA, USA, August 17-20, 2006.