Languages of Nested Trees
Rajeev Alur, Swarat Chaudhuri, P. Madhusudan, Rajeev Alur, Swarat Chaudhuri, P. Madhusudan · ScholarlyCommons (University of Pennsylvania) · 2006
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 jumpedges 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. 1