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Summary: Languages of Nested Trees
Rajeev Alur1
, Swarat Chaudhuri1
, and P. Madhusudan2
1
University of Pennsylvania, USA
2
University of Illinois at Urbana-Champaign, USA
Abstract. We study languages of nested trees--structures obtained by
augmenting trees with sets of nested jump-edges. These graphs can nat-
urally 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 va-
riety of branching-time, "context-free" requirements. We also show that
monadic second order logic (MSO) cannot exploit the structure: MSO on
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